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.expand_btn{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;margin-top:10px;min-width:55px;display:none;} @media (min-width:768px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .expand_btn{display:none;}} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{-webkit-flex:9;-ms-flex:9;flex:9;text-align:left;padding:21px 37px 10px 0px;font-size:16px;font-weight:700;} @media (min-width:768px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 18px 10px 18px;}} @media (min-width:992px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-text{padding:19px 21px 10px 21px;}} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{-webkit-flex:1;-ms-flex:1;flex:1;background:url('data:image/svg+xml;base64,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') no-repeat 6px;background-position:center;padding:16px 0 16px 0;min-width:62px;max-width:62px;} @media (min-width:768px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:16px 0 17px 0;min-width:52px;max-width:52px;}} @media (min-width:992px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url{padding:15px 0 17px 0;min-width:60px;max-width:60px;}} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption .caption-partial-url:hover{-webkit-text-decoration:none;text-decoration:none;} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption-text{font-size:14px;padding:0px 18px 17px 22px;} @media (min-width:768px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 15px 15px 18px;}} @media (min-width:992px){.iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption-text{padding:0px 18px 19px 21px;}} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption-text figcaption{margin:0;padding:0;} .iASKvs .floats-partial-section .floats-partial-footer .floats-partial-caption-text svg{max-width:100%;} .iASKvs ol{font-size:16px;padding-left:32px;font-family:STIXGeneral-Regular;line-height:24px;margin:15px 0;} .iASKvs ol li{margin:10px 0;padding-left:10px;word-break:normal;} .iASKvs ol li a{word-break:break-all;} .iASKvs ol li .reflinks{display:block;} .iASKvs ol li .reflinks a{color:#4D8A17;-webkit-text-decoration:none;text-decoration:none;cursor:pointer;} .iASKvs ol li .reflinks a:hover{-webkit-text-decoration:underline;text-decoration:underline;} .iASKvs ol li .reflinks .sep{color:#000000;} .iASKvs .table-wrapper{width:auto;overflow-x:auto;} .iASKvs .table-wrapper::-webkit-scrollbar{-webkit-appearance:none;width:5px;height:5px;} .iASKvs .table-wrapper::-webkit-scrollbar-thumb{border-radius:5px;background-color:rgba(0,0,0,.5);-webkit-box-shadow:0 0 1px rgba(255,255,255,.5);} @media (min-width:768px){.iASKvs .table-wrapper{overflow-x:auto;width:auto;-webkit-break-word:word-break;break-word:word-break;margin:0 auto;}} @media (min-width:992px){.iASKvs .table-wrapper{width:auto;}} @media (min-width:1324px){.iASKvs .table-wrapper{width:auto;}} @media (min-width:320px){.iASKvs{margin-bottom:33px;padding:0;}} @media (min-width:992px){.iASKvs{padding:0;margin-bottom:100px;}} @media (min-width:1325px){.iASKvs{margin-bottom:100px;}} .iASKvs .owl-stage{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .iASKvs .floats-partial-middle--thumbs{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;} .iASKvs .floats-partial-middle--thumbs .partial-carousel-dot svg{fill:#4D8A17;width:100%;} .iASKvs .floats-partial-middle--thumbs .partial-carousel-dot strong{color:#4D8A17;font-weight:500;} .iASKvs .floats-partial-middle--thumbs .partial-carousel-dot.active strong{color:#007B8B;} .iASKvs .floats-partial-middle--thumbs .partial-carousel-dot.active svg{fill:#007B8B;} .iASKvs .partial-carousel-dot{text-align:center;cursor:pointer;border:0;width:100px;padding-bottom:20px;background-color:#fff;display:table-cell;} .iASKvs .partial-carousel-dot:focus-visible{outline-offset:-3px;} .iASKvs .partial-carousel-dot strong{font-size:11px;padding-top:12px;} @media (min-width:767.5px){.iASKvs .partial-carousel-dot strong{font-size:16px;}} .iASKvs .partial-carousel-dot img{width:90px;height:90px;border:1px solid #979797;margin:10px 0;} .iASKvs .partial-carousel-wrapper .floats-partial-middle{border-top:1px solid #e3e3e3;display:block;margin-bottom:50px;padding-top:1px;} @media (min-width:767.5px){.iASKvs .partial-carousel-wrapper .floats-partial-middle{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;margin-bottom:0;}} .iASKvs .partial-carousel--single-image{overflow:hidden;text-align:center;} .iASKvs .partial-carousel--single-image 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href="//www.newsama.com/journals/mse/" aria-label="Modelling and Simulation in Engineering">建模和模拟在工程</gydF4y2Baa>/<gydF4y2Baa class="sc-htpNat bUhGXt link sc-eitiEO jXeALb breadCrumb" href="//www.newsama.com/journals/mse/contents/year/2014/" aria-label="2014">2014年</gydF4y2Baa>/<gydF4y2Baspan class="sc-bhlBdH UVThf">文章</gydF4y2Baspan> </div> <div class="threeColumn__ThreeColumnWrapper-sc-1bf4078-0 dDyxFF threeColumnWrapper"> <div class="threeColumn__LeftWrapper-sc-1bf4078-1 fkVFlF leftWrapper"> <button type="button" class="sc-eKZiaR dzZrgS section__button " id="sectionButton"><span class="sc-htoDjs diutvq icon__dots dots__detector icon-colored _3n-7Ho7DlfjMlZbrRr9Q4a icon-themeable" title="" font-size="22"></span>文章部分</gydF4y2Babutton> <div class="sc-bEjcJn jLUVhb static_contents__section_links links__hidden "> <div id="leftSectionMenu" class="sc-cbkKFq prcY sc-bGbJRg dVCLgr left_section_menu"> <p>在这一页上</gydF4y2Bap> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#abstract" aria-label="">文摘</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#introduction" aria-label="">介绍</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#related-work" aria-label="">相关工作</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#conclusions" aria-label="">结论</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#references" aria-label="">引用</gydF4y2Baa></span> <span class="sc-likbZx bBmZJZ grey" property="background-color" color="#D8D8D8"><a class="sc-htpNat bUhGXt link sc-ePZHVD ewHMLz" href="#copyright" aria-label="">版权</gydF4y2Baa></span> </div> </div> </div> <div class="threeColumn__ContentWrapper-sc-1bf4078-3 bbzREB contentWrapper"> <div class="threeColumn__Content-sc-1bf4078-4 jknsZc content"> <div class="articleContent__ArticleContentsWrapper-sc-2yl9jy-0 eSvjPB article_contents"> <div class="articleContent__ArticleContentsSectionsWrapper-sc-2yl9jy-1 jntdRu article_contents__sections_wrapper"> <div class="articleContent__ArticleWrapper-sc-2yl9jy-2 hAzjHP"> <div class="sc-chbbiW mBGSe article_header_class"> <div class="sc-kxynE fgGykB"> <span class="sc-cooIXK gQxyld">特殊的问题</gydF4y2Baspan> <h2 class="sc-fcdeBU bVtmCk">先进的通信模型和服务智能的世界</gydF4y2Bah2> <a class="sc-htpNat bUhGXt link sc-gmeYpB hSHJbi" href="//www.newsama.com/journals/mse/si/232608/" aria-label="">把这个特殊的问题</gydF4y2Baa> <hr class="sc-clNaTc ktFfKO"> </div> <p class="sc-kZmsYB bkiEfx article_type">研究文章|<gydF4y2Ba!-- -->开放获取</gydF4y2Bap> <div class="sc-RcBXQ ztvYg article_citation"> 体积<gydF4y2Ba!-- --> 2014年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</gydF4y2Baspan>文章的ID<gydF4y2Ba!-- --> 406462年<gydF4y2Ba!-- --> <span class="sc-fZwumE cUsFHx">|</gydF4y2Baspan> <a class="sc-htpNat bUhGXt link sc-fQejPQ duuwge" href="https://doi.org/10.1155/2014/406462" aria-label="Doi-link">https://doi.org/10.1155/2014/406462</gydF4y2Baa> </div> <div class="sc-LKuAh lcOiDF article_full_citation"> <div class="sc-hzNEM gsmOCv isHide"> <p>Sang-Seon Byun、季Kansanen Ilangko Balasingham, Joon-Min吉尔<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> ”<gydF4y2Baspan class="adjust-article-svg-size">实现公平的频谱分配和降低无线传感器网络的频谱切换:通过Biobjective优化建模</gydF4y2Baspan>”,<gydF4y2Ba!-- --><i>建模和模拟在工程</gydF4y2Bai>,<gydF4y2Ba!-- --> 卷。<gydF4y2Ba!-- -->2014年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 文章的ID<gydF4y2Ba!-- -->406462年<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 12<gydF4y2Ba!-- -->   页面<gydF4y2Ba!-- -->,<gydF4y2Ba!-- --> 2014年<gydF4y2Ba!-- -->。<gydF4y2Ba!-- --> https://doi.org/10.1155/2014/406462</gydF4y2Bap> </div> <button class="sc-hSdWYo 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src="data:image/svg+xml;base64,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" height="16"></a>,<gydF4y2Basup>1</gydF4y2Basup></span> <span class="">季Kansanen<gydF4y2Baa class="sc-htpNat bUhGXt link" href="http://orcid.org/0000-0002-7702-7143" aria-label="Redirect to Doi" target="_blank"><img alt="" class="sc-EHOje iiusBg sc-iybRtq iQSObO" title="" role="presentation" src="data:image/svg+xml;base64,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" height="16"></a>,<gydF4y2Basup>2</gydF4y2Basup></span> <span class="">Ilangko Balasingham<gydF4y2Ba!-- -->,<gydF4y2Basup>3</gydF4y2Basup> 和</gydF4y2Baspan> <span class=""><b>Joon-Min吉尔</gydF4y2Bab><a class="sc-htpNat bUhGXt link" href="mailto:" aria-label="Mail Option"><span class="sc-htoDjs kNoiZu sc-hjRWVT irNWJI icon-colored _2zt-1j0LmaF8UjTQAM413G icon-themeable" title="" font-size="16"></span></a><sup>4</gydF4y2Basup></span> <div class="sc-fHxwqH dMuGGA isHide"> <p><sup>1</gydF4y2Basup><span>计算机工程系,天主教大学的釜山韩国釜山</gydF4y2Baspan></p> <p><sup>2</gydF4y2Basup><span>电子与电信部门,挪威科技大学,挪威特隆赫姆,</gydF4y2Baspan></p> <p><sup>3</gydF4y2Basup><span>Rikshospitalet,奥斯陆,挪威奥斯陆大学医院</gydF4y2Baspan></p> <p><sup>4</gydF4y2Basup><span>信息技术工程学院的天主教大学的大邱,Gyeongsan,韩国庆北,韩国</gydF4y2Baspan></p> </div> <button class="sc-hSdWYo etauus sc-iQtOjA kfDwZY" color="">显示更多</gydF4y2Babutton> </div> <div class="articleContent__EditorWrapper-sc-2yl9jy-3 evMkvU"> <div class="articleContent__TextWrapper-sc-2yl9jy-8 fYrLtk"> <b>学术编辑器:</gydF4y2Bab>James j .公园</gydF4y2Badiv> <div class="articleContent__PublicationTimeLineWrapper-sc-2yl9jy-4 fjviok"> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2014年6月26日</gydF4y2Baspan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">接受</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2014年8月12日</gydF4y2Baspan> </div> <div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC isPublished"> <span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">发表</gydF4y2Baspan> <span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">2014年9月3日</gydF4y2Baspan> </div> </div> </div> <article class="sc-jtRlXQ iASKvs article_body "> <div> <div class="xml-content"> <h4 class="header" id="abstract">文摘</gydF4y2Bah4> <p>本文考虑了无线传感器网络的集中式频谱分配问题实现以下目标:(1)最大化公平,(2)反映传感器数据之间的优先级,和(3)避免不必要的频谱切换。我们把这个问题变成一个多目标混合整数非凸非线性规划,绝对是难以解决全球至少没有任何援助的转换或近似。解决这个棘手,我们首先使用算术几何平均convexify原问题的近似和对数变化决策变量,然后部署加权切比雪夫norm-based数值方法以崩溃多目标问题转化为单目标。最后,我们应用简单的舍入方法,以获得近似整数解。数值实验的结果表明,通过调整体重在每个目标函数,该算法分配频谱的乐队很好观察每个传感器的优先级和减少频谱的传递。</gydF4y2Bap> <span class="end-abs"></span> <h4 id="introduction">1。介绍</gydF4y2Bah4> <p>分配和使用无线电频率谱的需求快速增长是由于越来越多的无线和移动通信的应用程序,在该行业已经达到了目前的静态频谱分配的局限性。然而,实际测量说明稀缺不重使用光谱的结果。这仅仅是由于低效率的静态频谱分配所追求的监管机构(<gydF4y2Baa href="#B1">1</gydF4y2Baa>]。</gydF4y2Bap> <p>动态频谱分配可能解决这个悖论通过打开分配,但很少使用,二次用户频谱资源(<gydF4y2Baa href="#B2">2</gydF4y2Baa>- - - - - -<gydF4y2Baa href="#B4">4</gydF4y2Baa>]。它利用充分利用频谱资源以及时间或频率维度和提供高效和密集的动态频谱接入频谱的检测和自适应调制的机会。</gydF4y2Bap> <p>这样的动态频谱接入方案可以考虑无线传感器网络(网络)。典型的资源受限的传感器网络是由负责监控物理现象和报告沉点。网络的一个主要目标是及时和并发传输监测结果,不使用大量的网络资源。等一系列重要实现动态频谱接入变得非常及时和并发传输网络;例如,在传感器网络实时监测系统(<gydF4y2Baa href="#B32">5</gydF4y2Baa>,<gydF4y2Baa href="#B33">6</gydF4y2Baa>)或实时机器对机器通信(<gydF4y2Baa href="#B35">7</gydF4y2Baa>),捕获的视频或图像数据传输的传感器需要高带宽和多光谱(<gydF4y2Baa href="#B5">8</gydF4y2Baa>]。随后,以下主要原则。</gydF4y2Bap> <h5 id="sec1.1">1.1。公平分配空闲频谱</gydF4y2Bah5> <p>如果太多的传感器试图同时传输数据,当前的空闲频谱资源可能不足以支持所有传输。在这种情况下,应该尽可能公平地分配稀缺的频谱资源;此外,有必要优先传输。这可以通过最大化<gydF4y2Bai>比例公平</gydF4y2Bai>与要求的重量(<gydF4y2Baa href="#B6">9</gydF4y2Baa>]。的主要区别<gydF4y2Bai>不等式性质公平</gydF4y2Bai>和比例公平,后者是在某种意义上不公平的要求体积分配更有效的总利用率通过所有参与者(<gydF4y2Baa href="#B27">10</gydF4y2Baa>]。</gydF4y2Bap> <p></p> <p></p> <h5 id="sec1.2">1.2。避免不必要的频谱切换</gydF4y2Bah5> <p>网络的另一个主要目标是长时间的功能。然而,动态频谱访问会导致在每个传感器由于补充能源消耗<gydF4y2Bai>频谱切换</gydF4y2Bai>。频谱切换时<gydF4y2Basvg height="12.0395pt" id="M1" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> </g> </svg>检测到主用户<gydF4y2Basvg height="12.0395pt" id="M2" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg>目前的频谱条件变得更糟;传感器移动到“最佳匹配”可用频谱乐队。测量,不仅解码和信道估计还频率或时间同步消耗一定的功率(<gydF4y2Baa href="#B7">11</gydF4y2Baa>]。这意味着更频繁的光谱传递导致更多的能源消耗。此外,由于延迟引起的光谱传感,决定,和切换过程、质量恶化是不可避免的在频谱切换(<gydF4y2Baa href="#B8">12</gydF4y2Baa>]。因此应该消除不必要的频谱切换(<gydF4y2Baa href="#B30">13</gydF4y2Baa>,<gydF4y2Baa href="#B31">14</gydF4y2Baa>]。</gydF4y2Bap> <h5 id="sec1.3">1.3。集中式频谱分配</gydF4y2Bah5> <p>在蜂窝网络动态频谱分配的问题已被广泛研究。各种集中式或分布式算法进行了总结和比较<gydF4y2Baa href="#B9">15</gydF4y2Baa>]。集中的计划,一个集中的权威(如基站或专用协调员)检测和识别频谱机会和分配确定光谱二级用户按照预定义的政策。所有这些程序可以分别做不同的实体,即探测器,标识符和分配器。无疑有一个开销集中权威以来的消息交换(或分配器)应该传播频谱分配的结果到传感器群只要它接收传输请求。此外,如果传感器分布在一个广阔的区域内,可能需要更多的探测器。</gydF4y2Bap> <p>在分布式方案,每个二级用户彼此竞争访问可用的频谱资源。因此每个用户应该有能力探测光谱的机会和确定一个最优策略,最大限度地提高它的好处(例如,数量的光谱波段)。如果分布式部署方案基础上,所有的传感器都应该拥有一个完全操作认知无线电。然而这不是可行的实现的全部功能认知无线电等能源有限公司的传感器节点。因此,在一个中等规模的基础,传感器不分布广泛,例如,医疗系统在重症监护室,分布的集中方案者优先。</gydF4y2Bap> <p>在本文中,我们考虑问题的集中式频谱分配在一个中等大小的基础上;也就是说,所有的传感器都位于一个细胞或分段边界。我们假定传感器,将立即传输数据或在不久的将来,请求频谱资源专用的协调员。然后协调分配每个传感器频谱资源:<gydF4y2Basvg height="12.0395pt" id="M3" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg><i>尽可能公平</gydF4y2Bai>,<gydF4y2Basvg height="12.0395pt" id="M4" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg><i>反映传感器之间的优先级</gydF4y2Bai>,<gydF4y2Basvg height="12.0395pt" id="M5" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 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href="#B20">17</gydF4y2Baa>]。我们估计的整数解舍入方法通过比较它与NLP轻松的解决方案,使原油上界的原始问题。</gydF4y2Bap> <p>本文的其余部分组织如下。节<gydF4y2Baa href="#sec2">2</gydF4y2Baa>,我们提出相关的工作和总结我们的主要挑战。节<gydF4y2Baa href="#sec3">3</gydF4y2Baa>,问题公式化。节<gydF4y2Baa href="#sec4">4</gydF4y2Baa>,我们描述解决棘手的过程:凸化、数值和舍入。节<gydF4y2Baa href="#sec5">5</gydF4y2Baa>,数值实验的结果。最后我们得出本文的部分<gydF4y2Baa href="#sec6">6</gydF4y2Baa>。</gydF4y2Bap> <h4 id="related-work">2。相关工作</gydF4y2Bah4> <p>在[<gydF4y2Baa href="#B10">18</gydF4y2Baa>),作者认为认知无线电网络的部署和显示,通过调整星座大小,可以实现不同数据率将直接影响每个节点的能耗,反过来又会影响整个传感器网络的生命周期。他们部署分布式频谱分配策略与认知无线电的完整功能的假设,即检测、识别、和剥削的频谱机会,安装在每个传感器节点。在[<gydF4y2Baa href="#B11">19</gydF4y2Baa>),作者应用动态频谱访问在时域利用空白丛发性传输多路存取之间的沟通渠道。他们提到,如果传感器交流偶尔和低利率,似乎合理的假设,这样的系统可以有效地重用剩下的空白。</gydF4y2Bap> <p>有许多研究文献,调查了集中式频谱分配。下面我们列举一些。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B12">20.</gydF4y2Baa>),一个计划来实现比例公平分配提出了在多用户OFDMA系统。作者处理完全排斥副载波分配没有任何考虑的干扰。他们应用启发式算法的复杂度相对较高。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B13">21</gydF4y2Baa>,<gydF4y2Baa href="#B14">22</gydF4y2Baa>),基站之间的动态频谱分配。在[<gydF4y2Baa href="#B13">21</gydF4y2Baa>),作者应用遗传算法来分配光谱同时最大化频谱效率和满足每个基站的服务速率。然而,遗传算法并不适合多个约束的多目标优化,因为如果我们只考虑人口满足所有约束遗传算法的整个过程,在当地最优的解决方案往往停滞不前(<gydF4y2Baa href="#B15">23</gydF4y2Baa>]。如果我们使用的算法不涉及任何约束,一些解决方案可以获得所有的约束。在[<gydF4y2Baa href="#B14">22</gydF4y2Baa>),提出动态频谱规划反映支持需求的数量在每个基站根据其分布统计信息和本地干扰条件下,他们也解决长期稳定和比例公平。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B16">24</gydF4y2Baa>,<gydF4y2Baa href="#B17">25</gydF4y2Baa>),下行信道(或副载波)被认为是分配问题,和低复杂heuristic-based算法提出了为了在合理的时间解决这个问题。的主要目标是最小化所需的传输能量,同时满足速度要求和数据出错率约束每个用户的<gydF4y2Baa href="#B16">24</gydF4y2Baa>)和最大限度地活跃的副载波的总数,可以支持未经授权的用户(<gydF4y2Baa href="#B17">25</gydF4y2Baa>),分别。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B18">26</gydF4y2Baa>),作者提出了一个直观的启发式算法的比例公平的分配率。他们表达这个问题使用非线性凸规划和评估启发式算法通过比较其结果与最优的解决方案。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B19">27</gydF4y2Baa>),作者联合功率控制模型和速率分配问题在一个多用户CDMA系统的几何编程,可轻易转化为一个凸形式。他们还认为比例公平的分配率。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B26">28</gydF4y2Baa>),作者证明可行的区域signal-to-inference比率(先生)是严格凸如果对数刻度。结果,他们显示的问题找到一个力向量的加权和最大化对数先生是严格凸,而伴随着功率控制问题,实现用户之间的最大加权比例公平先生。</gydF4y2Bap> <p>在[<gydF4y2Baa href="#B34">29日</gydF4y2Baa>),作者认为基于博弈论的WiMax环境中带宽分配机制。</gydF4y2Bap> <p>比较上述相关工作,可以突出我们的主要贡献如下。我们考虑频谱切换的问题,这意味着问题是制定具有离散变量。已经建立了一个单独的目标函数的频谱切换而不是表达作为一个约束为了得到一些积极的解决方案。(如果我们包括频谱切换在约束集,光谱传递的数量将有界参数,不能调整在解决问题以达到降低频谱的传递。因此,如果决策者预计活动改进同时在两个或两个以上的目标只有一次性解决问题,这是不可避免的建模问题变为一个拖把。<gydF4y2Baa href="#B24">16</gydF4y2Baa>]。)因此,问题是制定作为多目标混合整数非线性规划(MO-MINLP)。此外,凸化、数值和舍入方法已经用来使问题更容易处理。</gydF4y2Bap> <h4 id="problem-formulation">3所示。问题公式化</gydF4y2Bah4> <p>我们制定作为MO-MINLP集中式频谱分配问题。描述制定之前,以下假设。<gydF4y2Baspan class="list"><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(1)</gydF4y2Baspan><span class="list-content">可用的频谱资源表示为一系列的谱单元,和每个光谱的带宽是固定的,例如,副载波OFDM或部分波段多波段ultrawide乐队(UWB)。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(2)</gydF4y2Baspan><span class="list-content">每个传感器可以同时在非连续频带传输(<gydF4y2Baa href="#B12">20.</gydF4y2Baa>,<gydF4y2Baa href="#B16">24</gydF4y2Baa>,<gydF4y2Baa href="#B21">30.</gydF4y2Baa>]。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(3)</gydF4y2Baspan><span class="list-content">类似于(<gydF4y2Baa href="#B18">26</gydF4y2Baa>,<gydF4y2Baa href="#B19">27</gydF4y2Baa>),每个接收器传感器宣布其所需的信号干扰噪声比(SINR)。SINR值反映了特定要求的水平的比特误码率(BER)之间存在一个显式的关系以来数量和SINR根据调制方案。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(4)</gydF4y2Baspan><span class="list-content">所有传感器可以访问整个空闲频谱资源。这意味着传感器分布在细胞内或分段边界主要节点相关联的地方。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(5)</gydF4y2Baspan><span class="list-content">类似于一般集中的方法,检测的频谱机会,识别、和剥削总是正确的,和一个专门协调所有这些过程。此外,专门协调也在同一细胞内或分段边界在于传感器。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(6)</gydF4y2Baspan><span class="list-content">频谱分配的过程在每一个预定义的时代开始,执行,协调器检测空闲频谱的单位和传感器,要求频谱资源。时代也可能开始时频谱的协调员收到要求单位或者定期。此外,没有通道条件在每个时代的变化。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(7)</gydF4y2Baspan><span class="list-content">我们只考虑之间的直接通信传感器所示(<gydF4y2Baa href="#B36">31日</gydF4y2Baa>]。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(8)</gydF4y2Baspan><span class="list-content">实际上,频谱切换发生在接收器和发射器。然而,它是不可能避免的传递在发射机和接收机如果都不耦合在过去的时代,目前不同的谱单元同步。因此,在本文中,我们只考虑频谱切换的发射机。</gydF4y2Baspan></span></span></p> <p>基于上述假设,MO-MINLP可以描述如下。</gydF4y2Bap> <p><i>参数</gydF4y2Bai><span class="list"><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(我)</gydF4y2Baspan><span class="list-content"> <svg height="9.21094pt" id="M6" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 9.74132 9.21094" width="9.74132pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z" id="g113-87"></path> </g> </svg>:设置传感器,请求光谱传输单位。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(2)</gydF4y2Baspan><span class="list-content"> <svg height="9.21094pt" id="M7" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 6.51834 9.21094" width="6.51834pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path> </g> </svg>:设置空闲频谱的单位。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(3)</gydF4y2Baspan><span class="list-content"> <svg height="12.4257pt" id="M8" style="vertical-align:-3.427751pt" version="1.1" viewbox="-0.0498162 -8.99795 15.5661 12.4257" width="15.5661pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,8.644,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,11.299,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path> </g> </svg>(二进制):它表明谱单元<gydF4y2Basvg height="6.42315pt" id="M9" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" id="g113-116"></path> </g> </svg>用传感器<gydF4y2Basvg height="9.21094pt" id="M10" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path> </g> </svg>在其之前的传播阶段。这意味着,目前,传感器<gydF4y2Basvg height="9.21094pt" id="M11" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>同步谱单元吗<gydF4y2Basvg height="6.42315pt" id="M12" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> </svg>。我们假设集<gydF4y2Basvg height="9.21094pt" id="M13" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 6.51834 9.21094" width="6.51834pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-84"></use> </g> </svg>和<gydF4y2Basvg height="9.21094pt" id="M14" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 9.74132 9.21094" width="9.74132pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-87"></use> </g> </svg>在每一个不同时代传播。因此,我们假设当前<gydF4y2Basvg height="9.04777pt" id="M15" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 7.61985 9.04777" width="7.61985pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-77"></use> </g> </svg>反映了对先前时代的最优解。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(iv)</gydF4y2Baspan><span class="list-content"> <svg height="9.63795pt" id="M16" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 12.6057 9.63795" width="12.6057pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 394 180L457 426L452 432L377 416L315 156C302 100 259 45 216 45C176 45 148 67 148 122C148 133 152 158 156 180C162 212 173 259 194 332C201 357 206 384 206 405C206 430 198 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C126 383 128 382 128 377C128 370 127 359 122 343C99 268 84 204 77 156C74 137 70 111 70 104C70 25 125 -12 180 -12C228 -12 276 12 319 50C338 8 378 -12 418 -12C549 -12 689 166 689 332Z" id="g113-120"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,9.308,3.264)"> <use xlink:href="#g50-106"></use> </g> </svg>:重量按照优先的传感器<gydF4y2Basvg height="9.21094pt" id="M17" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>。高优先级的一个传感器,将分配更多的谱单元。这意味着优先反映频谱的需求单位。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(v)</gydF4y2Baspan><span class="list-content"> <svg height="14.4105pt" id="M18" style="vertical-align:-4.1078pt" version="1.1" viewbox="-0.0498162 -10.3027 25.7612 14.4105" width="25.7612pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,8.365,-5.984)"> <path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,16.245,-5.984)"> <path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z" id="g58-95"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,20.504,-5.984)"> <path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M303 0V28C221 34 213 39 213 125V525C213 610 221 616 303 622V650H38V622C120 616 128 610 128 525V125C128 40 120 34 38 28V0H303Z" id="g190-74"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <path d="M719 650H483V622C553 619 576 606 581 560C585 532 588 487 588 394V148H585L167 650H20V622C67 618 88 610 109 585C127 562 129 557 129 484V264C129 173 126 124 123 93C118 44 92 31 35 28V0H272V28C204 32 181 44 176 95C173 124 170 172 170 264V515H172L598 -9H629V394C629 487 631 532 635 563C639 606 663 619 719 622V650Z" id="g190-79"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <path d="M409 504C401 567 396 607 392 642C354 654 312 665 266 665C137 665 60 583 60 487C60 374 161 325 225 290C300 250 355 215 355 141C355 68 311 21 235 21C131 21 86 122 71 183L41 176C48 128 61 42 68 21C78 16 93 8 118 0C142 -7 175 -15 216 -15C349 -15 438 69 438 174C438 287 344 333 265 374C186 414 138 449 138 522C138 576 172 631 249 631C336 631 363 562 380 499L409 504Z" id="g190-84"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <path d="M631 18C609 24 585 35 559 65C534 91 514 117 478 169C448 214 406 281 389 313C462 346 516 399 516 485C516 545 490 590 449 616C412 641 363 650 290 650H42V622C120 615 128 612 128 527V125C128 40 120 34 38 28V0H300V28C221 34 212 40 212 125V284H244C295 284 312 272 329 244C359 195 395 133 430 84C475 19 516 -3 592 -7C603 -8 615 -8 627 -8L631 18ZM212 316V563C212 591 215 602 223 607C231 613 248 617 277 617C352 617 423 577 423 469C423 415 407 375 368 345C343 324 310 316 260 316H212Z" id="g190-83"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>:1 /<gydF4y2Basvg height="12.2516pt" id="M21" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -12.0114 45.9258 12.2516" width="45.9258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,6.259,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.879,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.378,-5.984)"> <path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,39.986,-5.984)"> <path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path> </g> </svg>,在那里<gydF4y2Basvg height="12.2516pt" id="M22" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -12.0114 45.9258 12.2516" width="45.9258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,6.259,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.879,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.378,-5.984)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.986,-5.984)"> <use xlink:href="#g58-108"></use> </g> </svg>是最小的SINR对应于严格的QoS约束。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(七)</gydF4y2Baspan><span class="list-content"> <svg height="16.8141pt" id="M23" style="vertical-align:-6.440001pt" version="1.1" viewbox="-0.0498162 -10.3741 15.8952 16.8141" width="15.8952pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z" id="g113-72"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,9.267,-5.984)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,9.199,3.944)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,11.16,3.944)"> <path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z" id="g50-107"></path> </g> </svg>:传感器之间的信道增益<gydF4y2Basvg height="9.21094pt" id="M24" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>和<gydF4y2Basvg height="12.5699pt" id="M25" style="vertical-align:-3.57195pt" version="1.1" viewbox="-0.0498162 -8.99795 5.85199 12.5699" width="5.85199pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path> </g> </svg>在频谱单位<gydF4y2Basvg height="6.42315pt" id="M26" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> </svg>。</gydF4y2Baspan></span></span></p> <p><i>决策变量</gydF4y2Bai><span class="list"><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(我)</gydF4y2Baspan><span class="list-content"> <svg height="9.63795pt" id="M27" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 14.4238 9.63795" width="14.4238pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,7.506,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.161,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>(二进制):它表明传感器<gydF4y2Basvg height="9.21094pt" id="M28" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>占用频谱单位<gydF4y2Basvg height="6.42315pt" id="M29" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> </svg>。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(2)</gydF4y2Baspan><span class="list-content"> <svg height="10.6388pt" id="M30" style="vertical-align:-3.571919pt" version="1.1" viewbox="-0.0498162 -7.06688 14.6142 10.6388" width="14.6142pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,7.695,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.351,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>:传动功率传感器<gydF4y2Basvg height="9.21094pt" id="M31" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>谱单元<gydF4y2Basvg height="6.42315pt" id="M32" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> </svg>。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(3)</gydF4y2Baspan><span class="list-content"> <svg height="12.5481pt" id="M33" style="vertical-align:-3.42776pt" version="1.1" viewbox="-0.0498162 -9.12034 36.359 12.5481" width="36.359pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,32.125,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>:互惠的SINR的传感器<gydF4y2Basvg height="9.21094pt" id="M34" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>谱单元<gydF4y2Basvg height="6.42315pt" id="M35" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.19924 6.42315" width="5.19924pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> </svg>,定义为<gydF4y2Baspan class="equation" id="EEq1"><span class="left"> <svg class="labelnn" height="38.8104pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -38.7605 13.941 38.8104" width="13.941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="38.8104pt" id="M36" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -38.7605 177.658 38.8104" width="177.658pt" 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id="g119-65"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,63.18,-23.071)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,67.26,-23.071)"> <path d="M496 -1V52H376C259 52 161 132 147 236H496V289H147C162 392 259 473 376 473H496V526H374C213 526 83 408 83 262S213 -1 374 -1H496Z" id="g54-173"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,72.75,-23.071)"> <path d="M735 650H491L482 618L516 614C568 608 571 595 541 535L299 115H297L196 559C187 600 195 608 238 614L265 618L275 650H26L18 618C79 611 98 605 115 527L234 -9H272C389 197 542 449 591 523C647 608 656 612 726 618L735 650Z" id="g50-87"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,79.57,-23.071)"> <path d="M381 -163L112 704H48L317 -163H381Z" id="g50-93"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,83.63,-23.071)"> <path d="M300 -169V-136C225 -126 216 -88 216 -42C216 19 230 84 230 152C230 207 206 255 147 268V272C206 286 230 333 230 388C230 453 216 523 216 586C216 630 225 667 300 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</svg></span></span></span></span></span>在哪里<gydF4y2Basvg height="12.2911pt" id="M37" style="vertical-align:-0.2129993pt" version="1.1" viewbox="-0.0498162 -12.0781 12.9171 12.2911" width="12.9171pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-240"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.657,-5.984)"> <use xlink:href="#g50-51"></use> </g> </svg>噪声功率。</gydF4y2Bap> <p><i>目标。</gydF4y2Bai>考虑以下:<gydF4y2Baspan class="equation" id="EEq2"><span class="left"> <svg class="labelnn" height="77.2498pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -77.2 15.661 77.2498" width="15.661pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="77.2498pt" id="M38" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -77.2 174.906 77.2498" 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229 275 240V84Z" id="g190-98"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,17.79,-54.331)"> <path d="M474 0V26C414 34 401 43 364 100L267 248C300 297 324 332 345 358C381 400 394 405 455 411V437H272V411C316 406 323 401 305 370C287 337 267 306 247 276L188 369C169 397 173 405 215 411V437H16V411C71 404 83 396 114 348L201 212C171 167 144 127 116 92C77 42 66 34 4 26V0H190V26C139 34 136 43 156 77C175 113 198 150 220 183L294 66C311 39 302 31 260 26V0H474Z" id="g190-121"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,24.18,-54.331)"> <path d="M135 536C164 536 186 560 186 587C186 617 164 639 136 639C109 639 85 617 85 587C85 560 109 536 135 536ZM252 0V26C188 32 181 38 181 106V451C138 433 90 420 39 412V388C99 379 102 374 102 312V106C102 38 95 32 32 26V0H252Z" id="g190-106"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,27.81,-54.331)"> <path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 366C425 418 382 449 334 449C303 449 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transform="matrix(.0095,0,0,-0.0095,146.11,-39.954)"> <path d="M463 633C453 636 427 644 417 648C388 660 349 667 316 667C183 667 100 592 100 483C100 398 176 335 223 305L259 282C321 242 358 203 358 149C358 66 301 22 234 22C110 22 70 131 57 208L24 205L28 48C51 23 128 -17 215 -17C342 -17 446 60 446 174C446 262 394 310 317 361L284 383C229 420 183 455 183 515C183 569 222 628 298 628C384 628 418 563 428 481L461 487C459 527 458 593 463 633Z" id="g50-84"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,150.72,-54.331)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,158.22,-51.067)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,160.88,-51.067)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,165.01,-54.331)"> <path d="M626 271V272C626 845 478 1358 152 1678L120 1644C380 1367 528 839 528 271C528 -295 377 -825 120 -1102L152 -1136C478 -823 626 -308 626 271Z" id="g119-174"></path> </g> <g 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transform="matrix(.0095,0,0,-0.0095,138.83,-13.085)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,141.49,-13.085)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,145.62,-16.349)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,153.13,-13.085)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,155.78,-13.085)"> <use xlink:href="#g50-116"></use> </g> </svg></span><span class="right"> <svg class="label" height="77.2498pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -77.2 15.661 77.2498" width="15.661pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-54.099)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-54.099)"> <path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 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class="equation" id="EEq4"><span class="left"> <svg class="labelnn" height="76.3812pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -76.3314 16.091 76.3812" width="16.091pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="76.3812pt" id="M39" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -76.3314 216.128 76.3812" width="216.128pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-65.485)"> <path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,4.35,-62.221)"> <use xlink:href="#g50-50"></use> 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viewbox="0 -76.3314 16.091 76.3812" width="16.091pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-65.376)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.68,-65.376)"> <path d="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.42,-65.376)"> <use xlink:href="#g190-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,.58,-34.354)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,5.27,-34.354)"> <path d="M130 550H367L393 615L386 623H101L63 323C82 331 123 342 165 342C275 342 328 277 328 188C328 107 283 40 201 40C141 40 99 72 78 91C69 99 59 98 51 91C39 81 30 67 29 58C28 48 33 37 46 24C60 10 104 -12 149 -12C203 -11 269 14 323 59C384 109 412 165 412 225C412 308 347 399 219 399C193 399 146 382 104 367L130 550Z" id="g190-161"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.42,-34.354)"> <use xlink:href="#g190-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,.02,-4.08)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.71,-4.08)"> <path d="M143 344C173 483 265 547 326 576C363 593 402 605 434 611L429 641C389 634 343 623 301 608C195 570 43 456 43 236C43 81 135 -12 245 -12C368 -12 453 88 453 208C453 310 380 393 273 393C253 393 232 386 211 376L143 344ZM234 338C325 338 367 255 367 172C367 102 346 21 264 21C184 21 132 113 132 239C132 267 133 291 138 312C164 327 197 338 234 338Z" id="g190-227"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.42,-4.08)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span></p> <p>根据定义在[<gydF4y2Baa href="#B12">20.</gydF4y2Baa>),一个资源分配方案<gydF4y2Basvg height="9.04777pt" id="M40" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 8.4902 9.04777" width="8.4902pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-81"></use> </g> </svg>比例公平当且仅当,其他可行的配置方案<gydF4y2Basvg height="9.04777pt" id="M41" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 13.4946 9.04777" width="13.4946pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z" id="g113-78"></path> </g> </svg>,我们有<gydF4y2Baspan class="equation" id="EEq7"><span class="left"> <svg class="labelnn" height="29.5631pt" preserveaspectratio="xMaxYMin" 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<use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,66.82,-1.972)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,69.48,-1.972)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,74.97,-1.972)"> <use xlink:href="#g50-87"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,81.84,-16.196)"> <use xlink:href="#g113-120"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,91.14,-12.933)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,96.58,-16.196)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,100.01,-16.196)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,109.73,-16.196)"> <path d="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z" id="g113-83"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,118.22,-22.724)"> <path d="M309 -142C211 -61 151 99 151 271S210 601 309 683L288 710C141 611 75 451 75 272V271C75 90 141 -72 288 -169L309 -142Z" id="g50-41"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,121.62,-22.724)"> <use xlink:href="#g50-78"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,131.06,-22.724)"> <path d="M283 271C283 451 220 610 70 710L48 683C146 603 207 443 207 271S149 -59 48 -142L70 -169C220 -67 283 90 283 271Z" id="g50-42"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,118.16,-12.208)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,135.01,-16.196)"> <use xlink:href="#g113-45"></use> </g> </svg></span><span class="right"> <svg class="label" height="29.5631pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -29.5133 15.651 29.5631" width="15.651pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-11.264)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-11.264)"> <path d="M430 623H48C43 580 39 534 30 478H57C80 544 84 550 152 550H369C286 366 187 178 74 -1L81 -12L156 -2C249 201 343 408 438 611L430 623Z" id="g190-223"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,10.98,-11.264)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>在哪里<gydF4y2Basvg height="9.63795pt" id="M43" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 12.6057 9.63795" width="12.6057pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-120"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,9.308,3.264)"> <use xlink:href="#g50-106"></use> </g> </svg>用户的重量吗<gydF4y2Basvg height="9.21094pt" id="M44" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>和<gydF4y2Basvg height="17.4695pt" id="M45" style="vertical-align:-4.3756pt" version="1.1" viewbox="-0.0498162 -13.0939 25.4117 17.4695" width="25.4117pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.495,-6.304)"> <use xlink:href="#g50-41"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,11.89,-6.304)"> <use xlink:href="#g50-78"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.328,-6.304)"> <use xlink:href="#g50-42"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.427,4.212)"> <use xlink:href="#g50-106"></use> </g> </svg>用户的平均资源吗<gydF4y2Basvg height="9.21094pt" id="M46" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>由一个分配方案<gydF4y2Basvg height="9.04777pt" id="M47" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 13.4946 9.04777" width="13.4946pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-78"></use> </g> </svg>。权重反映了每个用户的优先级(即比例公平的分配。,我们把更多的资源给用户提供更高的优先级)<gydF4y2Baa href="#B6">9</gydF4y2Baa>,<gydF4y2Baa href="#B26">28</gydF4y2Baa>]。</gydF4y2Bap> <p>因此,通过最大化<gydF4y2Basvg height="13.2498pt" id="M48" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,我们可以实现最大比例公平的谱单元的数量分配给每个传感器和同时反映每个传感器的优先级。</gydF4y2Bap> <p>通过最大化<gydF4y2Basvg height="13.2498pt" id="M49" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>,我们可以让每个传感器中使用的频谱单位以前的传播时代。约束<gydF4y2Basvg height="9.52372pt" id="M50" style="vertical-align:-3.31356pt" version="1.1" viewbox="-0.0498162 -6.21016 9.59891 9.52372" width="9.59891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,4.349,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>表明,有一个相应的SINR阈值决定包传输是否成功。也就是说,如果<gydF4y2Basvg height="9.52372pt" id="M51" style="vertical-align:-3.31356pt" version="1.1" viewbox="-0.0498162 -6.21016 9.59891 9.52372" width="9.59891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,4.349,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>满足预期的接收者可以接收数据包正确,否则,数据包丢失(<gydF4y2Baa href="#B28">32</gydF4y2Baa>]。约束<gydF4y2Basvg height="9.52372pt" id="M52" style="vertical-align:-3.31356pt" version="1.1" viewbox="-0.0498162 -6.21016 9.59891 9.52372" width="9.59891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,4.349,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>表明没有传动功率传感器可以使用超过其最大可用输电能力。</gydF4y2Bap> <p>不像一般的公平“率”分配方案(<gydF4y2Baa href="#B12">20.</gydF4y2Baa>,<gydF4y2Baa href="#B18">26</gydF4y2Baa>,<gydF4y2Baa href="#B19">27</gydF4y2Baa>),我们认为公平”谱单元”分配因以下原因:如约束所示<gydF4y2Basvg height="9.52372pt" id="M53" style="vertical-align:-3.31356pt" version="1.1" viewbox="-0.0498162 -6.21016 9.59891 9.52372" width="9.59891pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,4.349,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>,每个传感器都是保证实现至少比SINR<gydF4y2Basvg height="12.2516pt" id="M54" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -12.0114 45.9258 12.2516" width="45.9258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,6.259,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.879,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.378,-5.984)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.986,-5.984)"> <use xlink:href="#g58-108"></use> </g> </svg>。自从SINR值直接对应利率如果是保证每个传感器达到相同的SINR<gydF4y2Basvg height="12.2516pt" id="M55" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -12.0114 45.9258 12.2516" width="45.9258pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,6.259,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.879,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.378,-5.984)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.986,-5.984)"> <use xlink:href="#g58-108"></use> </g> </svg>,公平的谱单元会产生“粗粒度”的公平分配率分配。</gydF4y2Bap> <p>然而,问题是棘手的由于其nonconvexity和离散变量。出于这个原因,我们操纵目标函数并应用一系列的近似。</gydF4y2Bap> <p>从今以后,我们只表示的单目标优化问题的目标函数<gydF4y2Basvg height="13.2498pt" id="M56" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>和约束条件<gydF4y2Basvg height="13.2498pt" id="M57" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>只有一个<gydF4y2Basvg height="13.2498pt" id="M58" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>和约束条件<gydF4y2Basvg height="13.2498pt" id="M59" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,分别。此外,我们表示问题的目标和约束<gydF4y2Basvg height="13.2498pt" id="M60" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 49.5055 13.2498" width="49.5055pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.442,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.446,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,44.58,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</gydF4y2Bap> <h4 id="tackling-the-intractability">4所示。解决棘手问题</gydF4y2Bah4> <p>我们开始放松整数约束的凸化过程;也就是说,我们下降(<gydF4y2Baa href="#EEq4">6</gydF4y2Baa>)。</gydF4y2Bap> <h5 id="sec4.1">4.1。凸化的<gydF4y2Basvg height="9.04777pt" id="M61" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M62" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>),<gydF4y2Basvg height="9.04777pt" id="M63" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M64" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>)</gydF4y2Bah5> <h6 id="sec4.1.1">以下4.4.1。凸化的<gydF4y2Basvg height="9.04777pt" id="M65" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M66" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>)</gydF4y2Bah6> <p>我们把原来的函数<gydF4y2Basvg height="13.2498pt" id="M67" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>成一个等效log-sum-exp函数形式,证明了凸(<gydF4y2Baa href="#B20">17</gydF4y2Baa>,<gydF4y2Baa href="#B19">27</gydF4y2Baa>,<gydF4y2Baa href="#B23">33</gydF4y2Baa>)通过定义<gydF4y2Basvg height="13.2498pt" id="M68" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 64.6175 13.2498" width="64.6175pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,7.533,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.188,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,18.108,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,29.846,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,33.274,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,40.725,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,45.413,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,52.918,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,55.574,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,59.709,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M69" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 63.176 13.2498" width="63.176pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M478 372C478 418 458 448 431 448C409 448 389 431 389 410C389 404 391 400 394 395C398 388 406 371 406 348C406 253 308 122 251 51H249C254 122 249 257 231 336C212 421 189 448 159 448C126 448 75 412 23 327L48 306C83 354 103 371 115 371C125 371 134 360 144 334C185 224 192 64 183 -19C146 -100 116 -202 110 -244L125 -261C154 -259 208 -234 222 -220C222 -194 225 -84 235 -23C247 -3 273 36 308 79C379 165 478 288 478 372Z" id="g113-225"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,5.907,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.563,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,16.482,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,28.22,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.648,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,39.099,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.787,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,51.482,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,54.138,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,58.273,0)"> <use xlink:href="#g113-42"></use> </g> </svg>对所有<gydF4y2Basvg height="9.65971pt" id="M70" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 28.2041 9.65971" width="28.2041pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,7.484,0)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,18.422,0)"> <use xlink:href="#g113-87"></use> </g> </svg>和<gydF4y2Basvg height="9.65971pt" id="M71" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 26.3682 9.65971" width="26.3682pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,8.866,0)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.804,0)"> <use xlink:href="#g113-84"></use> </g> </svg>,在那里<gydF4y2Basvg height="13.2498pt" id="M72" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 73.9374 13.2498" width="73.9374pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M535 230V280H52V230H535Z" id="g117-33"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,7.953,0)"> <path d="M983 225C983 348 891 448 766 448C646 448 579 377 521 276C458 383 382 448 256 448C165 448 37 373 37 208C37 98 119 -12 256 -12C375 -12 440 60 498 161C561 53 639 -12 766 -12C865 -12 983 64 983 225ZM478 196C428 106 365 21 266 21C183 21 129 114 129 240C129 353 183 415 244 415C352 415 420 301 478 196ZM889 204C889 66 838 21 776 21C666 21 598 135 540 241C590 331 655 415 754 415C842 415 889 320 889 204Z" id="g113-30"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,25.557,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.295,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,44.828,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,47.483,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,55.403,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,67.141,0)"> <use xlink:href="#g113-49"></use> </g> </svg>和<gydF4y2Basvg height="14.4105pt" id="M73" style="vertical-align:-4.1078pt" version="1.1" viewbox="-0.0498162 -10.3027 111.729 14.4105" width="111.729pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,7.953,0)"> <use xlink:href="#g113-30"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,25.557,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.295,0)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,43.202,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,45.857,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,53.777,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,65.515,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,68.943,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,76.394,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,81.082,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,89.446,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,97.327,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,101.585,-5.984)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,88.018,3.944)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,106.717,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。然后<gydF4y2Basvg height="9.04777pt" id="M74" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M75" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>)是新配方如下。</gydF4y2Bap> <p><i>目标。</gydF4y2Bai>考虑以下:<gydF4y2Baspan class="equation" id="EEq8"><span class="left"> <svg 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</g> <g transform="matrix(.0135,0,0,-0.0135,129.91,-16.349)"> <use xlink:href="#g119-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,139.87,-16.342)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,139.89,-1.972)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,143.5,-1.972)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,148.99,-1.972)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,153.59,-16.349)"> <path d="M391 364C391 409 353 448 295 448C249 448 198 426 152 393C65 331 23 225 23 139C23 14 96 -12 146 -12C198 -12 280 9 367 101L351 124C300 78 242 48 194 48C129 48 109 107 109 162V191C208 213 391 266 391 364ZM313 350C313 305 268 261 113 223C132 334 187 381 217 398C227 404 244 405 261 405C290 405 313 385 313 350Z" id="g113-102"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,159.2,-22.876)"> <path d="M563 583C563 664 501 710 433 710C381 710 334 692 285 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97 309C97 248 143 215 199 179C254 144 264 123 264 101C264 77 242 42 196 42C156 42 112 77 90 109C83 119 76 123 55 112C40 104 25 89 25 66C25 31 88 -12 141 -12C238 -12 336 62 336 140C336 194 300 230 238 264C200 285 168 308 168 347C168 383 200 399 223 399C263 399 285 381 306 348C310 341 322 335 334 342C352 352 363 374 363 392Z" id="g176-116"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,170.14,-16.349)"> <use xlink:href="#g119-174"></use> </g> </svg></span><span class="right"> <svg class="label" height="39.2674pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -39.2176 15.801 39.2674" width="15.801pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-16.116)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-16.116)"> <path d="M246 635C138 635 67 554 67 471C67 401 116 348 178 315C143 296 103 268 87 252C65 231 42 203 42 157C42 50 128 -12 234 -12C319 -12 432 52 432 169C432 256 370 303 299 344C347 376 373 399 381 408C399 430 408 459 408 487C408 569 341 635 246 635ZM235 603C284 603 334 567 334 483C334 420 306 383 273 358C202 393 142 427 142 503C142 552 173 603 235 603ZM245 21C179 21 122 70 122 163C122 219 155 270 204 300C279 263 352 219 352 144C352 66 308 21 245 21Z" id="g190-152"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,11.13,-16.116)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>酸处理<gydF4y2Baspan class="equation" id="EEq9"><span class="left"> <svg class="labelnn" height="159.865pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -159.815 15.971 159.865" width="15.971pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="159.865pt" id="M77" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -159.815 313.638 159.865" width="313.638pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-148.777)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,-148.777)"> <path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,17.43,-148.777)"> <path d="M332 -241C217 -138 149 60 149 271C149 483 216 680 332 783L312 808C148 686 74 491 74 272V271C74 50 148 -146 312 -266L332 -241Z" id="g119-5"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,22.67,-148.777)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,27.02,-145.513)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.15,-148.777)"> <path d="M311 271V272C311 491 237 686 73 808L53 783C169 680 236 483 236 271C236 60 168 -138 53 -241L73 -266C237 -146 311 50 311 271Z" id="g119-6"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,23.71,-110.94)"> <use xlink:href="#g113-59"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,30.58,-110.94)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.01,-110.94)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.73,-110.94)"> <path d="M660 -1246C379 -940 215 -355 215 271C215 898 376 1482 660 1788L626 1823C273 1470 113 904 113 272V271C113 -367 273 -935 626 -1281L660 -1246Z" id="g119-225"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,62.65,-110.933)"> <use 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xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,56.27,-1.972)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,64.51,-16.349)"> <use xlink:href="#g119-165"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,74.91,-25.215)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,80.52,-31.199)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,85.85,-29.009)"> <use xlink:href="#g176-106"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,87.8,-29.009)"> <use xlink:href="#g176-116"></use> </g> <rect height="0.679945" width="16.5657" x="74.91" y="-20.1563"></rect> <g transform="matrix(.0135,0,0,-0.0135,76.11,-6.734)"> <path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 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</svg></span></span>如果和不平等成为平等<gydF4y2Baspan class="equation" id="EEq12"><span class="left"> <svg class="labelnn" height="35.7805pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -35.7307 18.521 35.7805" width="18.521pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="35.7805pt" id="M79" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -35.7307 163.818 35.7805" width="163.818pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-14.091)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.36,-10.827)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.02,-10.827)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,17.94,-14.091)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,44.2,-22.958)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,49.81,-28.941)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,55.14,-26.752)"> <use xlink:href="#g176-106"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,57.08,-26.752)"> <use xlink:href="#g176-116"></use> </g> <rect height="0.679945" width="43.2227" x="30.87" y="-17.8989"></rect> <g transform="matrix(.0135,0,0,-0.0135,30.87,-4.081)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.07,-.476)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,44.68,-.476)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,50.17,-.476)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,57.53,-4.088)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,63.14,-8.44)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,68.47,-6.25)"> <use xlink:href="#g176-106"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,70.41,-6.25)"> <use xlink:href="#g176-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,75.29,-14.091)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,90.61,-14.091)"> <use xlink:href="#g117-46"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,98.37,-14.091)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,105.86,-14.091)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,116.8,-14.091)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,124.64,-14.091)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,134.54,-14.091)"> <use xlink:href="#g113-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,143.41,-14.091)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,154.35,-14.091)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,160.74,-14.091)"> <use xlink:href="#g113-47"></use> </g> </svg></span><span class="right"> <svg class="label" height="35.7805pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -35.7307 18.521 35.7805" width="18.521pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-14.373)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-14.373)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.27,-14.373)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,13.85,-14.373)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span></p> <p>目的是凝聚<gydF4y2Baspan class="equation" id="EEq13"><span class="left"> <svg class="labelnn" height="77.2498pt" preserveaspectratio="xMaxYMin" version="1.1" 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transform="matrix(.0135,0,0,-0.0135,172.62,-16.349)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,177.85,-16.349)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,185.38,-13.085)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,188.04,-13.085)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,195.2,-16.349)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,206.18,-16.349)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,209.61,-16.349)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,219.33,-16.349)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,226.69,-13.085)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,229.35,-13.085)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,233.48,-16.349)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,241.07,-16.349)"> <use xlink:href="#g113-45"></use> </g> </svg></span><span class="right"> <svg class="label" height="77.2498pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -77.2 20.281 77.2498" width="20.281pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-35.107)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-35.107)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.31,-35.107)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.61,-35.107)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>变成了仿射,可以通过凝聚算法解决优化问题,算法<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/alg1/" target="_blank">1</gydF4y2Baa>(<gydF4y2Baa href="#B20">17</gydF4y2Baa>]。</gydF4y2Bap> <p></p> <div class="floats-partial-section partial-other-wrapper" data-section="alg1"> <div class="floats-partial-content fig-content-alg1"> <table> <tbody> <tr> <td> <table class="algorithm" id="alg1"> <tbody> <tr> <td colspan="2"><i>步骤1。</gydF4y2Bai>产生初始可行解向量<gydF4y2Basvg height="13.0595pt" id="M81" style="vertical-align:-3.36801pt" version="1.1" viewbox="-0.0498162 -9.69149 8.327 13.0595" width="8.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z" id="g5-224"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="605" vert-adv-y="605"></glyph.data> </g> </svg>和<gydF4y2Basvg height="9.68693pt" id="M82" style="vertical-align:-3.36797pt" version="1.1" viewbox="-0.0498162 -6.31896 7.1575 9.68693" width="7.1575pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M498 369C498 423 469 454 440 454C415 454 388 432 388 408C388 398 391 390 395 384C401 375 413 354 413 330C413 269 332 132 280 70H278C285 133 286 231 273 319C259 412 231 454 191 454C147 454 85 416 21 322L49 293C91 339 110 351 119 351C129 351 132 349 142 324C181 225 194 56 178 -19C148 -80 115 -167 107 -224L125 -246C167 -243 241 -219 265 -202C260 -169 255 -95 256 -21C261 -11 268 2 323 70C438 212 498 291 498 369Z" id="g5-225"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="519" vert-adv-y="519"></glyph.data> </g> </svg>。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤2。</gydF4y2Bai>对所有<gydF4y2Basvg height="9.65971pt" id="M83" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 28.2041 9.65971" width="28.2041pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,7.484,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,18.422,0)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z" id="g113-87"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="709" vert-adv-y="709"></glyph.data> </g> </svg>和<gydF4y2Basvg height="9.65971pt" id="M84" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 26.3682 9.65971" width="26.3682pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" id="g113-116"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="375" vert-adv-y="375"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,8.866,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,19.804,0)"> <path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="472" vert-adv-y="472"></glyph.data> </g> </svg>、评估<gydF4y2Basvg height="9.63795pt" id="M85" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 14.2742 9.63795" width="14.2742pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M545 106L524 126C493 85 467 65 455 65C438 65 427 113 405 238C448 295 498 362 543 439L533 448L478 435C453 386 423 331 398 295H395C370 404 347 448 282 448C169 448 23 309 23 153C23 54 65 -12 128 -12C203 -12 283 70 339 155H341C360 29 380 -12 411 -12C444 -12 491 11 545 106ZM333 204C265 95 210 54 169 54C137 54 113 96 113 171C113 302 191 405 252 405C301 405 318 306 333 204Z" id="g113-223"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="568" vert-adv-y="568"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.357,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,10.012,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data> </g> </svg>与初始向量</gydF4y2Batd> </tr> <tr> <td colspan="2"> <svg height="13.0595pt" id="M86" style="vertical-align:-3.36801pt" version="1.1" viewbox="-0.0498162 -9.69149 8.327 13.0595" width="8.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z" id="g5-224"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="605" vert-adv-y="605"></glyph.data> </g> </svg>和<gydF4y2Basvg height="9.68693pt" id="M87" style="vertical-align:-3.36797pt" version="1.1" viewbox="-0.0498162 -6.31896 7.1575 9.68693" width="7.1575pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M498 369C498 423 469 454 440 454C415 454 388 432 388 408C388 398 391 390 395 384C401 375 413 354 413 330C413 269 332 132 280 70H278C285 133 286 231 273 319C259 412 231 454 191 454C147 454 85 416 21 322L49 293C91 339 110 351 119 351C129 351 132 349 142 324C181 225 194 56 178 -19C148 -80 115 -167 107 -224L125 -246C167 -243 241 -219 265 -202C260 -169 255 -95 256 -21C261 -11 268 2 323 70C438 212 498 291 498 369Z" id="g5-225"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="519" vert-adv-y="519"></glyph.data> </g> </svg>使用(<gydF4y2Baa href="#EEq12">11</gydF4y2Baa>)。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤3。</gydF4y2Bai>浓缩目标函数<gydF4y2Basvg height="14.52pt" id="M88" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 15.1445 14.52" width="15.1445pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.944)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg>成<gydF4y2Basvg height="14.52pt" id="M89" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path> <glyph.data ascent="712" descent="-215" horiz-adv-x="447" vert-adv-y="447"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg>。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤4。</gydF4y2Bai>解决由此产生的NLP。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>第5步。</gydF4y2Bai>终止<gydF4y2Basvg height="9.89089pt" id="M90" style="vertical-align:-0.2129898pt" version="1.1" viewbox="-0.0498162 -9.6779 6.9399 9.89089" width="6.9399pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 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transform="matrix(.0135,0,0,-0.0135,73.029,0)"> <path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="503" vert-adv-y="503"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,82.872,0)"> <path d="M535 230V280H52V230H535Z" id="g117-33"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,93.853,0)"> <path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="480" vert-adv-y="480"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,100.356,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,105.044,0)"> <path d="M162 -163V703H101V-163H162Z" id="g113-9"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,112.392,0)"> <path d="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z" id="g117-93"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,124.13,0)"> <path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data> </g> </svg>。否则</gydF4y2Batd> </tr> <tr> <td colspan="2">转到第2步解向量<gydF4y2Basvg height="13.0595pt" id="M92" style="vertical-align:-3.36801pt" version="1.1" viewbox="-0.0498162 -9.69149 8.327 13.0595" width="8.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z" id="g5-224"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="605" vert-adv-y="605"></glyph.data> </g> </svg>和<gydF4y2Basvg height="9.68693pt" id="M93" style="vertical-align:-3.36797pt" version="1.1" viewbox="-0.0498162 -6.31896 7.1575 9.68693" width="7.1575pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M498 369C498 423 469 454 440 454C415 454 388 432 388 408C388 398 391 390 395 384C401 375 413 354 413 330C413 269 332 132 280 70H278C285 133 286 231 273 319C259 412 231 454 191 454C147 454 85 416 21 322L49 293C91 339 110 351 119 351C129 351 132 349 142 324C181 225 194 56 178 -19C148 -80 115 -167 107 -224L125 -246C167 -243 241 -219 265 -202C260 -169 255 -95 256 -21C261 -11 268 2 323 70C438 212 498 291 498 369Z" id="g5-225"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="519" vert-adv-y="519"></glyph.data> </g> </svg>在步骤4。</gydF4y2Batd> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">算法1</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/alg1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 凝聚算法。</gydF4y2Badiv> </div> </div> <p></p> <p>冷凝目标函数<gydF4y2Basvg height="14.52pt" id="M94" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 15.1445 14.52" width="15.1445pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.944)"> <use xlink:href="#g50-50"></use> </g> </svg>成<gydF4y2Basvg height="14.52pt" id="M95" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>总收益率低估了解决方案,冷凝的迭代循环中的每个NLP试图改善的准确性近似特定最大原始可行域。此外,该算法是收敛的,总是产生近似解满足最初的问题的Karush-Kuhn-Tucker条件(<gydF4y2Baa href="#B20">17</gydF4y2Baa>]。</gydF4y2Bap> <h6 id="sec4.1.2">4.1.2。凸化的<gydF4y2Basvg height="13.2498pt" id="M96" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg></h6> <p>作为凸化的完成<gydF4y2Basvg height="13.2498pt" id="M97" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,我们让<gydF4y2Basvg height="13.2498pt" id="M98" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 64.6175 13.2498" width="64.6175pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.533,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.188,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,18.108,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,29.846,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,33.274,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,40.725,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,45.413,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,52.918,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,55.574,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,59.709,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M99" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 63.176 13.2498" width="63.176pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,5.907,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.563,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,16.482,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,28.22,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.648,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,39.099,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.787,0)"> <use xlink:href="#g113-113"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,51.482,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,54.138,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,58.273,0)"> <use xlink:href="#g113-42"></use> </g> </svg>对所有<gydF4y2Basvg height="9.65971pt" id="M100" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 28.2041 9.65971" width="28.2041pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,7.484,0)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,18.422,0)"> <use xlink:href="#g113-87"></use> </g> </svg>和<gydF4y2Basvg height="9.65971pt" id="M101" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 26.3682 9.65971" width="26.3682pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,8.866,0)"> <use xlink:href="#g117-173"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.804,0)"> <use xlink:href="#g113-84"></use> </g> </svg>,在那里<gydF4y2Basvg height="13.2498pt" id="M102" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 73.9374 13.2498" width="73.9374pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,7.953,0)"> <use xlink:href="#g113-30"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,25.557,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.295,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,44.828,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,47.483,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,55.403,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,67.141,0)"> <use xlink:href="#g113-49"></use> </g> </svg>和<gydF4y2Basvg height="14.4105pt" id="M103" style="vertical-align:-4.1078pt" version="1.1" viewbox="-0.0498162 -10.3027 111.729 14.4105" width="111.729pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,7.953,0)"> <use xlink:href="#g113-30"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,25.557,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.295,0)"> <use xlink:href="#g113-225"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,43.202,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,45.857,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,53.777,0)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,65.515,0)"> <use xlink:href="#g121-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,68.943,0)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,76.394,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,81.082,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,89.446,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,97.327,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,101.585,-5.984)"> <use xlink:href="#g58-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,88.018,3.944)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,106.717,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。然后<gydF4y2Basvg height="13.2498pt" id="M104" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>转化为一个凸形式:<gydF4y2Baspan class="equation" id="EEq14"><span class="left"> <svg class="labelnn" height="29.7154pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -29.6656 20.061 29.7154" width="20.061pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="29.7154pt" id="M105" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -29.6656 182.758 29.7154" width="182.758pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-16.349)"> <use xlink:href="#g190-78"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.97,-16.349)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.6,-16.349)"> <path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g190-111"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,23.01,-16.349)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,26.65,-16.349)"> <use xlink:href="#g190-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.74,-16.349)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,41.37,-16.349)"> <use xlink:href="#g190-123"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,47.06,-16.349)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,55.29,-16.349)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,64.34,-16.349)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,72.72,-16.349)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,77.96,-16.349)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,84.96,-13.085)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,90.1,-16.349)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,99.14,-16.349)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,110.88,-16.342)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,110.9,-1.972)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,114.51,-1.972)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,120,-1.972)"> <use xlink:href="#g50-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,127.52,-16.342)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,126.87,-2.124)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,129.53,-2.124)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,135.02,-2.124)"> <use xlink:href="#g50-87"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,141.88,-16.349)"> <use xlink:href="#g113-77"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,150.53,-13.085)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,153.18,-13.085)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,157.32,-16.349)"> <use xlink:href="#g113-102"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,162.93,-22.876)"> <use xlink:href="#g54-33"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,168.72,-22.876)"> <use xlink:href="#g50-224"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,174.05,-20.687)"> <use xlink:href="#g176-106"></use> </g> <g transform="matrix(.0068,0,0,-0.0068,176,-20.687)"> <use xlink:href="#g176-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,179.68,-16.349)"> <use xlink:href="#g113-47"></use> </g> </svg></span><span class="right"> <svg class="label" height="29.7154pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -29.6656 20.061 29.7154" width="20.061pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-11.34)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-11.34)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.27,-11.34)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.39,-11.34)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span></p> <p>上述配方使<gydF4y2Basvg height="13.2498pt" id="M106" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 14.451 13.2498" width="14.451pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-224"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.533,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.188,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>接近于0,<gydF4y2Basvg height="12.4257pt" id="M107" style="vertical-align:-3.427751pt" version="1.1" viewbox="-0.0498162 -8.99795 37.6463 12.4257" width="37.6463pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-77"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.644,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,11.299,3.264)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.219,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,30.957,0)"> <use xlink:href="#g113-50"></use> </g> </svg>为了减少它的价值。因此我们可以得出相同的结果的获得最大化<gydF4y2Basvg height="13.2498pt" id="M108" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>。</gydF4y2Bap> <h5 id="sec4.2">4.2。多目标优化问题的数值</gydF4y2Bah5> <p>为解决拖把,最普遍的方法之一是数值<gydF4y2Bai>,</gydF4y2Bai>拖把在哪里被合适的标量优化(即所取代。,single objective optimization) problems involving possibly some additional parameters and constraints. With the help of the scalar problem, not only can one optimal solution of the multiobjective optimization problem be found but also approximations of the whole solution set can be generated by a variation of the parameters. In this paper, we are interested in maintaining the convexity of the scalarized problem as well as guaranteeing weak Pareto optimality at least by minimizing the distance between ideal solutions (i.e., Pareto Frontier) and feasible objective region. To this end, we deploy a scalarization method based on weighted Chebyshev norm problem [<a href="#B24">16</gydF4y2Baa>]。</gydF4y2Bap> <p>我们考虑一个拖把与决策变量的向量<gydF4y2Basvg height="5.93359pt" id="M109" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -5.88377 6.81753 5.93359" width="6.81753pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M494 0V32C450 38 426 53 393 105L296 260C330 305 354 338 375 361C411 396 421 401 476 410V442H293V410C332 402 337 394 323 371C311 351 295 324 274 293L227 371C213 393 218 402 252 410V442H16V410C70 402 80 391 108 344L196 199C166 159 140 123 115 95C81 54 61 43 7 32V0H196V32C156 41 150 53 167 81C182 105 199 138 219 166L269 79C287 49 283 38 245 32V0H494Z" id="g13-118"></path> </g> </svg>和目标函数的向量<gydF4y2Basvg height="16.2579pt" id="M110" style="vertical-align:-3.5719pt" version="1.1" viewbox="-0.0498162 -12.686 136.169 16.2579" width="136.169pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M52 442L22 406L27 394H92V108C92 45 88 39 30 32V0H302V32C227 39 220 45 220 108V394H321C335 401 339 431 335 442H220L218 477C214 562 214 597 220 616C224 631 233 642 251 642C279 642 311 617 335 593C345 583 355 583 369 593C384 605 395 618 399 629C406 644 405 659 391 673C374 689 349 701 309 703C261 697 226 679 190 649C133 601 112 553 105 531C97 507 92 486 92 464V442H52Z" id="g13-100"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,5.477,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.165,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,16.858,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,25.331,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.069,0)"> <path d="M290 -163V-135C183 -126 181 -122 181 -44V583C181 662 184 666 290 675V703H120V-163H290Z" id="g113-92"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,41.743,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,48.747,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,53.881,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,58.569,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,65.262,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,69.95,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,75.31,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,80.67,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,86.03,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,91.425,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,96.785,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,103.789,3.264)"> <path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z" id="g50-115"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,108.352,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,113.04,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,119.733,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,124.421,0)"> <path d="M226 -163V703H56V676C162 667 165 662 165 584V-43C165 -122 162 -126 56 -136V-163H226Z" id="g113-94"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,129.325,-6.249)"> <path d="M655 676H628C608 656 600 650 571 650H156C118 650 114 651 102 676H77C63 615 45 548 24 485L60 486C81 531 97 562 114 580C134 603 148 611 252 611H308L217 127C201 41 196 38 105 32L98 0H384L393 32C300 38 288 41 304 127L393 611H466C553 611 571 604 582 580C592 559 597 530 595 485L630 489C636 548 645 624 655 676Z" id="g50-85"></path> </g> </svg>如下。</gydF4y2Bap> <p><i>目标。</gydF4y2Bai>考虑以下:<gydF4y2Baspan class="equation" id="EEq15"><span class="left"> <svg class="labelnn" height="14.501pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 20.451 14.501" width="20.451pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="14.501pt" id="M111" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 173.977 14.501" width="173.977pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.773)"> <use xlink:href="#g190-78"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.98,-4.773)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.61,-4.773)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,23.02,-4.773)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,26.65,-4.773)"> <use xlink:href="#g190-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.75,-4.773)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,41.38,-4.773)"> <use xlink:href="#g190-123"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,47.07,-4.773)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,57.57,-4.773)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,64.57,-1.51)"> <path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,75.01,-4.583)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,79.71,-4.773)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,86.4,-4.583)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,93.4,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,108.73,-4.773)"> <path d="M766 88L752 113C719 83 690 64 681 64C674 64 672 74 679 103L724 292C758 436 724 448 701 448C680 448 666 442 639 429C594 407 514 350 441 252H439L447 289C476 423 450 448 419 448C398 448 379 441 355 427C307 400 234 344 162 249H160L180 324C203 409 197 448 170 448C144 448 82 413 23 349L35 321C57 343 96 374 108 374C115 374 117 371 111 341C87 227 57 112 24 -6L32 -12C53 -4 81 4 108 6C119 68 134 128 149 171C177 229 309 383 364 383C387 383 388 355 373 282C354 190 330 92 303 -6L309 -12C332 -4 356 3 386 6C396 63 411 122 424 171C458 236 590 383 642 383C658 383 664 369 652 315L603 91C587 20 593 -12 619 -12C642 -12 708 23 766 88Z" id="g113-110"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,123.2,-4.773)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,134.94,-4.773)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,141.44,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,146.8,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,152.16,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,157.52,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,162.92,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,168.28,-4.773)"> <path d="M393 379C402 394 400 411 393 422C384 437 365 448 348 448C301 448 237 372 186 285H182L193 335C210 408 205 448 178 448C150 448 80 402 29 344L45 321C80 355 114 373 122 373C128 373 130 365 124 330C106 228 76 98 50 -5L57 -12C82 -5 112 3 132 6L172 203C196 256 234 304 254 329C275 355 293 367 306 367C318 367 330 360 342 348C347 343 355 343 365 350S386 367 393 379Z" id="g113-115"></path> </g> </svg></span><span class="right"> <svg class="label" height="14.501pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 20.451 14.501" width="20.451pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.08)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.68,-4.08)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.05,-4.08)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.78,-4.08)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>酸处理<gydF4y2Baspan class="equation" id="EEq16"><span class="left"> <svg class="labelnn" height="14.501pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 20.091 14.501" width="20.091pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="14.501pt" id="M112" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 125.958 14.501" width="125.958pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.773)"> <path d="M499 88L487 113C459 86 422 65 413 65C403 65 403 74 409 98L461 318C487 426 460 448 431 448C408 448 383 441 352 424C305 398 223 344 157 257H155L243 674C249 702 249 712 240 712C227 712 170 680 87 673L82 648H117C155 648 162 644 150 590L23 -4L30 -12C55 -4 81 3 105 8C113 53 131 150 143 187C199 281 323 387 372 387C390 387 393 369 380 311L328 86C313 19 319 -12 347 -12C379 -12 442 24 499 88Z" id="g113-105"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,6.92,-1.51)"> <path d="M238 675C244 702 241 710 231 710C220 710 155 682 74 673L70 643H101C147 643 151 635 142 594L39 111C18 11 36 -12 55 -12C89 -12 170 38 223 103L207 129C176 98 130 68 118 68C113 68 108 72 114 102L238 675Z" id="g50-109"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,12.27,-4.583)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,16.98,-4.773)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,23.67,-4.583)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.19,-4.773)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.92,-4.773)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,50.43,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,65.75,-4.773)"> <path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z" id="g113-109"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,73.18,-4.773)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,84.92,-4.773)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,91.42,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,96.78,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,102.14,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,107.5,-4.773)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,112.9,-4.773)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,118.26,-4.773)"> <path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,122.88,-4.773)"> <use xlink:href="#g113-47"></use> </g> </svg></span><span class="right"> <svg class="label" height="14.501pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.4512 20.091 14.501" width="20.091pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.08)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-4.08)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.27,-4.08)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.42,-4.08)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span></p> <p>首先,我们每个正常化<gydF4y2Basvg height="6.42315pt" id="M113" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 10.8292 6.42315" width="10.8292pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-110"></use> </g> </svg>th目标函数<gydF4y2Basvg height="13.2498pt" id="M114" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 15.2914 13.2498" width="15.2914pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-110"></use> </g> </svg>是最小值指定为0和1的最大价值如下:<gydF4y2Baspan class="equation" id="EEq17"><span class="left"> <svg class="labelnn" height="34.9511pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -34.9012 20.581 34.9511" width="20.581pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="34.9511pt" id="M115" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -34.9012 156.578 34.9511" width="156.578pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-13.958)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7,-10.694)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,14.64,-10.694)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,22.31,-13.768)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.01,-13.958)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,33.71,-13.768)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,42.22,-13.958)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,58.59,-23.864)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,65.6,-20.6)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,76.03,-23.673)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,80.73,-23.864)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,87.43,-23.673)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,95.18,-23.864)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,106.16,-23.864)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,113.17,-20.6)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,123.6,-23.863)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,128.84,-23.864)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,135.53,-29.847)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,135.37,-19.92)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,143.53,-23.863)"> <use xlink:href="#g119-6"></use> </g> <rect height="0.679945" width="97.1526" x="55.15" y="-17.7657"></rect> <g transform="matrix(.0135,0,0,-0.0135,55.15,-4.058)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,62.16,-.794)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,69.79,-.794)"> <path d="M698 334C698 397 680 451 655 451C627 451 602 424 602 397C602 389 605 383 614 371C622 360 624 340 624 317C624 161 546 47 458 47C419 47 389 69 389 125C389 142 391 162 397 185L457 430L451 435L380 421L315 164C301 107 266 47 222 47C182 47 153 69 153 126C153 137 157 162 161 185C166 214 179 265 197 334C203 358 208 385 208 407C208 433 201 451 176 451C124 451 64 404 24 348L44 320C86 366 113 382 121 382C126 382 128 381 128 374C128 368 126 356 122 341C102 266 88 204 81 164C77 143 73 121 73 107C73 23 131 -12 187 -12C234 -12 281 10 322 45C343 5 383 -12 422 -12C559 -12 698 174 698 334Z" id="g50-120"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,79.46,-3.868)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,84.17,-4.058)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,90.86,-3.868)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,98.62,-4.058)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,109.6,-4.058)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,116.61,-.794)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,127.04,-4.058)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,132.27,-4.058)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,138.97,-8.41)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,138.8,-.114)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,146.96,-4.058)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,153.5,-13.958)"> <use xlink:href="#g113-45"></use> </g> </svg></span><span class="right"> <svg class="label" height="34.9511pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -34.9012 20.581 34.9511" width="20.581pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-13.958)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-13.958)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.2,-13.958)"> <use xlink:href="#g190-227"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.91,-13.958)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>在哪里<gydF4y2Basvg height="16.9664pt" id="M116" style="vertical-align:-6.440001pt" version="1.1" viewbox="-0.0498162 -10.5264 125.683 16.9664" width="125.683pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,14.639,3.264)"> <use xlink:href="#g50-120"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,25.823,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.561,0)"> <use xlink:href="#g121-107"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,48.616,0)"> <use xlink:href="#g121-95"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,54.564,0)"> <use xlink:href="#g121-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,61.074,3.264)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,65.153,3.264)"> <path d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z" id="g54-34"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,70.947,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,75.566,3.264)"> <path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z" id="g50-45"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,77.814,3.264)"> <path d="M117 -12C153 -12 178 12 178 50C178 84 153 110 118 110C84 110 59 84 59 50C59 12 84 -12 117 -12Z" id="g50-47"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,80.061,3.264)"> <use xlink:href="#g50-47"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,82.309,3.264)"> <use xlink:href="#g50-47"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,84.582,3.264)"> <use xlink:href="#g50-45"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,86.829,3.264)"> <use xlink:href="#g50-115"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,91.462,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,98.467,3.264)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,103.058,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,107.746,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,114.439,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,114.276,3.944)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,120.754,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="16.9664pt" id="M117" style="vertical-align:-6.440001pt" version="1.1" viewbox="-0.0498162 -10.5264 13.1319 16.9664" width="13.1319pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.693,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.53,3.944)"> <use xlink:href="#g50-107"></use> </g> </svg>是优化设计向量获得只有吗<gydF4y2Basvg height="15.4379pt" id="M118" style="vertical-align:-5.759999pt" version="1.1" viewbox="-0.0498162 -9.6779 11.7217 15.4379" width="11.7217pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-107"></use> </g> </svg>是最小化。也就是说,其最优解之间的距离和糟糕的解决方案可实现每一个目标函数。然后定义的加权切比雪夫范数问题是额外的变量<gydF4y2Basvg height="6.70873pt" id="M119" style="vertical-align:-0.3081903pt" version="1.1" viewbox="-0.0498162 -6.40054 6.8719 6.70873" width="6.8719pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M475 445L452 468C423 436 401 426 385 426S352 427 305 436C268 443 216 448 185 448C156 448 128 425 102 382C89 360 77 338 64 304L89 291C117 340 143 380 190 380C214 380 268 376 295 373C320 370 344 371 362 374L70 101C32 65 23 36 23 18C23 5 27 -3 31 -8C36 -8 39 -6 42 -1C52 15 67 31 80 40S110 49 143 33C195 8 257 -20 290 -20C339 -20 382 11 439 129L416 148C366 74 334 55 305 55C278 55 236 68 203 81C169 94 141 100 122 96C205 170 348 308 411 376L475 445Z" id="g113-123"></path> </g> </svg>如下。</gydF4y2Bap> <p><i>目标。</gydF4y2Bai>考虑以下:<gydF4y2Baspan class="equation" id="EEq18"><span class="left"> <svg class="labelnn" height="14.4466pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.3968 20.141 14.4466" width="20.141pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="14.4466pt" id="M120" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.3968 65.128 14.4466" width="65.128pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.828)"> <use xlink:href="#g190-78"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.98,-4.828)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.61,-4.828)"> <use xlink:href="#g190-111"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,23.02,-4.828)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,26.65,-4.828)"> <use xlink:href="#g190-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.75,-4.828)"> <use xlink:href="#g190-106"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,41.38,-4.828)"> <use xlink:href="#g190-123"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,47.07,-4.828)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,55.3,-4.828)"> <use xlink:href="#g113-123"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,62.05,-4.828)"> <use xlink:href="#g113-45"></use> </g> </svg></span><span class="right"> <svg class="label" height="14.4466pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.3968 20.141 14.4466" width="20.141pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-4.08)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-4.08)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.19,-4.08)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.47,-4.08)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>酸处理<gydF4y2Baspan class="equation" id="EEq19"><span class="left"> <svg class="labelnn" height="36.4816pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -36.4318 20.301 36.4816" width="20.301pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="36.4816pt" id="M121" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -36.4318 166.968 36.4816" width="166.968pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-26.754)"> <path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,6.67,-23.49)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.83,-26.754)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.83,-23.49)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.47,-23.49)"> <use xlink:href="#g50-111"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.14,-26.564)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,41.84,-26.754)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,48.54,-26.564)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,57.05,-26.754)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,68.79,-26.754)"> <use xlink:href="#g113-123"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,75.54,-26.754)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,90.86,-26.754)"> <use xlink:href="#g117-46"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,98.62,-26.754)"> <use xlink:href="#g113-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,113.1,-26.754)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,124.84,-26.754)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,131.34,-26.754)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,136.7,-26.754)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,142.06,-26.754)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,147.42,-26.754)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,152.81,-26.754)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,158.17,-26.754)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,163.89,-26.754)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.55,-4.08)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,27.47,-.816)"> <use xlink:href="#g50-109"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.82,-3.889)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.53,-4.08)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,44.22,-3.889)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,52.74,-4.08)"> <use xlink:href="#g117-93"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,64.47,-4.08)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,70.98,-4.08)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,86.3,-4.08)"> <use xlink:href="#g113-109"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,93.73,-4.08)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,105.47,-4.08)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,111.97,-4.08)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,117.33,-4.08)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,122.69,-4.08)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,128.05,-4.08)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,133.45,-4.08)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,138.81,-4.08)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,143.43,-4.08)"> <use xlink:href="#g113-45"></use> </g> </svg></span><span class="right"> <svg class="label" height="36.4816pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -36.4318 20.301 36.4816" width="20.301pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,-14.723)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.68,-14.723)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,9.2,-14.723)"> <use xlink:href="#g190-152"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.63,-14.723)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>在哪里<gydF4y2Basvg height="13.1057pt" id="M122" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 37.0316 13.1057" width="37.0316pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,18.612,0)"> <path d="M512 230V281L75 514V456L453 256V254L75 55V-3L512 230Z" id="g117-92"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,30.35,0)"> <use xlink:href="#g113-49"></use> </g> </svg>的重量是<gydF4y2Basvg height="13.2498pt" id="M123" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 15.2914 13.2498" width="15.2914pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-110"></use> </g> </svg>(注意,<gydF4y2Basvg height="13.1057pt" id="M124" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 14.9515 13.1057" width="14.9515pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-110"></use> </g> </svg>表达相对体重而不是绝对重量)。通过求解这个scalarized问题,理想的解决方案之间的最大距离<gydF4y2Basvg height="14.6342pt" id="M125" style="vertical-align:-4.1078pt" version="1.1" viewbox="-0.0498162 -10.5264 48.8282 14.6342" width="48.8282pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,11.692,3.264)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.853,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,24.541,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,31.234,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,31.071,3.944)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,39.232,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.92,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和可行的目标区域(<gydF4y2Basvg height="13.2498pt" id="M126" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 15.2914 13.2498" width="15.2914pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-110"></use> </g> </svg>(<gydF4y2Bab>x</gydF4y2Bab>)是最小化。(此scalarized问题对应的问题在min-max达到目标之间的加权公平值(即。上确界,也称为maxminimization)标准。还有另一种数值方法,认为客观值之间的比例公平(<gydF4y2Baa href="#B29">35</gydF4y2Baa>]。但不能维持原来的凸性问题)。很容易检查加权切比雪夫范数问题保持凸凸性如果原始问题;也就是说,所有<gydF4y2Basvg height="13.2498pt" id="M127" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.4198 13.2498" width="31.4198pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.166,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.853,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,26.547,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.1057pt" id="M128" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 26.2549 13.1057" width="26.2549pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-105"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.923,3.264)"> <use xlink:href="#g50-109"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.001,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.689,0)"> <use xlink:href="#g13-118"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,21.382,0)"> <use xlink:href="#g113-42"></use> </g> </svg>是凸的。无疑,作为一个目标函数具有较高的体重,这是容易被强调相对比其他人更。</gydF4y2Bap> <p>我们可以设想目标函数的线性组合,如<gydF4y2Basvg height="13.2498pt" id="M129" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 62.117 13.2498" width="62.117pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.8,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,18.804,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,26.966,0)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,37.947,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,44.613,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,49.747,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,56.751,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,为了scalarize多目标优化问题。然而,切比雪夫正常化是首选的线性组合由于以下原因。<gydF4y2Baspan class="list"><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(1)</gydF4y2Baspan><span class="list-content">每个目标的单位和规模是不同的:一个表达传递的数量,另一个表示公平值的频谱的数量。所以我们需要规范化的尺度目标。</gydF4y2Baspan></span><span class="list-item"><span class="list-label" style="font-family:MinionPro-Regular">(2)</gydF4y2Baspan><span class="list-content">的线性组合并不能保证两个目标之间的平衡(公平)。当然,调整每一个目标都可能产生的重量平衡的结果,但很难找到足够的重量。然而,我们的方法产量平衡输出(即没有重量值。,delta_1 delta_2)。然后我们可以控制每个目标的重量通过调整权重值。当然,这种方法更简单。</gydF4y2Baspan></span></span></p> <p>如果我们表示<gydF4y2Basvg height="14.52pt" id="M130" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M131" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 36.892 13.2498" width="36.892pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.987,0)"> <use xlink:href="#g113-42"></use> </g> </svg>通过<gydF4y2Basvg height="9.7821pt" id="M132" style="vertical-align:-3.57194pt" version="1.1" viewbox="-0.0498162 -6.21016 12.6315 9.7821" width="12.6315pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path> </g> <g transform="matrix(.0095,0,0,-0.0095,7.37,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>和<gydF4y2Basvg height="9.7821pt" id="M133" style="vertical-align:-3.57194pt" version="1.1" viewbox="-0.0498162 -6.21016 12.6315 9.7821" width="12.6315pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-104"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.37,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>分别这个问题<gydF4y2Basvg height="13.2498pt" id="M134" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 49.5055 13.2498" width="49.5055pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.442,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.446,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,44.58,0)"> <use xlink:href="#g113-42"></use> </g> </svg>转换为单目标优化问题,切比雪夫范数问题。</gydF4y2Bap> <p><i>目标。</gydF4y2Bai>考虑以下:<gydF4y2Baspan class="equation" id="EEq21"><span class="left"> <svg class="labelnn" height="14.4466pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -14.3968 20.411 14.4466" width="20.411pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" 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14.1518 14.52" width="14.1518pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-104"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.71,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.37,3.944)"> <use xlink:href="#g50-50"></use> </g> </svg>最优值只有吗<gydF4y2Basvg height="14.52pt" id="M138" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>最小化,<gydF4y2Basvg height="14.52pt" id="M139" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 14.1518 14.52" width="14.1518pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-104"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.71,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.37,3.944)"> <use xlink:href="#g50-51"></use> </g> </svg>最优值只有吗<gydF4y2Basvg height="13.2498pt" id="M140" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 36.892 13.2498" width="36.892pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.987,0)"> <use xlink:href="#g113-42"></use> </g> </svg>是最小化。同样的,<gydF4y2Bai>g</gydF4y2Bai><sub>1<gydF4y2Bai>w</gydF4y2Bai></sub>的值是<gydF4y2Basvg height="14.52pt" id="M141" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>当只有<gydF4y2Basvg height="13.2498pt" id="M142" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 36.892 13.2498" width="36.892pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.987,0)"> <use xlink:href="#g113-42"></use> </g> </svg>最小化,<gydF4y2Bai>g</gydF4y2Bai><sub>2<gydF4y2Bai>w</gydF4y2Bai></sub>的值是<gydF4y2Basvg height="13.2498pt" id="M143" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 36.892 13.2498" width="36.892pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,31.987,0)"> <use xlink:href="#g113-42"></use> </g> </svg>当只有<gydF4y2Basvg height="14.52pt" id="M144" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>是最小化。我们应用<gydF4y2Basvg height="9.63795pt" id="M145" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 14.2742 9.63795" width="14.2742pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-223"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.357,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.012,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>当获得解决<gydF4y2Basvg height="9.04777pt" id="M146" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M147" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>由凝结)。因此,解决之前<gydF4y2Basvg height="13.2498pt" id="M148" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 49.5055 13.2498" width="49.5055pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,32.442,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,39.446,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,44.58,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,我们应该解决<gydF4y2Basvg height="13.2498pt" id="M149" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M150" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>分别;所有这些问题的全球解决方案可以使用一般的NLP解决计算方法等<gydF4y2Bai>内点方法</gydF4y2Bai>(<gydF4y2Baa href="#B25">36</gydF4y2Baa>]。</gydF4y2Bap> <h5 id="sec4.3">4.3。舍入算法</gydF4y2Bah5> <p>不管凸性和线性整数约束的问题一般很难解决。在本文中,我们使用一个简单的舍入方法介绍(<gydF4y2Baa href="#B22">34</gydF4y2Baa>)寻找近似整数解<gydF4y2Basvg height="9.04777pt" id="M151" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M152" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,<gydF4y2Basvg height="13.2498pt" id="M153" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>)。我们也使用舍入方法找到的整数解<gydF4y2Basvg height="13.2498pt" id="M154" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M155" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>为目的的评估。舍入方法的算法作为算法<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/alg2/" target="_blank">2</gydF4y2Baa>。</gydF4y2Bap> <p></p> <div class="floats-partial-section partial-other-wrapper" data-section="alg2"> <div class="floats-partial-content fig-content-alg2"> <table> <tbody> <tr> <td> <table class="algorithm" id="alg2"> <tbody> <tr> <td colspan="2"><i>步骤1。best_sol</gydF4y2Bai>:= 0;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>old_sol</gydF4y2Bai>:= 0;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i> <svg height="13.0595pt" id="M156" style="vertical-align:-3.36801pt" version="1.1" viewbox="-0.0498162 -9.69149 8.327 13.0595" width="8.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M584 573C584 646 528 703 441 703C387 703 327 679 274 632C202 568 166 493 132 302L57 -122C43 -201 35 -214 21 -227L25 -246C54 -244 122 -236 156 -203C168 -191 175 -162 195 -40L261 369C291 556 318 652 391 652C431 652 465 620 465 543C465 497 449 456 408 422C395 411 364 405 340 403L309 336C386 319 447 279 447 188C447 105 419 50 329 50C290 50 253 63 226 77L216 55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z" id="g5-224"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="605" 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-24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,12.234,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,14.89,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data> </g> </svg>:<gydF4y2Basvg height="9.65971pt" id="M158" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 35.9963 9.65971" width="35.9963pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M563 650H502L416 416H157L71 650H10L256 -15H317L563 650ZM397 366L287 68H286L176 366H397Z" id="g117-46"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="573" vert-adv-y="573"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,7.763,0)"> <path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,15.247,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,26.186,0)"> <path d="M697 650H468L461 623L492 619C539 613 547 605 518 546C481 471 367 264 278 116H276C239 278 197 500 186 567C180 604 185 613 226 619L252 623L260 650H24L17 623C78 617 92 613 108 533L216 -11H247C365 200 515 462 560 529C616 612 624 615 689 623L697 650Z" id="g113-87"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="709" vert-adv-y="709"></glyph.data> </g> </svg>和<gydF4y2Basvg height="12.0395pt" id="M159" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 38.8793 12.0395" width="38.8793pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M563 650H502L416 416H157L71 650H10L256 -15H317L563 650ZM397 366L287 68H286L176 366H397Z" id="g117-46"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="573" vert-adv-y="573"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,7.763,0)"> <path d="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z" id="g113-116"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="375" vert-adv-y="375"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,16.629,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" vert-adv-y="528"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,27.567,0)"> <path d="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z" id="g113-84"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="472" vert-adv-y="472"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,33.962,0)"> <path d="M283 255V284C195 290 192 337 192 375C192 436 200 508 200 580C200 696 116 709 54 709V681C127 671 139 634 139 588C138 524 125 452 125 387C125 333 149 286 209 272V268C148 253 125 206 125 151C126 87 139 16 139 -47C139 -92 127 -131 54 -141V-169C115 -169 200 -152 200 -41C200 32 192 104 192 164C192 202 195 249 283 255Z" id="g113-126"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="347" vert-adv-y="347"></glyph.data> </g> </svg>;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i> <svg height="9.68693pt" id="M160" style="vertical-align:-3.36797pt" version="1.1" viewbox="-0.0498162 -6.31896 7.1575 9.68693" width="7.1575pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g 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</svg>:<gydF4y2Basvg height="9.65971pt" id="M162" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 35.9963 9.65971" width="35.9963pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M563 650H502L416 416H157L71 650H10L256 -15H317L563 650ZM397 366L287 68H286L176 366H397Z" id="g117-46"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="573" vert-adv-y="573"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,7.763,0)"> <path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data> </g> 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</svg>;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤3。 </gydF4y2Bai><b>为每一个</gydF4y2Bab> <svg height="13.2634pt" id="M166" style="vertical-align:-3.57191pt" version="1.1" viewbox="-0.0498162 -9.69149 41.9707 13.2634" width="41.9707pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data> </g> <g 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horiz-adv-x="605" vert-adv-y="605"></glyph.data> </g> </svg><b>开始</gydF4y2Bab></td> </tr> <tr> <td colspan="2"><i></i><b>如果</gydF4y2Bab> <svg height="15.1401pt" id="M167" style="vertical-align:-4.1023pt" version="1.1" viewbox="-0.0498162 -11.0378 115.654 15.1401" width="115.654pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,2.07113e-005)"> <path d="M332 -241C217 -138 149 60 149 271C149 483 216 680 332 783L312 808C148 686 74 491 74 272V271C74 50 148 -146 312 -266L332 -241Z" id="g119-5"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="385" vert-adv-y="385"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,5.236,-6.949)"> <path d="M162 0V316H101V0H162Z" id="g119-34"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,5.236,-3.196)"> <path d="M162 0V316H101V0H162Z" id="g119-34"></path> <glyph.data 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="559" vert-adv-y="559"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.506,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 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60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,12.138,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg>,</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>int_sol</gydF4y2Bai>:=<gydF4y2Basvg height="13.2498pt" id="M182" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 71.8647 13.2498" width="71.8647pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,11.8,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,18.804,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,23.423,3.264)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,31.84,0)"> <path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z" id="g117-36"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="587" vert-adv-y="587"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,42.821,0)"> <path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,49.486,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,54.62,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,61.625,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,66.244,3.264)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512"></glyph.data> </g> </svg></td> </tr> <tr> <td colspan="2"><i></i>在哪里<gydF4y2Basvg height="13.2498pt" id="M183" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 17.1382 13.2498" width="17.1382pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,11.623,3.264)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512"></glyph.data> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M184" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 17.1382 13.2498" width="17.1382pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,11.623,3.264)"> <path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z" id="g50-111"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="512" vert-adv-y="512"></glyph.data> </g> </svg>是归一化<gydF4y2Basvg height="13.2498pt" id="M185" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M186" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg>分别计算(<gydF4y2Baa href="#EEq17">16</gydF4y2Baa>)。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤6。 </gydF4y2Bai><b>如果</gydF4y2Bab>(<gydF4y2Bai>int_sol</gydF4y2Bai>><gydF4y2Bai>best_sol</gydF4y2Bai>)</gydF4y2Batd> </tr> <tr> <td colspan="2"><i><i></i>best_sol</gydF4y2Bai>:=<gydF4y2Bai>int_sol</gydF4y2Bai>;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i>步骤7。 </gydF4y2Bai><b>为每一个</gydF4y2Bab> <svg height="13.2634pt" id="M187" style="vertical-align:-3.57191pt" version="1.1" viewbox="-0.0498162 -9.69149 37.4287 13.2634" width="37.4287pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.533,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,10.188,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 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55C218 23 252 -16 286 -16C324 -16 369 3 419 31C488 69 575 149 575 238C575 325 516 369 437 400C516 443 584 486 584 573Z" id="g5-224"></path> <glyph.data ascent="3481" descent="-2878" horiz-adv-x="605" vert-adv-y="605"></glyph.data> </g> </svg><b>开始</gydF4y2Bab></td> </tr> <tr> <td colspan="2"><i></i><b>如果</gydF4y2Bab> <svg height="13.1057pt" id="M188" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 45.9144 13.1057" width="45.9144pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z" id="g113-224"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="581" vert-adv-y="581"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.533,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,10.188,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data> </g> </svg>作为一个参数下舍入迭代。</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i><b>结束</gydF4y2Bab></td> </tr> <tr> <td colspan="2"><i>步骤8。 </gydF4y2Bai><b>如果</gydF4y2Bab>(<gydF4y2Basvg height="12.1687pt" id="M193" 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36C231 31 219 30 207 30C147 30 111 78 111 154C111 302 180 380 220 399C231 404 246 407 264 407C311 407 355 367 355 280Z" id="g113-112"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="468" vert-adv-y="468"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,87.036,0)"> <path d="M238 681C243 705 239 712 230 712C217 712 156 682 75 674L70 648H105C148 648 153 641 144 598L39 110C18 11 35 -12 55 -12C90 -12 166 36 221 103L205 125C174 93 130 65 118 65C112 65 108 68 114 96L238 681Z" id="g113-109"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="269" vert-adv-y="269"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,90.682,.252)"> <path d="M162 -163V703H101V-163H162Z" id="g113-9"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="263" vert-adv-y="263"></glyph.data> </g> </svg><<gydF4y2Basvg height="6.42315pt" id="M194" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 5.67521 6.42315" width="5.67521pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data> </g> </svg>)</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i><b>终止算法</gydF4y2Bab>;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i><b>其他的</gydF4y2Bab></td> </tr> <tr> <td colspan="2"><i>old_sol</gydF4y2Bai>:=<gydF4y2Bai>int_sol</gydF4y2Bai>;</gydF4y2Batd> </tr> <tr> <td colspan="2"><i></i><b>转到步骤</gydF4y2Bab> <svg height="8.65339pt" id="M195" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.60357 6.89913 8.65339" width="6.89913pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M440 175C403 110 395 108 335 108H173L293 222C391 316 432 379 432 457C432 568 349 635 250 635C187 635 137 610 100 573L36 479L65 456C97 502 138 544 199 544C268 544 303 495 303 425C303 349 264 274 194 191C145 133 86 78 33 26V0H434C445 42 457 105 473 164L440 175Z" id="g13-48"></path> <glyph.data ascent="1024" descent="-360" horiz-adv-x="500" vert-adv-y="500"></glyph.data> </g> </svg>;</gydF4y2Batd> </tr> </tbody> </table></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">算法2</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/alg2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 舍入算法。</gydF4y2Badiv> </div> </div> <p></p> <p>在步骤2中,我们首先解决NLP轻松convexified问题。在步骤3中,舍入和舍入距离执行<gydF4y2Basvg height="12.7195pt" id="M196" style="vertical-align:-2.6064pt" version="1.1" viewbox="-0.0498162 -10.1131 6.19196 12.7195" width="6.19196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path> </g> </svg>之间的距离<gydF4y2Basvg height="9.63795pt" id="M197" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 14.4238 9.63795" width="14.4238pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.506,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,10.161,3.264)"> <use xlink:href="#g50-116"></use> </g> </svg>和它最近的整数。然后用圆形的可行性检查解决方案在步骤3中。如果全面解决方案不可行,我们减少舍入的距离<gydF4y2Basvg height="12.7195pt" id="M198" style="vertical-align:-2.6064pt" version="1.1" viewbox="-0.0498162 -10.1131 6.19196 12.7195" width="6.19196pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-236"></use> </g> </svg>(即。,the rounding condition is made stricter) and perform the rounding and feasibility check again. Otherwise, in Step 5, we compute integer solutions using the original objective functions for the problem<svg height="13.2498pt" id="M199" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M200" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,对于这个问题<gydF4y2Basvg height="13.2498pt" id="M201" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 27.264 13.2498" width="27.264pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,<gydF4y2Basvg height="13.2498pt" id="M202" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 16.9696 13.2498" width="16.9696pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,12.138,0)"> <use xlink:href="#g113-42"></use> </g> </svg>计算的加权求和,我们两个标准化客观值从一个单值度量需要进一步确定迭代是否应该继续。在步骤6中,我们最好的解决方案,直到当前迭代更新和修复的解决方案作为参数为下一次迭代步骤7。最后,如果我们得出这样的结论:整数解聚合在一定水平,我们终止舍入算法。</gydF4y2Bap> <p>虽然舍入算法非常有效,易于实现,它经常产生不可行的解决方案。让事情更糟的是,它是极难适应全面解决方案的约束。但是我们注意到,它适用于我们的问题,因为所有的目标函数和约束涉及指数函数,这意味着NLP解决者倾向于产生平分成非常小的或大的变量值以寻求最大(或最小)的结果。为了说明这一现象,我们选择了一个小型的感应器拓扑5传感器均匀分布在一个20 m×20平方20空闲频谱并承担单位。我们计算NLP轻松解决的所有问题,并把它们在图<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig1/" target="_blank">1</gydF4y2Baa>这个问题,在哪里<gydF4y2Basvg height="13.2498pt" id="M203" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>,凝聚算法的输出是策划。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig1"> <div class="floats-partial-content fig-content-fig1"> <div class="partial-carousel--single-image"> <img alt="(一)”name="406462.fig.001a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001a.jpg"> <br> <strong>(一)</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(b)”name="406462.fig.001b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001b.jpg"> <br> <strong>(b)</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(c)”name="406462.fig.001c" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001c.jpg"> <br> <strong>(c)</gydF4y2Bastrong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig1"> <button class="partial-carousel-dot" aria-label="(a) For"><img alt="(一)”name="406462.fig.001a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001a.jpg"><br><strong>(一)</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(b) For"><img alt="(b)”name="406462.fig.001b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001b.jpg"><br><strong>(b)</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(c) For"><img alt="(c)”name="406462.fig.001c" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.001c.jpg"><br><strong>(c)</gydF4y2Bastrong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig1"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="9.63795pt" id="M204" style="vertical-align:-3.42779pt" version="1.1" viewbox="-0.0498162 -6.21016 14.4238 9.63795" width="14.4238pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M536 404C536 423 520 448 491 448C445 448 398 404 308 283L286 338C255 416 242 448 217 448C182 448 138 402 92 341L111 321C149 368 169 378 178 378C188 378 198 363 214 320L254 212C185 117 138 65 107 65C98 65 85 69 82 75C79 82 73 86 65 86C44 86 23 60 23 39C23 7 44 -12 71 -12C119 -12 168 33 265 177L306 61C321 17 347 -12 373 -12C413 -12 465 33 507 96L491 119C459 84 432 60 413 60C395 60 378 92 358 148L321 250C341 279 369 310 389 332C417 363 439 382 456 382C466 382 475 376 481 368C486 361 492 358 496 358C513 358 536 381 536 404Z" id="g113-121"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="559" vert-adv-y="559"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.506,3.264)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,10.161,3.264)"> <path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data> </g> </svg> <svg height="9.65971pt" id="M205" style="vertical-align:-0.6617603pt" version="1.1" viewbox="-0.0498162 -8.99795 28.2041 9.65971" width="28.2041pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M244 607C244 633 228 655 200 655C166 655 146 618 146 594C146 564 166 546 191 546C221 546 244 574 244 607ZM222 91L209 114C184 94 148 66 133 66C127 66 124 73 130 96L201 370C213 416 211 448 191 448C162 448 88 407 29 352L42 328C73 354 104 371 114 371C120 371 119 365 115 345L53 92C32 5 45 -12 68 -12C103 -12 186 50 222 91Z" id="g113-106"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="273" vert-adv-y="273"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,7.484,0)"> <path d="M448 1V51H364C248 51 153 129 140 230H448V280H140C153 381 248 459 364 459H448V509H365C208 509 80 395 80 255S208 1 365 1H448Z" id="g117-173"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="528" 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-147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg> <table> NLP轻松解决方案的变量gydF4y2Ba对所有gydF4y2Ba和,gydF4y2Ba因为gydF4y2Ba。我们把冷凝后的解决方案。</gydF4y2Batable> </div> </div> </div> <p>如图<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig1/" target="_blank">1</gydF4y2Baa>,我们观察到一些变量是非常接近1,其中一些是1,而其他一些变量相对很小。因此,我们很容易将这些一分为二的变量参数化在第一排,使下舍入开始减少的一组变量。另外,我们观察到的变量收敛于可行的整数解几舍入迭代。在下一节中我们将展示这个结果。</gydF4y2Bap> <h4 id="numerical-experiments">5。数值实验</gydF4y2Bah4> <p>实验中,我们考虑一个传感器100 m×100 m的矩形区域15传感器均匀分布,假设所有传感器传输请求。我们随机生成每个传感器的传播目标,这可能会导致一对多或多对一的通讯以及一对一的。表中列出的其他主要实验参数<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/tab1/" target="_blank">1</gydF4y2Baa>。我们使用通道获得建模为<gydF4y2Basvg height="18.533pt" 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style="vertical-align:-5.759999pt" version="1.1" viewbox="-0.0498162 -9.6779 13.3522 15.4379" width="13.3522pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.626,3.264)"> <use xlink:href="#g50-107"></use> </g> </svg>是随机的高斯变量与零均值和标准差等于6 dB,<gydF4y2Basvg height="12.4257pt" id="M213" style="vertical-align:-3.427751pt" version="1.1" viewbox="-0.0498162 -8.99795 14.8889 12.4257" width="14.8889pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-76"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,9.619,3.264)"> <use xlink:href="#g50-49"></use> </g> </svg>= 10<gydF4y2Basup>3</gydF4y2Basup>捕获系统和传播效果,如天线增益和载波频率<gydF4y2Basvg height="15.4379pt" id="M214" style="vertical-align:-5.759999pt" version="1.1" viewbox="-0.0498162 -9.6779 14.1409 15.4379" width="14.1409pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.452,3.264)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,9.412,3.264)"> <use xlink:href="#g50-107"></use> </g> </svg>传感器之间的距离吗<gydF4y2Basvg height="9.21094pt" id="M215" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 3.81214 9.21094" width="3.81214pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-106"></use> </g> </svg>和<gydF4y2Basvg height="12.5699pt" id="M216" style="vertical-align:-3.57195pt" version="1.1" viewbox="-0.0498162 -8.99795 5.85199 12.5699" width="5.85199pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-107"></use> </g> </svg>,<gydF4y2Basvg height="6.42315pt" id="M217" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 6.62713 6.42315" width="6.62713pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M457 332C457 400 429 448 397 448C384 448 371 441 365 435L366 428C376 413 388 372 388 315C388 152 306 45 220 45C166 45 134 85 158 180L197 332C204 361 207 385 207 402C207 434 196 448 174 448C125 448 66 406 23 342L43 319C84 368 110 383 121 383C130 383 129 374 122 343L76 156C71 137 69 120 69 105C69 25 125 -12 181 -12C314 -12 457 166 457 332Z" id="g113-242"></path> </g> </svg>是功率下降的因素。我们让<gydF4y2Basvg height="8.91176pt" id="M218" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -8.69876 28.7073 8.91176" width="28.7073pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-242"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.289,0)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,22.027,0)"> <use xlink:href="#g113-52"></use> </g> </svg>。我们使用IPOPT实现C语言中的所有实验代码(<gydF4y2Baa href="#B25">36</gydF4y2Baa>)库,实现了NLP与内点方法求解。说明,凝聚算法产生聚合NLP问题的解决方案<gydF4y2Basvg height="13.2498pt" id="M219" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>我们测量的函数值,<gydF4y2Basvg height="14.52pt" id="M220" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>定义在(<gydF4y2Baa href="#EEq15">14</gydF4y2Baa>)——冷凝过程的每个迭代和人物<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig2/" target="_blank">2</gydF4y2Baa>显示测量结果。如图表所示,我们可以观察到的函数值<gydF4y2Basvg height="14.52pt" id="M221" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <use xlink:href="#g185-40"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <use xlink:href="#g113-42"></use> </g> </svg>收敛于一个固定值作为冷凝所得。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-content fig-content-tab1"> <table class="table-group" id="tab1"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="2"> <hr></td> </tr> <tr class="thead"> <td align="left">实验参数</gydF4y2Batd> <td align="center">价值</gydF4y2Batd> </tr> <tr> <td class="thead-hr" colspan="2"> <hr></td> </tr> <tr> <td align="left">数量的传感器<gydF4y2Basvg height="12.0395pt" id="M222" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.3368 12.0395" width="16.3368pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z" id="g113-111"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="502" vert-adv-y="502"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,11.489,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> <td align="center">15</gydF4y2Batd> </tr> <tr> <td align="left">数量的空闲频谱的单位</gydF4y2Batd> <td align="center">60</gydF4y2Batd> </tr> <tr> <td align="left">重量<gydF4y2Basvg height="13.1057pt" id="M223" style="vertical-align:-3.427799pt" version="1.1" viewbox="-0.0498162 -9.6779 22.0161 13.1057" width="22.0161pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M689 332C689 394 670 448 646 448C620 448 597 421 597 396C597 386 600 381 608 372C619 359 620 334 620 315C620 150 538 45 454 45C414 45 386 67 386 122C386 138 388 158 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vert-adv-y="280"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,17.159,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> <td align="center">分配一个1到20之间的均匀随机变量在每个传感器</gydF4y2Batd> </tr> <tr> <td align="left"><span style="width: 26.5418ptpx;"> <svg height="12.4067pt" id="M224" style="vertical-align:-3.408751pt" version="1.1" viewbox="-0.0498162 -8.99795 26.5418 12.4067" width="26.5418pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path> 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vert-adv-y="487"></glyph.data> </g> </svg></span></td> <td align="center">10<gydF4y2Basup>−10</gydF4y2Basup>W</gydF4y2Batd> </tr> <tr> <td align="left"><span style="width: 25.7612ptpx;"> <svg height="14.4105pt" id="M226" style="vertical-align:-4.1078pt" version="1.1" viewbox="-0.0498162 -10.3027 25.7612 14.4105" width="25.7612pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="617" vert-adv-y="617"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,8.365,-5.984)"> <path d="M810 0V30C751 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vert-adv-y="481"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,3.944)"> <path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data> </g> </svg></span></td> <td align="center">−10 dB</gydF4y2Batd> </tr> <tr> <td align="left">凝聚算法终止条件<gydF4y2Basvg height="6.42315pt" id="M229" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 8.77576 6.42315" width="8.77576pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M615 290C615 392 563 448 529 448C511 448 491 441 484 434L483 425C518 400 546 349 546 273C546 158 504 46 417 46C381 46 356 77 356 142C356 184 380 293 392 334L387 340L307 323C305 288 296 228 287 188C265 94 221 52 180 52C144 52 112 89 112 171C112 278 164 372 241 430L226 454C106 394 23 288 23 155C23 40 79 -12 139 -12C184 -12 245 32 285 85C292 31 322 -12 376 -12C423 -12 470 18 501 45C570 104 615 184 615 290Z" id="g113-246"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="638" vert-adv-y="638"></glyph.data> </g> </svg></td> <td align="center">0.1</gydF4y2Batd> </tr> <tr> <td align="left">最初的舍入的距离<gydF4y2Basvg height="12.7195pt" id="M230" style="vertical-align:-2.6064pt" version="1.1" viewbox="-0.0498162 -10.1131 15.6024 12.7195" width="15.6024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="448" vert-adv-y="448"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.758,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> <td align="center">0.9999</gydF4y2Batd> </tr> <tr> <td align="left">舍入距离衰减<gydF4y2Basvg height="12.7195pt" id="M231" style="vertical-align:-2.6064pt" version="1.1" viewbox="-0.0498162 -10.1131 15.6024 12.7195" width="15.6024pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <path d="M425 682C425 693 422 699 407 699C369 699 308 677 260 646C213 651 191 674 191 701C191 715 195 726 200 734L183 740C153 730 118 709 118 681C118 644 163 619 218 615C168 582 115 534 115 463C115 418 147 382 180 369C102 329 23 261 23 163C23 74 74 38 158 14C183 7 201 2 221 -2C279 -15 290 -33 290 -58C290 -94 251 -145 230 -169L252 -189C280 -171 367 -103 367 -25C367 20 333 51 266 68C245 73 218 80 191 89C139 106 107 135 107 192C107 261 161 329 221 355C248 350 281 347 314 347C330 347 370 388 370 406C370 418 366 422 352 422C321 422 280 413 255 407C218 413 192 448 192 493C192 544 229 588 266 610C309 610 354 615 376 623C397 631 425 651 425 682Z" id="g113-236"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="448" vert-adv-y="448"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.758,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> <td align="center">0.0001</gydF4y2Batd> </tr> <tr> <td align="left">舍入算法终止条件<gydF4y2Basvg 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<glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.244,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> <td align="center">10<gydF4y2Basup>−8</gydF4y2Basup>为<gydF4y2Basvg height="13.2498pt" id="M233" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="757" vert-adv-y="757"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M234" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 27.264 13.2498" width="27.264pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="757" vert-adv-y="757"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg>,<gydF4y2Basvg height="13.2498pt" id="M235" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 16.9696 13.2498" width="16.9696pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,12.138,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg>和0<gydF4y2Basvg height="13.2498pt" id="M236" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M719 146L691 147C666 77 657 72 612 72H528C572 125 688 224 688 364C688 546 558 665 384 665C212 665 77 541 77 361C77 221 188 124 239 72H150C110 72 97 80 73 147L46 146L63 0H307L314 18C284 71 178 203 178 360C178 529 256 631 383 631C509 631 588 523 588 363C588 197 485 67 453 18L458 0H701L719 146Z" id="g113-153"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="757" vert-adv-y="757"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg></td> </tr> <tr class="table-tr"> <td colspan="2"> <hr class="tbody-hr"></td> </tr> </tbody> </table></td> </tr> <tr class="table-fn"> <td> <svg height="12.4067pt" id="M237" style="vertical-align:-3.408751pt" version="1.1" viewbox="-0.0498162 -8.99795 26.5418 12.4067" width="26.5418pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M541 160L512 170C485 116 462 88 439 67C411 41 376 35 318 35C272 35 238 37 224 48C207 61 205 85 212 121L290 533C305 611 308 615 391 622L397 650H139L133 622C217 615 221 612 206 533L126 118C111 41 103 34 23 26L17 0H474C489 31 528 124 541 160Z" id="g113-77"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="553" vert-adv-y="553"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,8.644,3.264)"> <path d="M513 0V26C455 31 447 37 447 103V278C447 398 390 449 309 449C255 449 202 412 166 376V712C127 700 67 684 19 677V653C85 647 87 643 87 580V103C87 37 79 31 19 26L18 0H231V26C171 32 166 39 166 103V341C194 373 232 392 270 392C337 392 368 351 368 269V103C368 38 360 32 302 26V0H513Z" id="g190-105"></path> <glyph.data ascent="989" descent="-360" horiz-adv-x="534" vert-adv-y="534"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,13.67,3.264)"> <path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z" id="g190-112"></path> <glyph.data ascent="989" descent="-360" horiz-adv-x="510" vert-adv-y="510"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,18.44,3.264)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g190-109"></path> <glyph.data ascent="989" descent="-360" horiz-adv-x="253" vert-adv-y="253"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,20.839,3.264)"> <path d="M517 51L485 54C448 58 441 63 441 115V712C404 700 337 684 285 678V653C357 648 362 645 362 580V437C339 446 309 449 295 449C159 449 38 340 38 201C38 61 143 -12 223 -12C234 -12 261 -6 301 17L362 53V-12C420 9 495 22 517 26V51ZM362 85C338 67 301 51 266 51C201 51 128 109 128 228C128 373 212 411 259 411C296 411 338 395 362 360V85Z" id="g190-101"></path> <glyph.data ascent="989" descent="-360" horiz-adv-x="528" vert-adv-y="528"></glyph.data> </g> </svg>:概率,每个传感器持有谱单元在其之前的传播阶段。<gydF4y2Babr></td> </tr> </tbody> </table> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 主要实验参数。</gydF4y2Badiv> </div> </div> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig2"> <div class="floats-partial-content fig-content-fig2"> <div class="partial-carousel--single-image"> <img alt="" name="406462.fig.002" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.002.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="14.52pt" id="M238" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 39.7723 14.52" width="39.7723pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 -16 489 2 522 10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data> </g> <g transform="matrix(.0136,0,0,-0.0136,9.05,0)"> <path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path> <glyph.data ascent="712" descent="-215" horiz-adv-x="447" vert-adv-y="447"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,15.161,0)"> <path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,19.848,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,28.553,-5.984)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,26.853,3.944)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,34.867,0)"> <path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="346" vert-adv-y="346"></glyph.data> </g> </svg> <table> 函数值的转换gydF4y2Ba冷凝所得。</gydF4y2Batable> </div> </div> </div> <p>表<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/tab2/" target="_blank">2</gydF4y2Baa>列出了所需要的舍入迭代数到达给定的终止条件<gydF4y2Basvg height="12.2911pt" id="M239" style="vertical-align:-0.2129993pt" version="1.1" viewbox="-0.0498162 -12.0781 45.2331 12.2911" width="45.2331pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 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407C406 428 417 458 417 487C417 568 348 635 253 635ZM240 600C288 600 340 563 340 481C340 423 313 387 279 360C207 394 148 427 148 499C148 549 182 600 240 600ZM252 23C188 23 129 73 129 163C129 217 162 266 211 298C289 260 360 217 360 144C360 69 312 23 252 23Z" id="g50-57"></path> </g> </svg>。可以看出舍入算法收敛于几个迭代终止条件通常除了问题的情况下<gydF4y2Basvg height="13.2498pt" id="M240" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 31.9692 13.2498" width="31.9692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,10.256,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.944,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,21.948,3.264)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.082,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</gydF4y2Bap> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-content fig-content-tab2"> <table class="table-group" id="tab2"> <tbody> <tr> <td> <table class="table"> <tbody> <tr> <td class="thead-hr" colspan="2"> <hr></td> </tr> <tr class="thead"> <td align="left">问题</gydF4y2Batd> <td align="center"><span style="width: 40.1168ptpx;"> <svg height="9.21094pt" id="M242" style="vertical-align:-0.2129908pt" version="1.1" viewbox="-0.0498162 -8.99795 40.1168 9.21094" width="40.1168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M822 650H589L583 622C660 617 677 607 674 561C672 534 664 481 647 390L600 137H596L273 650H126L120 622C176 620 194 615 207 594C221 571 225 557 214 504L161 257C141 166 129 112 121 85C108 42 83 30 29 28L23 0H260L266 28C193 33 173 42 176 89C178 122 186 172 202 255L256 527H259L583 -8H612L690 390C708 481 720 535 728 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>和<gydF4y2Basvg height="12.9915pt" id="M267" style="vertical-align:-3.3136pt" version="1.1" viewbox="-0.0498162 -9.6779 11.9243 12.9915" width="11.9243pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>。结果绘制在图<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig3/" target="_blank">3</gydF4y2Baa>;我们执行这个评价60个不同的随机渠道满足95%最大允许误差为0.1 dB和情节的平均价值在这些样品。的标签<gydF4y2Basvg height="9.04777pt" id="M268" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.5029 9.04777" width="10.5029pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z" id="g113-89"></path> </g> </svg>设在每个图对应的重量在每个目标函数;从左到右,而<gydF4y2Basvg height="12.9915pt" id="M269" style="vertical-align:-3.3136pt" version="1.1" viewbox="-0.0498162 -9.6779 11.9243 12.9915" width="11.9243pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>的增加,<gydF4y2Basvg height="12.9915pt" id="M270" style="vertical-align:-3.3136pt" version="1.1" viewbox="-0.0498162 -9.6779 11.9243 12.9915" width="11.9243pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-226"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,6.666,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>减少。在传说中,“INT-f1”和“INT-f2”相关的整数对应的目标函数的最优值由数值方法和舍入算法;“NLP-f1”和“NLP-f2”对应NLP轻松获得相应的目标函数的最优值后的数值。此外,传说中“*”的项目对应于单一目标的解决方案。在这个图中,我们绘制NLP放松和整数解使用原目标函数,<gydF4y2Basvg height="13.2498pt" id="M271" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M272" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>在(<gydF4y2Baa href="#EEq2">2</gydF4y2Baa>)和(<gydF4y2Baa href="#EEq2">3</gydF4y2Baa>),分别。非凡的结果如下:(i)的NLP轻松的解决方案和整数解<gydF4y2Basvg height="13.2498pt" id="M273" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>和<gydF4y2Basvg height="13.2498pt" id="M274" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>在<gydF4y2Basvg height="9.04777pt" id="M275" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.3941 9.04777" width="10.3941pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-153"></use> </g> </svg>(<gydF4y2Basvg height="13.2498pt" id="M276" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,<gydF4y2Basvg height="13.2498pt" id="M277" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>)显然是与各自的重量成正比;(ii)的解决方案由数值方法是严格限制的单目标的解决方案;(3)整数解非常接近NLP轻松解决方案的因素都小于2的目标函数<gydF4y2Baa href="#B31">14</gydF4y2Baa>]。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig3"> <div class="floats-partial-content fig-content-fig3"> <div class="partial-carousel--single-image"> <img alt="(一)评价”name="406462.fig.003a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.003a.jpg"> <br> <strong>(一)评价</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(b)的评估”name="406462.fig.003b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.003b.jpg"> <br> <strong>(b)的评估</gydF4y2Bastrong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig3"> <button class="partial-carousel-dot" aria-label="(a) Evaluation of"><img alt="(一)评价”name="406462.fig.003a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.003a.jpg"><br><strong>(一)评价</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(b) Evaluation of"><img alt="(b)的评估”name="406462.fig.003b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.003b.jpg"><br><strong>(b)的评估</gydF4y2Bastrong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig3"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.2498pt" id="M278" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg> <svg height="13.2498pt" id="M279" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg> <svg height="9.04777pt" id="M280" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.99795 10.5029 9.04777" width="10.5029pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z" id="g113-89"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="765" vert-adv-y="765"></glyph.data> </g> </svg> <svg height="12.9915pt" id="M281" style="vertical-align:-3.3136pt" version="1.1" viewbox="-0.0498162 -9.6779 40.3534 12.9915" width="40.3534pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M360 -163L167 270L360 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descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,17.395,0)"> <path d="M95 130C70 130 46 113 46 88C46 72 54 64 59 64C93 55 121 33 121 -3C121 -41 93 -68 44 -88L55 -117C117 -98 186 -56 186 22C186 91 131 130 95 130Z" id="g113-45"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="228" vert-adv-y="228"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,22.755,0)"> <path d="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,29.421,3.264)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> <g transform="matrix(.0135,0,0,-0.0135,34.555,0)"> <path d="M307 267V273L115 703H53L246 270L53 -163H115L307 267Z" id="g113-63"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="413" vert-adv-y="413"></glyph.data> </g> </svg> <table> 评价gydF4y2Ba和gydF4y2Ba通过数值方法。的标签gydF4y2Ba设在每个图对应的重量在每个目标函数,gydF4y2Ba。舍入算法获得的整数解也评估通过比较他们NLP轻松的解决方案。</gydF4y2Batable> </div> </div> </div> <p>接下来我们衡量公平分配频谱资源。为了展示这一点,我们计算<gydF4y2Bai>公平指数</gydF4y2Bai>使用(<gydF4y2Baa href="#EEq26">21</gydF4y2Baa>它在图)和阴谋<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig4/" target="_blank">4</gydF4y2Baa>。公平指数被广泛使用公制测量水平的公平。接近于1,分配是公平的。我们还阴谋频谱利用率使用(<gydF4y2Baa href="#EEq26">22</gydF4y2Baa>)为了显示频谱资源利用。我们小区的平均结果超过60个不同的随机频道:<gydF4y2Baspan class="equation" id="EEq26"><span class="left"> <svg class="labelnn" height="82.979pt" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -82.9292 22.031 82.979" width="22.031pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"></svg></span><span class="middle" xmlns:xlink="http://www.w3.org/1999/xlink"> <svg class="contentdisp" height="82.979pt" id="M284" preserveaspectratio="xMaxYMin" version="1.1" viewbox="0 -82.9292 164.178 82.979" width="164.178pt" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(.0135,0,0,-0.0135,0,-59.291)"> <path d="M493 503C489 551 484 614 483 650H43V622C120 616 128 611 128 525V126C128 40 120 34 40 28V0H312V28C221 34 213 40 213 126V307H316C407 307 412 296 424 227H453V420H424C412 355 407 346 316 346H213V584C213 613 216 616 246 616H322C398 616 419 607 436 579C449 559 455 539 464 499L493 503Z" id="g190-71"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,7.17,-59.291)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.62,-59.291)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,33.46,-69.226)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,38.69,-69.219)"> <use xlink:href="#g119-65"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,48.89,-65.614)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,51.55,-65.614)"> <use xlink:href="#g54-173"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,57.04,-65.614)"> <use xlink:href="#g50-87"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,66.67,-69.226)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,71.91,-69.226)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,77.14,-69.219)"> <use 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transform="matrix(.0135,0,0,-0.0135,0,-12.4)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.69,-12.4)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.06,-12.4)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,17.35,-12.4)"> <use xlink:href="#g190-42"></use> </g> </svg></span></span>在哪里<gydF4y2Basvg height="6.42315pt" id="M285" style="vertical-align:-0.2129903pt" version="1.1" viewbox="-0.0498162 -6.21016 6.92631 6.42315" width="6.92631pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-111"></use> </g> </svg>是传感器的数量。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig4"> <div class="floats-partial-content fig-content-fig4"> <div class="partial-carousel--single-image"> <img alt="" name="406462.fig.004" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.004.jpg"> <br> <strong></strong> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> 根据权重公平指数和频谱利用率。</gydF4y2Batable> </div> </div> </div> <p>图<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig4/" target="_blank">4</gydF4y2Baa>表明,随着体重<gydF4y2Basvg height="13.2498pt" id="M286" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>增加,还公平指数增加。可以看出公平指数是最高的了<gydF4y2Basvg height="11.9171pt" id="M287" style="vertical-align:-2.2392pt" version="1.1" viewbox="-0.0498162 -9.6779 49.0151 11.9171" width="49.0151pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-61"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,5.595,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,12.098,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,15.188,0)"> <path d="M153 550H386L412 615L406 623H120L82 318C104 327 142 338 184 338C294 338 347 275 347 187C347 112 305 39 221 39C160 39 119 71 97 89C88 97 80 96 71 90C59 80 50 67 49 57C48 45 52 36 66 23C80 9 123 -12 169 -12C221 -11 288 15 342 59C403 109 431 165 431 225C431 308 366 395 238 395C212 395 165 379 127 364L153 550Z" id="g113-54"></path> </g> <g transform="matrix(.0135,0,0,-0.0135,21.691,0)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,27.051,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,33.554,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,36.643,0)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,43.146,0)"> <use xlink:href="#g113-63"></use> </g> </svg>,当<gydF4y2Basvg height="13.2498pt" id="M288" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>得到更多的体重,略有减少,这符合比例公平的属性;如果有未分配的资源,实现最大比例公平分配他们尽管痛苦的恶化公平指数。另一方面,最大最小不等式(或min-max)或严格公平不忍受这样的恶化。</gydF4y2Bap> <p>补充的评估结果,我们测量两个整数,NLP放松函数的值<gydF4y2Basvg height="13.2498pt" id="M289" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>,<gydF4y2Basvg height="14.52pt" id="M290" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 15.1445 14.52" width="15.1445pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.944)"> <use xlink:href="#g50-50"></use> </g> </svg>,<gydF4y2Basvg height="13.2498pt" id="M291" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>,<gydF4y2Basvg height="14.52pt" id="M292" style="vertical-align:-3.993601pt" version="1.1" viewbox="-0.0498162 -10.5264 15.1445 14.52" width="15.1445pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.944)"> <use xlink:href="#g50-51"></use> </g> </svg>和公平指数和频谱利用率(即在不同的SINR约束。与不同,<gydF4y2Basvg height="10.5429pt" id="M293" style="vertical-align:-0.2402pt" 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-100"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,4.349,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>)固定重量对< 0.5、0.5 >。我们也测量平均值超过60随机采样通道在这些实验。结果绘制在图<gydF4y2Baa href="//www.newsama.com/journals/mse/2014/406462/fig5/" target="_blank">5</gydF4y2Baa>。正如所料,注意到所有函数值和频谱利用率增加<gydF4y2Basvg height="10.5429pt" id="M295" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -10.3027 46.8396 10.5429" width="46.8396pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>增加。关于公平、公平指数时取得了最高的<gydF4y2Basvg height="10.5429pt" id="M296" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -10.3027 46.8396 10.5429" width="46.8396pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>=−10 dB,测量为0.8563129;当<gydF4y2Basvg height="10.5429pt" id="M297" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -10.3027 46.8396 10.5429" width="46.8396pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>=−7 dB,公平指数是测量为0.8515264,低于的情况<gydF4y2Basvg height="10.5429pt" id="M298" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -10.3027 46.8396 10.5429" width="46.8396pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>=−10 dB。然而,整数和NLP放松的值<gydF4y2Basvg height="13.2498pt" id="M299" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>当高<gydF4y2Basvg height="10.5429pt" id="M300" style="vertical-align:-0.2402pt" version="1.1" viewbox="-0.0498162 -10.3027 46.8396 10.5429" width="46.8396pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g190-74"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.62,0)"> <use xlink:href="#g190-79"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,14.686,0)"> <use xlink:href="#g190-84"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,20.945,0)"> <use xlink:href="#g190-83"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,29.469,-5.984)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,37.35,-5.984)"> <use xlink:href="#g58-95"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,41.608,-5.984)"> <use xlink:href="#g58-118"></use> </g> </svg>=−7 dB由于更高的频谱利用率,符合比例公平的属性,不公平但更高的利用率。</gydF4y2Bap> <div class="floats-partial-section partial-carousel-wrapper" data-section="fig5"> <div class="floats-partial-content fig-content-fig5"> <div class="partial-carousel--single-image"> <img alt="(一)功能的价值”name="406462.fig.005a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005a.jpg"> <br> <strong>(一)功能的价值</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(b)的函数值”name="406462.fig.005b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005b.jpg"> <br> <strong>(b)的函数值</gydF4y2Bastrong> </div> <div class="partial-carousel--single-image"> <img alt="(c)公平指数和频谱利用率”name="406462.fig.005c" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005c.jpg"> <br> <strong>(c)公平指数和频谱利用率</gydF4y2Bastrong> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs fig-thumbs-fig5"> <button class="partial-carousel-dot" aria-label="(a) Function value of"><img alt="(一)功能的价值”name="406462.fig.005a" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005a.jpg"><br><strong>(一)功能的价值</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(b) Function value of"><img alt="(b)的函数值”name="406462.fig.005b" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005b.jpg"><br><strong>(b)的函数值</gydF4y2Bastrong></button> <button class="partial-carousel-dot" aria-label="(c) Fairness index and spectrum utilization"><img alt="(c)公平指数和频谱利用率”name="406462.fig.005c" src="https://static-01.hindawi.com/articles/mse/volume-2014/406462/figures/406462.fig.005c.jpg"><br><strong>(c)公平指数和频谱利用率</gydF4y2Bastrong></button> </div> <div class="partial-carousel-next-prev fig-nav-fig5"> <button class="carousel-prev" aria-label="Previous"></button> <button class="carousel-next" aria-label="Next"></button> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</gydF4y2Baspan> <a aria-label="full view" class="caption-partial-url" href="//www.newsama.com/journals/mse/2014/406462/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <svg height="13.2498pt" id="M301" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <path d="M619 670C619 686 593 712 555 712S459 686 410 634S335 504 320 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320 430H250L219 400L222 388H312L258 73C223 -133 201 -166 187 -180C175 -191 158 -199 140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 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140 -199C123 -199 88 -188 74 -172C68 -166 63 -164 54 -171C38 -185 23 -201 23 -215C23 -236 60 -261 93 -261C122 -261 161 -247 207 -200C268 -138 300 -71 337 94C365 220 376 277 394 387L501 399L521 430H401C432 623 464 665 501 665C524 665 544 651 567 627C577 617 583 618 592 625C601 631 619 651 619 670Z" id="g113-103"></path> <glyph.data ascent="3473" descent="-2876" horiz-adv-x="642" vert-adv-y="642"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,8.704,-5.984)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z" id="g50-43"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="611" vert-adv-y="611"></glyph.data> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.944)"> <path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path> <glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data> </g> </svg> <table> 评价函数的值gydF4y2Ba和,gydF4y2Ba公平指数,根据不同的频谱利用率gydF4y2Ba。“INSR”gydF4y2Ba设在表示gydF4y2Ba。我们测量两个整数,NLP放松函数的值,gggydF4y2BaydF4y2BaydF4y2Ba,,ggydF4y2BaydF4y2Ba。</gydF4y2Batable> </div> </div> </div> <h4 id="conclusions">6。结论</gydF4y2Bah4> <p>本文阐述了资源受限的无线传感器网络中的频谱分配问题与下列目标:<gydF4y2Basvg height="12.0395pt" id="M312" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg><i>最大化的公平</gydF4y2Bai>,<gydF4y2Basvg height="12.0395pt" id="M313" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg><i>反映了传感器数据之间的优先级</gydF4y2Bai>,<gydF4y2Basvg height="12.0395pt" id="M314" style="vertical-align:-2.3616pt" version="1.1" viewbox="-0.0498162 -9.6779 16.0376 12.0395" width="16.0376pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,4.688,0)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.0135,0,0,-0.0135,11.191,0)"> <use xlink:href="#g113-42"></use> </g> </svg><i>避免不必要的频谱切换</gydF4y2Bai>。前两个目标是通过加权比例公平最大化。因此被制定为一个优化问题有两个不同的目标函数:多目标优化。多目标优化决策的一个不可或缺的工具如果决定的好处并不仅仅取决于一个对象。对象由一个纯量值进一步映射函数,数值。我们部署基于切比雪夫范数问题的数值方法为了保持目标函数的凸性和约束。应用数值之前,原目标函数由算术几何平均convexified近似和对数变化的决策变量。此外,所有的约束都变成log-sum-exp严格凸函数形式。此外,为了找到好的近似整数解,一个简单的圆算法,它是相当高效由于指数特性的问题。数值实验说明了解决方案的效率包括冷凝和舍入算法。 Furthermore, by the discreet adjustment of the weight on each objective function, the proposed algorithm performs well in achieving the balanced multiobjective solutions. Finally, it is illustrated that, given the weight of each sensor, the algorithm allocates spectrum units fairly as well as yielding high spectrum utilizations when<svg height="13.2498pt" id="M315" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-50"></use> </g> </svg>相对较高的体重比吗<gydF4y2Basvg height="13.2498pt" id="M316" style="vertical-align:-3.571899pt" version="1.1" viewbox="-0.0498162 -9.6779 12.2643 13.2498" width="12.2643pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0135,0,0,-0.0135,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0095,0,0,-0.0095,7.004,3.264)"> <use xlink:href="#g50-51"></use> </g> </svg>。</gydF4y2Bap> <h4 id="conflict-of-interests">利益冲突</gydF4y2Bah4> <p>作者宣称没有利益冲突有关的出版。</gydF4y2Bap> <h4 id="acknowledgment">承认</gydF4y2Bah4> <p>这项研究受到了基础科学研究项目通过韩国国家研究基金会(NRF)由教育部科技(2012 r1a1a4a01015777)。</gydF4y2Bap> </div> <div class="xml-content"> <h4 class="references" id="references">引用</gydF4y2Bah4> <ol> <li id="B1">问:赵和b·m·萨德勒”动态频谱接入的调查。”<gydF4y2Bai>IEEE信号处理杂志</gydF4y2Bai>,24卷,不。3、79 - 89年,2007页。<gydF4y2Baspan class="reflinks">视图:<gydF4y2Baa href="https://doi.org/10.1109/MSP.2007.361604">出版商的网站</gydF4y2Baa><span class="sep">|</gydF4y2Baspan><a href="https://scholar.google.com/scholar_lookup?title=A%20survey%20of%20dynamic%20spectrum%20access&author=Q. 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class="journal_article__ArticleStickyTopToolbar-sc-12fk6zy-0 gbrQxi article_sticky_top_toolbar"> <div class="sc-cBdUnI hRnXob article_top_toolbar"> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo hymroZ pdf_desktop button__group" href="https://downloads.hindawi.com/journals/mse/2014/406462.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="https://static-01.hindawi.com/next_assets/ROIjnaKw_H8OUEtgga6i7/_next/static/node_modules/hindawi-ui/src/icon/svg/pdf.svg" height="24"><span class="text">PDF</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-kcDeIU cbcyj ref_desktop" href="//www.newsama.com/journals/mse/2014/406462.ris" aria-label="" target="" id="toolbar__dcNavLarge"><span><img alt="" class="sc-EHOje 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height="24"><span class="text">下载引用</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> <a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-BngTV hmDWcT ref_desktop" href="//www.newsama.com/journals/mse/2014/406462.ris" aria-label="" target="" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" 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height="24"><span class="text">引用</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a> </div> </div> <div class="journal_article__ArticleStickyBottomToolbar-sc-12fk6zy-1 isgRZA article_sticky_bottom_toolbar"> <div class="sc-cTjmhe ihmyEq article_bottom_toolbar"> <div class="sc-cugefK itFKcQ accordion" property="background-color" color="#D8D8D8" id="toolbar__dofNav"> <span><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="sc-dRFtgE jrsDZP">下载其他格式</gydF4y2Baspan><span class="sc-gkFcWv gWTCXQ">更多的</gydF4y2Baspan></span> <span class="sc-htoDjs bMdQcY sc-gbOuXE jGPvPL icon-colored _1CwL9R82TPl2HxDleeYGDR icon-themeable" title="" font-size="11"></span> </div> <div class="sc-fnwBNb etzuBr"> <a class="sc-htpNat bUhGXt link sc-iNhVCk gWgCNb open_panel" href="//www.newsama.com/downloads/journals/mse/2014/406462.epub" aria-label="ePub" property="background-color" color="#D8D8D8"> <div class="sc-eAKXzc WHkfb"> ePub</gydF4y2Badiv><img alt="" class="sc-EHOje jOLhQl sc-bfYoXt cGuwDn" title="" role="presentation" 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