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<div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__0jAuv"> <div class="TableOfContents_tableOfContents__title__CH9Lz"> 在这一页上</d我v> <a class="TableOfContents_tableOfContents__item__JJil1" href="#abstract">文摘</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#introduction">介绍</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#simulation-experiment-and-analysis">分析</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conclusion-and-outlook">结论</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#data-availability">数据可用性</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#conflicts-of-interest">的利益冲突</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#authors’-contributions">作者的贡献</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#acknowledgments">确认</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#references">引用</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#copyright">版权</一个> <a class="TableOfContents_tableOfContents__item__JJil1" href="#related-articles">相关文章</一个> </div> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__sbd41"> <div class="ArticleMiddleSection_articleMiddleSection__gAv9z"> <div class="articleHeader"> <strong>研究文章|开放获取</strong> <div class="articleHeader__meta"> <span>体积2022年|</span> <span>文章的ID1811689|</span> <span class="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2022/1811689" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2022/1811689</一个></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</button> </div> <h1 class="articleHeader__title">多目标绿色时间Location-Routing问题和算法</h1> <div class="articleHeader__authors"> <span class="articleHeader__authors_author">花心张<sup>1</sup></span> <span class="articleHeader__authors_author">和<strong>Chun-Miao张</strong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><a href="https://orcid.org/0000-0002-1412-9054" aria-label="Redirect to Doi" target="_blank" rel="noreferrer"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" viewbox="0 0 256 256" xml:space="preserve" width="1em" height="1em"> <path d="M256 128c0 70.7-57.3 128-128 128S0 198.7 0 128 57.3 0 128 0s128 57.3 128 128z" fill="#a6ce39"></path> <path d="M86.3 186.2H70.9V79.1h15.4v107.1zm22.6-107.1h41.6c39.6 0 57 28.3 57 53.6 0 27.5-21.5 53.6-56.8 53.6h-41.8V79.1zm15.4 93.3h24.5c34.9 0 42.9-26.5 42.9-39.7C191.7 111.2 178 93 148 93h-23.7v79.4zM88.7 56.8c0 5.5-4.5 10.1-10.1 10.1s-10.1-4.6-10.1-10.1c0-5.6 4.5-10.1 10.1-10.1s10.1 4.6 10.1 10.1z" fill="#fff"></path> </svg></span></a><sup>2</sup></span> </div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</button> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</strong> <span>Saurabh普拉塔普</span> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</strong> <span>2022年2月06</span> </div> <div class="articleHeader__timeline_item "> <strong>修改后的</strong> <span>2022年3月18日</span> </div> <div class="articleHeader__timeline_item "> <strong>接受</strong> <span>2022年4月25日</span> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</strong> <span>2022年5月21日</span> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>减少物流成本和碳排放和提高客户满意度,本研究提出了一种多目标绿色时间位置路由问题(MOGTDLRP)模型的目标是最小化配送总成本,交货时间和燃料消耗。该模型能够解决的几个hyperheuristic算法包括高级启发式和低级的启发式。有三个验收标准的解决方案:改进和相同的情况下,所有的行动和接受所有的解决方案,和动态验收标准。通过情况下,算法的性能和各种因素的影响在本研究分析了解决方案。实验结果表明,该模型可以有效地降低物流成本,碳排放,车辆旅行时间。</p> <span class="end-abs"></span> <h4 id="introduction">1。介绍</h4> <p>城市物流中扮演一个重要的角色在经济活力的城市。绿色物流是指物流活动的计划和执行以更环保的方式通过考虑外部因素,如浪费,噪音、能源使用和温室气体(GHG)排放(<一个href="#B1">1</一个>,<一个href="#B2">2</一个>]。与此同时,城市货物运输负责拥堵而闻名。location-routing问题(单体)是最重要的一个组合优化问题在供应链管理和物流系统规划进行共同决策关于任意类型的设施的位置和车辆的路由<一个href="#B3">3</一个>]。含碘与环境问题被称为绿色单体(GLRP)其目的是为了减少燃料消耗和汽车尾气排放<一个href="#B4">4</一个>]。Koc [<一个href="#B5">5</一个>)提出了一个模型,旨在最小化总成本包括仓库费用,车辆和路由成本和碳排放成本。于(<一个href="#B6">6</一个>)调查时间要求为一个扩展的location-routing问题location-routing问题,考虑到时间的需求特点。Alamatsaz [<一个href="#B7">7</一个>)开发了一个混合整数规划模型为客户考虑时间窗和司机。还有许多其他的研究人员(<一个href="#B8">8</一个>- - - - - -<一个href="#B11">11</一个>)调查了绿色单体模型的目标最小化总成本包括仓库费用,车辆和路由成本和发射成本。然而,除了降低成本外,其他因素,如旅行时间、燃料消耗,和客户满意度应该认真对待。因此,多目标GLRP (MOGLRP)自2019年以来逐渐成为一个研究热点问题。托罗(<一个href="#B12">12</一个>GLRP]提出了一种多目标模型以减少运营成本和环境影响。拉巴尼(<一个href="#B13">13</一个>)引入了一个新变种的MOGLRP最小化总旅行距离和总成本包括车辆固定成本和有限公司<sub>2</sub>排放。唐(<一个href="#B14">14</一个>)建立了biobjective模式来降低成本和碳排放从可持续的角度供应链网络。</p> <p>进一步分析,论文GLRP表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab1/" target="_blank">1</一个>与五个因素:(i),(2)目标函数的数量,(iii)时间窗口,(iv)车辆速度和(v)算法。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> GLRP论文。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <p>有11个文件关于单一GLRP和论文10多目标GLRP表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab1/" target="_blank">1</一个>。在上面的模型中,一些不考虑车辆的速度,和其他认为速度是一个常数。然而,速度是关键参数在计算油耗和排放<一个href="#B25">25</一个>]。燃料消耗是接受由许多因素影响的车辆速度是最关键的一个,和车辆排放燃料消耗成正比(<一个href="#B26">26</一个>]。在真实道路网络中,车辆速度是时间函数由于交通流,天气、事故,和其他因素。基于时间道路网络模型更有益的真正的物流配送。所以,名叫three-objective模型多目标绿色时间位置路由问题(MOGTDLRP,如图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig1/" target="_blank">1</一个>。其目的是为了减少总成本(包括打开仓库费用,车辆成本,和分销成本),车辆燃料消耗和交付时间。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-b7534572f9a1d2a02f9d0b07d1f8c795"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-b7534572f9a1d2a02f9d0b07d1f8c795 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b7534572f9a1d2a02f9d0b07d1f8c795 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> MOGTDLRP图。</d我v> </div> </div> </div> <p>由于含碘是一个np难问题,MOGTDLRP也是np难问题。MOGTDLRP,不同类型的道路上的车辆以不同的速度在不同的时间,并向客户发货的时间内窗口。因为精确算法只能解决小规模优化问题在合理的时间内,选择metaheuristics解决大规模问题。这些metaheuristics包括遗传算法(<一个href="#B27">27</一个>- - - - - -<一个href="#B29">29日</一个>),蚁群优化(<一个href="#B30">30.</一个>),和一个禁忌搜索(<一个href="#B17">17</一个>]。不同于metaheuristics,几个hyperheuristics(美国卫生和公众服务部)提出了研究。hyperheuristic系统,试图找到合适的启发式序列在特定情况下直接而不是试图解决一个问题,被定义为“启发式选择启发式算法(<一个href="#B32">32</一个>,<一个href="#B33">33</一个>]。HH,域屏障隔离高级启发式(通过),包括运营商的选择策略和解决方案的接收机制和低级启发式(LLH),包含一系列的低级运营商、问题定义、目标函数和其他信息。选择策略的作用是监控的性能信息LLH选择一个好的和合适的运营商,和接受机制决定取代孩子的父母解决方案根据质量解决方案和控制算法的搜索方向和收敛速度。在这项研究中,我们设计美国卫生和公众服务部与启发式算法(人工蜂群算法(ABC),蚁群优化(ACO)和禁忌搜索算法(TS))作为解决MOGTDLRP通过。我们设计三个验收标准(ACs)的解决方案,改善和相等(IE),所有动作(AM)和接受所有的解决方案,和动态验收标准(DA)和一系列的低级操作符符合。</p> <p>总之,本研究的主要贡献和创新如下:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">多个目标的影响,时间依赖网络,和燃料消耗是MOGTDLRP构造数学模型</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">三通过三ACs合并形成九HH分析算法的性能</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">我们提出一套基准的MOGTDLRP并分析仿真结果</span></span></span></p> <p>本研究的建设如下。部分<一个href="#sec2">2</一个>是关于MOGTDLRP模型。部分<一个href="#sec3">3</一个>是一个介绍美国卫生和公众服务部。部分<一个href="#sec4">4</一个>结果和分析。部分<一个href="#sec5">5</一个>是结论和展望。</p> <h4 id="the-model-of-mogtdlrp">2。MOGTDLRP模型</h4> <p>MOGTDLRP模型有三个优化目标将在这一节中介绍。MOGTDLRP可以定义在一个不对称有向图<我>G</我>= (<我>V</我>,<我>E</我>),<我>V</我>是由一组候选仓库吗<我>D</我>(<span class="inline_break"> <svg height="11.5564pt" id="M1" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 21.221 11.5564" width="21.221pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M743 375C743 570 607 650 407 650H136L130 622C214 612 220 606 204 526L125 122C110 43 105 36 24 27L17 0H250C382 0 482 23 571 76C680 141 743 248 743 375ZM644 379C644 188 520 36 305 36C277 36 249 38 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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> <g transform="matrix(.013,0,0,-0.013,85.543,0)"> <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> </g> </svg>)</span></span>和客户的设置<我>C</我>(<span class="inline_break"> <svg height="11.5564pt" id="M2" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 19.947 11.5564" width="19.947pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M645 631C614 643 545 666 457 666C215 666 23 519 23 283C23 90 158 -16 337 -16C412 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15.996 12.7178" width="15.996pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,182.286,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,191.418,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="201.86418379999998 -9.28833 15.133 12.7178" width="15.133pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,201.914,0)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,211.872,0)"> <use xlink:href="#g113-126"></use> </g> </svg>)。</span></span>的需求<我>问</我><sub><i>我</我></sub>、服务时间<我>圣</我><sub><i>我</我></sub>、协调(<我>x</我><sub><i>我</我></sub>,<我>y</我><sub><i>我</我></sub>),和硬时间窗<我>一个</我><sub><i>我</我></sub>,<我>e</我><sub><i>我</我></sub>的客户<我>我</我>电子商务是已知的。的能力<我>P</我><sub><i>j</我></sub>、租金成本<我>FD</我><sub><i>j</我></sub><i>,</我>和坐标(<我>x</我><sub><i>j</我></sub>,<我>y</我><sub><i>j</我></sub>得宝)的候选人<我>j</我>(<我>j</我>E<我>D</我>)是已知的。每辆车<我>h</我>均匀的舰队有相同的能力<我>问</我><sub><i>h</我></sub>和租金成本<我>艘渔船</我><sub><i>h</我></sub>。符号<我>d</我><sub><i>ij</我></sub>两个节点之间的距离吗<我>我</我>和<我>j</我>(<span class="inline_break"> <svg height="12.0653pt" id="M4" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 14.854 12.0653" width="14.854pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.854,0)"> <use xlink:href="#g117-145"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.181,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="12.0653pt" style="vertical-align:-3.4294pt" version="1.1" viewbox="18.4231838 -8.6359 15.996 12.0653" width="15.996pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,18.473,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.605,0)"> <use xlink:href="#g117-173"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="12.0653pt" style="vertical-align:-3.4294pt" version="1.1" viewbox="38.0501838 -8.6359 9.41 12.0653" width="9.41pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,38.1,0)"> <use xlink:href="#g113-87"></use> </g> </svg>)。</span></span>车辆的交货时间取决于距离,速度的变化根据出发的时间和电弧被遍历。<svg height="12.5794pt" id="M5" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 26.2503 12.5794" width="26.2503pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-87"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.332,3.132)"> <path d="M509 90L493 118C465 91 427 70 418 70S409 77 415 103L469 327C494 429 466 451 436 451C412 451 387 444 356 427C307 400 222 342 160 264H158L246 667C253 701 252 710 243 710C228 710 169 680 87 673L83 644H117C155 644 160 640 149 588L24 -4L32 -12C57 -4 86 4 108 9L143 187C198 275 324 386 375 386C394 386 399 367 385 311L331 87C315 22 322 -12 351 -12C387 -12 452 24 509 90Z" id="g50-105"></path> </g> <g transform="matrix(.013,0,0,-0.013,12.644,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.142,0)"> <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(.013,0,0,-0.013,21.575,0)"> <use xlink:href="#g113-42"></use> </g> </svg>旅游车辆的速度吗<我>h</我>遍历不同的弧线。<我>TT</我><sub><i>ij</我></sub>节点之间的旅行时间吗<我>我</我>和<我>j</我>。<我>K</我><sub><i>ijh</我></sub>是负载车辆<我>h</我>离开<我>我</我>和旅行<我>j</我>。<我>圣</我><sub><i>j</我></sub>是客户的服务时间<我>j</我>。<我>在</我><sub><i>jh</我></sub>当车辆吗<我>h</我>到达节点<我>j</我>。决策变量<我>y</我><sub><i>r</我></sub>= 1,如果仓库<我>r</我>否则是开放和= 0。<我>z</我><sub><i>即时通讯</我></sub>= 1,如果客户<我>我</我>有仓库<我>米</我>否则,= 0。<我>x</我><sub><i>ijh</我></sub>如果车辆= 1<我>h</我>从<我>我</我>来<我>j</我>否则,= 0。<我>F</我><sub><i>ijh</我></sub>CMEM模型,可以计算的(<一个href="#B8">8</一个>),是车辆的燃料消耗<我>h</我>旅行从节点<我>我</我>到节点<我>j</我>。表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab2/" target="_blank">2</一个>给MOGTDLRP模型中使用的参数。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 参数和值。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <p>需要满足一些假设:(1)每个客户必须只服务一次,(2)每辆车必须回到原来的仓库,(3)每辆车不得超载,和(4)每个仓库的负荷不得超过其能力。</p> <p>基于上述假设和定义,模型可以表示如下:<span class="equation_break" id="EEq1"><span class="left_break" id="L7"></span><span class="middle_break"><span class="center_break" id="M7"> <svg height="116.967pt" id="M7-1" version="1.1" viewbox="0 0 34.652 116.967" width="34.652pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-1"> <g transform="matrix(.013,0,0,-0.013,0,12.205)"> <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 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g121-107"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.65,12.205)"> <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="g121-103"></path> </g> <g transform="matrix(.013,0,0,-0.013,14.13,12.205)"> <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="g121-108"></path> </g> <g transform="matrix(.013,0,0,-0.013,23.5,12.205)"> <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> </g> <g transform="matrix(.0091,0,0,-0.0091,30.22,15.337)"> <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> </g> </g> </svg> <svg height="116.967pt" id="M7-2" version="1.1" viewbox="0 0 262.094 116.967" width="262.094pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B7-2"> <g transform="matrix(.013,0,0,-0.013,0,12.205)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.82,12.212)"> <path d="M956 -188L922 -180C881 -295 847 -317 759 -317H196L640 311L259 873H678C777 873 812 865 833 838C853 816 869 781 885 721L918 727L902 932H77V907L514 253L53 -396V-421H902L956 -188Z" id="g119-73"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,11.27,25.854)"> <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> <g transform="matrix(.0091,0,0,-0.0091,15.18,25.854)"> <path d="M496 -1V52H376C259 52 161 132 147 236H496V289H147C162 392 259 473 376 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(<一个href="#EEq4">10</一个>)禁止非法路线对应的车辆不返回离开仓库。约束(<一个href="#EEq4">11</一个>)和(<一个href="#EEq4">12</一个>确保每个客户的需求是满意。约束(<一个href="#EEq4">13</一个>)保证每个选择的负载仓库必须小于它的容量。约束(<一个href="#EEq4">14</一个>)是动态平衡负载的每辆车在访问客户<我>j</我>。约束(<一个href="#EEq4">15</一个>)和(<一个href="#EEq4">16</一个>)保证重载是不允许的。约束(<一个href="#EEq4">17</一个>)和(<一个href="#EEq4">18</一个>)每个节点的到达时间界限:车辆必须在关闭之前到达客户的时间窗口。最后,最后三个约束是决策变量。</p> <h4 id="algorithms">3所示。算法</h4> <p>Metaheuristics是广泛的。然而,选择最好的算法和配置参数和操作符来解决这个问题是非常困难的(<一个href="#B34">34</一个>]。数值实验表明,它是不可能发展一个metaheuristics算法总是有效的各种优化问题。Hyperheuristic算法(HH)是一个超启发式算法,它提供了一个高层次的启发式方法(通过)。它可以解决各种组合优化问题,通过管理或操纵的一系列低级启发式(LLH)。美国卫生和公众服务部可以帮助研究人员来减少所需的固有时间和精力建立一个新的领域,因为它是一项艰巨的任务,测试人员没有深在特定领域的知识(<一个href="#B35">35</一个>]。在HH的设计主要有两个任务:一个是高层选择策略,另一种是问题域算子的设计。使用HH解决MOGTDGLRP问题可以解决局部优化运营商的选择问题。如果迭代所有运营商,将浪费大量的时间。HH才能决定是否使运营商通过合理选择机制根据运营商的历史,它不仅节省时间,还可以提高解决方案的质量。通过,有两种不同的目标策略:运营商选择策略与和解接收机制。此外,还有一个信息之间的发射机通过LLH,传输信息,如选择算子的信息,判断信息的接收机制,运营商的运行时间和频率,电流的连续的未被利用的次数的解决方案。因此,通过起着至关重要的作用在提高HH的性能。在这项研究中,我们设计了九个运营商和三个通过包括禁忌搜索算法(TS),蚁群优化(ACO)和人工蜂群算法(ABC)。接下来,我们将介绍HH根据以下步骤:(1)编码方法和初始种群生成; (2) HLHs; (3) acceptance criteria; (4) the LLHs pool of operators,<我>ξ</我>。</p> <h5 id="sec3.1">3.1。编码方法和初始种群生成</h5> <p>MOGTDLRP问题域,一个完整的解决方案是所有航线的集合<span class="inline_break"> <svg height="12.5794pt" id="M9" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 19.414 12.5794" width="19.414pt" 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transform="matrix(.013,0,0,-0.013,23.046,0)"> <use xlink:href="#g113-124"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.557,0)"> <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> <g transform="matrix(.0091,0,0,-0.0091,32.458,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.404,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.5794pt" style="vertical-align:-3.29107pt" version="1.1" viewbox="42.4981838 -9.28833 12.811 12.5794" width="12.811pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,42.548,0)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,47.448,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.395,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="12.5794pt" style="vertical-align:-3.29107pt" version="1.1" viewbox="57.488183799999995 -9.28833 18.427 12.5794" width="18.427pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,57.538,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,62.681,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.824,0)"> <use xlink:href="#g113-47"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.001,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span><span class="nowrap"> <svg height="12.5794pt" style="vertical-align:-3.29107pt" version="1.1" viewbox="78.09418380000001 -9.28833 14.867 12.5794" width="14.867pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,78.144,0)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,83.045,3.132)"> <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(.013,0,0,-0.013,88.22,0)"> <use xlink:href="#g113-126"></use> </g> </svg>。</span></span>每一个路由<我>r</我><sub><i>我</我></sub>具有相同的结构:第一个和结束节点是打开仓库,中间部分是客户数量。例如,{的路线<我>D</我><sub><i>2</我></sub><i>- c</我><sub><i>1</我></sub><i>- c</我><sub><i>3</我></sub><i>- c</我><sub><i>10</我></sub><i>- d</我><sub><i>2</我></sub>}意味着一个特定的车辆离开仓库<我>D</我><sub><i>2</我></sub>发货给客户<我>C</我><sub><i>1</我></sub>,<我>C</我><sub><i>3</我></sub>,<我>C</我><sub><i>10</我></sub>,然后返回<我>D</我><sub><i>2</我></sub>。最初的解决方案对最终解决方案的质量至关重要。在传统的单体,在生成一个初始的路线,只有能力约束的仓库和车辆需要满足,和优化目标是分布的距离。然而,在MOGTDLRP,还必须满足仓库和客户的时间窗口。为了生产高质量的初步解决方案,有必要设计更高效的算法。有两种经典算法有时间窗车辆路径问题(VRP)供参考:所罗门的插入算法(<一个href="#B36">36</一个>)和影响算法(<一个href="#B37">37</一个>]。然而,这两个算法需要设置很多参数。张(<一个href="#B8">8</一个>),在其论文中,设计一个算法基于行程时间的插入方法(IMTT)来生成初始解。这种方法有很好的解决方案质量,不需要设置许多参数。因此,本研究利用IMTT生成最初的解决方案。其步骤如下:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">第一步:选择打开仓库根据重心的方法</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第二步:随机选择一个客户节点生成一个新的路线</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第三步:计算这条路线的总旅行时间</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第四步:计算剩下的客户的影响值插入到路线</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第五步:插入新客户路线根据影响值,直到一个或多个约束并不满意</span></span></span></p> <p>图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig2/" target="_blank">2</一个>显示了初始解的生成过程。得宝<sub><i>0</我></sub>所选仓库;<我>Ins</我><sub><i>我</我></sub>代表可插入的位置;<我>C</我><sub><i>我</我></sub>是客户的路线。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-54f12a58e79fa8ffe85f237e4251b339"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.002.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-54f12a58e79fa8ffe85f237e4251b339 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-54f12a58e79fa8ffe85f237e4251b339 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 初始解的生成过程。</d我v> </div> </div> </div> <h5 id="sec3.2">3.2。高层启发式</h5> <h6 id="sec3.2.1">3.2.1之上。人工蜂群算法(ABC)</h6> <p>美国广播公司包括三个要素:食物,蜜蜂,蜜蜂和失业者的旁观者蜜蜂和巡防队组成。食物是MOGTDLRP中的解决方案。采用蜜蜂负责寻找食物,携带的信息。旁观者蜜蜂蜜蜂按照雇佣有一定概率选择食物。童子军负责寻找食物随机提高算法跳出局部最优解的能力。在ABC算法的初始化阶段,SN的解决方案,食物来源的位置,是由IMTT生成的。然后,这些最初的解决方案评估来获得他们的健身价值。</p> <p>ABCHH,食物来源是运营商,底部和优化过程是蜜蜂殖民地寻找食物的过程。美国广播公司的高层战略思想如下。</p> <p>首先,20%的蜜蜂殖民地设置为侦察蜂的角色找到很好的食物来源。每只蜜蜂蜜蜂计算在每个运营商的20倍。伯爵表评分(<我>我</我>)的运营商<我>我</我>将增加1点,当健康改善。运营商在降序排序根据他们的成绩优秀被发现食物时,所有人都成为雇佣蜂享受食物,和个人更新由以下方程:<span class="equation_break" id="EEq22"><span class="left_break" id="L10"></span><span class="middle_break"><span class="center_break" id="M10"> <svg height="54.0503pt" id="M10-1" version="1.1" viewbox="0 0 23.102 54.0503" width="23.102pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B10-1"> <g transform="matrix(.013,0,0,-0.013,0,12.113)"> <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 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</svg></span></span>在哪里<我>我</我>代表了<我>我</我><sub><i>th</我></sub>个人的人口,<我>t</我>是迭代的数量,<我>年代</我><sub><i>一个</我></sub>代表了<我>一个</我>th操作员的集合,<我>SC</我><sub><i>一个</我></sub>是运营商的得分排名<我>年代</我><sub><i>一个</我></sub>,<我>P</我><sub><i>我</我></sub><i>·年代</我><sub><i>一个</我></sub>意味着<我>年代</我><sub><i>一个</我></sub>选择算子的概率<我>P</我><sub><i>我</我></sub>。当<我>t</我>生成解决方案<我>X</我><sub><i>“透明国际”</我></sub>比<我>t</我>1代的解决方案,<我>p</我><sub><i>我</我></sub>= 1;否则,它是根据计算方程。兰特(<我>年代</我>- - - - - -<我>年代</我><sub><i>一个</我></sub>- - - - - -<我>年代</我><sub>最好的</sub>后)意味着一个算子随机选择算子集<我>年代</我>消除了<我>年代</我><sub><i>一个</我></sub>和<我>年代</我><sub>最好的</sub>操作符和<我>年代</我><sub>最好的</sub>运营商与得分最高的吗<我>年代</我>集。</p> <h6 id="sec3.2.2">3.2.2。相关定义</h6> <p><span class="statement" id="deff1"><span class="statement-title"><i class="statement-title">定义1。</我></span>状态-。<br>实数编码的问题,让蜜蜂的状态<我>我</我>是<我>x</我><sub><i>id</我></sub>。根据方程(<一个href="#EEq23">23</一个>),蜜蜂<我>我</我>随机方法的位置<我>x</我><sub><i>kd</我></sub>另一个蜜蜂的信息传输:<span class="equation_break" id="EEq23"><span 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transform="matrix(.013,0,0,-0.013,149.23,11.958)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,159.19,11.958)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="38.0421pt" id="I11" version="1.1" viewbox="0 0 162.53 38.0421" width="162.53pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B11-1"></use> <use transform="matrix(1 0 0 1 0 22.12)" xlink:href="#B11-2"></use> </svg></span></span><span class="right_break" id="R11"> <svg class="label" height="11.44pt" id="M11-3" version="1.1" viewbox="0 0 21.018 11.44" width="21.018pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B11-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.64,9.26)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.52,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="38.0421pt" id="IL11" version="1.1" viewbox="0 0 21.1 38.0421" width="21.1pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 13.09)" xlink:href="#B11-3"></use> </svg></span></span>这意味着一个操作<我>d</我>是随机选择的,相对应的元素<我>d</我>一些<我>x</我><sub><i>id</我></sub>和<我>x</我><sub><i>kd</我></sub>表单字段(<我>一个b</我>),<我>一个</我>是一个价值和小一点的吗<我>b</我>是一个更大的价值。然后,<我>λ</我>(<我>x</我><sub><i>id</我></sub><i>- x</我><sub><i>kd</我></sub>)是相反的顺序<我>x</我><sub><i>id</我></sub>从<我>一个</我>来<我>b</我>。<br>例如,我们<span class="inline_break"> <svg height="14.5316pt" id="M12" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 29.717 14.5316" width="29.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.086,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="33.299183799999994 -10.5932 83.31 14.5316" width="83.31pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.349,2.33939e-05)"> <path d="M308 -259V-228H299C192 -219 190 -215 190 -109V616C190 755 193 759 299 768H308V799H127V-259H308Z" id="g119-1"></path> </g> <g transform="matrix(.013,0,0,-0.013,41.192,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.433,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.674,-.718)"> <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 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path> </g> <g transform="matrix(.013,0,0,-0.013,77.915,-.718)"> <path d="M456 178V225H360V632H320C217 496 115 347 20 206V178H280V106C280 40 276 34 189 27V0H445V27C364 34 360 39 360 106V178H456ZM280 225H82C149 335 214 431 278 520H280V225Z" id="g113-53"></path> </g> <g transform="matrix(.013,0,0,-0.013,90.156,-.718)"> <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(.013,0,0,-0.013,102.397,-.718)"> <path d="M137 343C167 482 260 545 321 574C357 591 397 603 429 609L423 641C382 634 335 622 295 608C189 570 37 457 37 238C37 84 125 -12 242 -12C362 -12 447 89 447 209C447 311 374 393 267 393C247 393 226 386 204 376L137 343ZM227 337C318 337 361 256 361 173C361 105 336 22 258 22C176 22 126 120 126 240C126 266 127 291 132 310C155 323 189 337 227 337Z" id="g113-55"></path> </g> <g transform="matrix(.013,0,0,-0.013,111.649,2.33939e-05)"> <path d="M244 -259V799H63V768H72C178 759 181 755 181 616V-109C181 -215 179 -219 72 -228H63V-259H244Z" id="g119-2"></path> </g> </svg>,</span></span><span class="inline_break"> <svg height="14.5316pt" id="M13" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 31.809 14.5316" width="31.809pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.879,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,24.178,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="35.3911838 -10.5932 83.309 14.5316" width="83.309pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,35.441,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.284,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,55.525,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.766,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.007,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.248,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,104.489,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,113.741,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>,</span></span>和随机数<我>β</我>= 4;然后,<我>x</我><sub><i>id</我></sub>(4)= 4,<我>x</我><sub><i>kd</我></sub>(4)= 1,<span class="inline_break"> <svg height="14.5316pt" id="M14" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 45.649 14.5316" width="45.649pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.843,-.666)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.423,-.666)"> <use xlink:href="#g113-99"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.532,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.018,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="49.2311838 -10.5932 34.318 14.5316" width="34.318pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,49.281,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.124,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.365,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,78.617,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>。</span></span>根据定义,<我>x</我><sub><i>id</我></sub>−<我>x</我><sub><i>kd</我></sub>意味着的1 - 4位<我>x</我><sub><i>id</我></sub>以相反的顺序排列,从而产生一个新的解决方案吗<span class="inline_break"> <svg height="15.3797pt" id="M15" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.4361 29.717 15.3797" width="29.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.267,-5.741)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.784)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.086,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="15.3797pt" style="vertical-align:-3.9436pt" version="1.1" viewbox="33.299183799999994 -11.4361 83.31 15.3797" width="83.31pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.349,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.192,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.433,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.674,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.915,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.156,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.397,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,111.649,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>。</span></span></span></p> <p><span class="statement" id="deff2"><span class="statement-title"><i class="statement-title">定义2。</我></span>国家数字乘法。<br><i>C</我>×<我>x</我><sub><i>id</我></sub>表示乘法数州,这意味着第一个。<br> <svg height="11.439pt" id="M16" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 42.7994 11.439" width="42.7994pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M348 662V703H120V-163H181V570C181 649 184 662 290 662H348Z" id="g113-3"></path> </g> <g transform="matrix(.013,0,0,-0.013,5.239,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.829,0)"> <path d="M528 54L331 254L528 455L492 493L294 291L96 493L60 455L257 254L60 54L96 16L294 217L492 16L528 54Z" id="g117-42"></path> </g> <g transform="matrix(.013,0,0,-0.013,27.365,0)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.324,0)"> <path d="M284 -163V703H56V663H114C220 663 223 649 223 571V-163H284Z" id="g113-4"></path> </g> </svg>的元素<我>x</我><sub><i>id</我></sub>和象征<svg height="11.439pt" id="M17" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 10.6169 11.439" width="10.6169pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-3"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.239,0)"> <use xlink:href="#g113-4"></use> </g> </svg>表明围捕。<br>例如,<span class="inline_break"> <svg height="14.5316pt" id="M18" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 29.717 14.5316" width="29.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.086,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="33.299183799999994 -10.5932 83.31 14.5316" width="83.31pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.349,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.192,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.433,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.674,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.915,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.156,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.397,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,111.649,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg></span>和<我>C</我>= 0.5;然后,<span class="inline_break"> <svg height="11.439pt" id="M19" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 53.825 11.439" width="53.825pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-3"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.239,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.829,0)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.365,0)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.324,0)"> <use xlink:href="#g113-4"></use> </g> <g transform="matrix(.013,0,0,-0.013,46.194,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="11.439pt" style="vertical-align:-2.15067pt" version="1.1" viewbox="57.4071838 -9.28833 6.529 11.439" width="6.529pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,57.457,0)"> <use xlink:href="#g113-52"></use> </g> </svg></span>和<span class="inline_break"> <svg height="15.3797pt" id="M20" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -11.4361 29.717 15.3797" width="29.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.267,-5.741)"> <use xlink:href="#g50-31"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.784)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.784)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.086,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="15.3797pt" style="vertical-align:-3.9436pt" version="1.1" viewbox="33.299183799999994 -11.4361 46.587 15.3797" width="46.587pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.349,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.192,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.433,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.674,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.926,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>。</span></span></span></p> <p><span class="statement" id="deff3"><span class="statement-title"><i class="statement-title">定义3。</我></span>地位和。<br>状态和2-opt切换操作。<br>例如,我们<span class="inline_break"> <svg height="14.5316pt" id="M21" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 29.717 14.5316" width="29.717pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,22.086,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="33.299183799999994 -10.5932 83.31 14.5316" width="83.31pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,33.349,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.192,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,53.433,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.674,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.915,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.156,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.397,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,111.649,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg></span>和<span class="inline_break"> <svg height="14.5316pt" id="M22" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 29.14 14.5316" width="29.14pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <path d="M655 0V28C585 35 563 50 517 120C469 193 414 280 360 366C427 469 460 516 481 545C526 604 545 614 619 622V650H391V622C457 614 462 604 438 560C411 511 381 463 339 398C295 466 258 523 225 580C210 606 211 615 272 622V650H26V622C98 614 111 603 154 538C189 482 235 408 288 324C200 188 149 116 124 85C95 47 64 34 7 28V0H236V28C169 36 164 46 188 89C220 148 261 217 310 291C372 193 417 118 442 77C461 44 454 35 392 28V0H655Z" id="g190-89"></path> </g> <g transform="matrix(.013,0,0,-0.013,8.098,0)"> <path d="M381 665C170 665 44 498 44 318C44 125 188 -15 369 -15C552 -15 703 117 703 333C703 534 550 665 381 665ZM359 629C491 629 601 517 601 306C601 114 502 21 390 21C249 21 146 158 146 346S248 629 359 629Z" id="g190-80"></path> </g> <g transform="matrix(.013,0,0,-0.013,21.509,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="32.722183799999996 -10.5932 58.8 14.5316" width="58.8pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,32.772,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,40.614,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.855,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.096,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.337,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,86.59,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>。</span></span>首先,我们把XO XO = ((2,3) (1、4))。然后,<我>x</我><sub><i>id</我></sub>+ XO表明,第二位和第三位<我>x</我><sub><i>id</我></sub>交换,<span class="inline_break"> <svg height="14.5316pt" id="M23" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 34.166 14.5316" width="34.166pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.928,3.132)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.535,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="37.7481838 -10.5932 83.309 14.5316" width="83.309pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,37.798,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.641,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.882,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.122,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.364,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.604,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.845,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,116.098,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>,</span></span>然后,第一位和第四位<我>x</我><sub><i>id</我></sub>交换的结果<span class="inline_break"> <svg height="14.5316pt" id="M24" style="vertical-align:-3.9384pt" version="1.1" viewbox="-0.0498162 -10.5932 34.166 14.5316" width="34.166pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-121"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.202,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,12.796,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.928,3.132)"> <use xlink:href="#g50-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.535,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.5316pt" style="vertical-align:-3.9384pt" version="1.1" viewbox="37.7481838 -10.5932 83.309 14.5316" width="83.309pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,37.798,2.33939e-05)"> <use xlink:href="#g119-1"></use> </g> <g transform="matrix(.013,0,0,-0.013,45.641,-.718)"> <use xlink:href="#g113-53"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.882,-.718)"> <use xlink:href="#g113-52"></use> </g> <g transform="matrix(.013,0,0,-0.013,70.122,-.718)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.364,-.718)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,94.604,-.718)"> <use xlink:href="#g113-54"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.845,-.718)"> <use xlink:href="#g113-55"></use> </g> <g transform="matrix(.013,0,0,-0.013,116.098,2.33939e-05)"> <use xlink:href="#g119-2"></use> </g> </svg>。</span></span>如果XO元素是奇数,最后一点是省略了。</span></p> <h6 id="sec3.2.3">3.2.3。蚁群优化(ACO)算法</h6> <p>高层的战略是基于配电网。有<我>米</我>蚂蚁分布在底部。每只蚂蚁根据信息素决定了下一个顶点在每个路线,能见度和操作员的质量评估函数<我>η</我><sub><i>我</我></sub>:<span class="equation_break" id="EEq24"><span class="left_break" id="L25"></span><span class="middle_break"><span class="center_break" id="M25"> <svg height="36.1428pt" id="M25-1" version="1.1" viewbox="0 0 156.954 36.1428" width="156.954pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B25-1"> <g transform="matrix(.013,0,0,-0.013,0,20.415)"> <path d="M471 401C471 442 455 448 440 448C421 448 389 439 366 424C314 390 233 331 165 242H163L187 345C193 372 197 393 197 409C197 435 189 448 174 448C146 448 80 408 23 349L40 327C64 351 97 373 107 373C115 373 118 366 111 337L29 -4L36 -12C56 -4 83 3 110 9C123 69 136 126 150 172C227 283 336 381 377 381C392 381 396 370 379 298L326 74C290 -77 273 -172 273 -197C273 -219 316 -261 346 -261L353 -246C348 -227 352 -174 374 -66L457 310C467 352 471 381 471 401Z" id="g113-229"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.1,23.547)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.7,20.598)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.21,20.415)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,21.65,20.598)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,29.81,20.415)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,41.07,20.415)"> <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(.013,0,0,-0.013,47.72,20.415)"> <use xlink:href="#g113-229"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,53.82,23.547)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,60.42,20.598)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,64.94,20.415)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,72.28,20.415)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.81,20.415)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.05,20.598)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,96.54,20.415)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,109.98,5.65)"> <use xlink:href="#g50-110"></use> </g> <g transform="matrix(.013,0,0,-0.013,107.08,20.422)"> <use xlink:href="#g119-73"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,111.34,34.548)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,130.5,9.325)"> <path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z" id="g113-74"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,135.22,12.457)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,139.27,12.457)"> <use xlink:href="#g50-107"></use> </g> <rect height="0.65243" width="31.3518" x="121.44" y="16.761"></rect> <g transform="matrix(.013,0,0,-0.013,121.44,29.64)"> <use xlink:href="#g113-85"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,128.62,32.772)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,132.66,32.772)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,139.29,29.823)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,143.8,29.64)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,148.23,29.823)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,153.99,20.415)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="36.1428pt" id="I25" version="1.1" viewbox="0 0 156.95 36.1428" width="156.95pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B25-1"></use> </svg></span></span><span class="right_break" id="R25"> <svg class="label" height="11.44pt" id="M25-2" version="1.1" viewbox="0 0 21.318 11.44" width="21.318pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B25-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.49,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.36,9.26)"> <use xlink:href="#g190-166"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.82,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="36.1428pt" id="IL25" version="1.1" viewbox="0 0 21.4 36.1428" width="21.4pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 12.14)" xlink:href="#B25-2"></use> </svg></span></span>在哪里<我>我</我><sub><i>kj</我></sub>(<我>t</我>)是改善价值ant后(可以是负的)<我>k</我>适用于底部操作符<我>j</我>在一代<我>t</我>,<我>T</我><sub><i>kj</我></sub>(<我>t</我>)是CPU运行时间的计算,和<我>γ</我>是一个值在0和1之间。</p> <p>的方程<我>τ</我><sub><i>ij</我></sub>(<我>t</我>),每个弧上的信息素,如下:<span class="equation_break" id="EEq25"><span class="left_break" id="L26"></span><span class="middle_break"><span class="center_break" id="M26"> <svg height="37.4111pt" id="M26-1" version="1.1" viewbox="0 0 27.368 37.4111" width="27.368pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B26-1"> <g transform="matrix(.013,0,0,-0.013,0,21.683)"> <path d="M471 456L444 459C426 433 414 430 388 430C324 430 270 434 216 434C103 434 51 374 23 338L43 317C96 366 146 380 221 375L154 109C149 86 147 68 147 52C147 4 168 -12 197 -12C240 -12 291 25 334 71L320 96C295 75 268 58 252 58C238 58 227 79 238 138C251 211 272 296 292 372C310 372 332 368 350 368C391 368 421 369 434 371C444 388 455 413 471 456Z" id="g113-241"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,5.43,24.815)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.31,24.815)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.93,21.866)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,18.44,21.683)"> <use xlink:href="#g113-117"></use> </g> <g 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xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,88.06,31.183)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.5,31.365)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,97.03,31.183)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,132.47,21.683)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="85.9797pt" id="I26" version="1.1" viewbox="0 0 163.27 85.9797" width="163.27pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -12.5)" xlink:href="#B26-1"></use> <use transform="matrix(1 0 0 1 13.59 12.49)" xlink:href="#B26-2"></use> <use transform="matrix(1 0 0 1 27.79 48.57)" xlink:href="#B26-3"></use> </svg></span></span><span class="right_break" id="R26"> <svg class="label" height="11.44pt" id="M26-4" version="1.1" viewbox="0 0 21.078 11.44" width="21.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B26-4"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.68,9.25)"> <use xlink:href="#g190-161"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.58,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="85.9797pt" id="IL26" version="1.1" viewbox="0 0 21.16 85.9797" width="21.16pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 37.06)" xlink:href="#B26-4"></use> </svg></span></span>在哪里<我>ρ</我>(0<我><</我><i>ρ</我><i><</我>1)是信息素的蒸发系数,<svg height="12.7178pt" id="M27" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 35.8966 12.7178" width="35.8966pt" xmlns="http://www.w3.org/2000/svg" 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transform="matrix(.013,0,0,-0.013,16.301,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,20.735,0)"> <use xlink:href="#g113-42"></use> </g> </svg>代表了蚂蚁的顺序<我>k</我>选择底部的运营商,<svg height="14.8173pt" id="M29" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 47.017 14.8173" width="47.017pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g121-33"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.24,3.132)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.121,3.132)"> <use xlink:href="#g50-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.556,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.054,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.71,3.132)"> <use xlink:href="#g50-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.858,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,33.356,0)"> <use xlink:href="#g113-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,37.789,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.287,0)"> <use xlink:href="#g113-42"></use> </g> </svg>代表了电弧的次数(<我>我</我>,<我>j</我>)出现在蚂蚁的路线<我>k</我>,<svg height="12.5794pt" id="M30" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 40.0219 12.5794" width="40.0219pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-74"></use> </g> <g transform="matrix(.013,0,0,-0.013,5.567,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.065,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,16.721,3.132)"> <use xlink:href="#g50-108"></use> </g> <g 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xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.63,9.26)"> <use xlink:href="#g190-223"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.66,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="55.8027pt" id="IL33" version="1.1" viewbox="0 0 21.23 55.8027" width="21.23pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 21.97)" xlink:href="#B33-2"></use> </svg></span></span>在哪里<我>H</我>底部的集合操作符,<我>n</我>= |<我>H</我>|是底部运营商的数量,<我>ε</我>和<我>σ</我>可以确保底层启发式算子与表现不佳仍有一个小但非零的概率被选中。如果弧(<我>我</我>,<我>j</我>)是一个非法的弧,<我>光伏</我><sub><i>ij</我></sub>(<我>t</我>)= 0。如果所有底运营商的性能不好,<我>问</我>= 0,并设置<我>光伏</我>值为1,以确保所有底运营商选择概率相等。弧的概率(<我>我</我>,<我>j</我>选择)可以表示为<span class="equation_break" 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<g transform="matrix(.013,0,0,-0.013,74.94,29.604)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.72,20.196)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R34"> <svg class="label" height="11.44pt" id="M34-3" version="1.1" viewbox="0 0 21.298 11.44" width="21.298pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B34-3"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.62,9.25)"> <use xlink:href="#g190-152"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.8,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <h6 id="sec3.2.4">3.2.4。禁忌搜索(TS)算法</h6> <p>TS的高层战略观点如下。分数评估操作的性能。然后,选择一个操作符与更大的分数提高当前迭代过程中的解决方案。每个运营商都有相同的初始评分。当运营商改善当前的解决方案,这个操作符将加1的分数;否则,它将减去1。详细过程如下。</p> <p>首先,首次得分<我>r</我><sub><i>k</我></sub>= 0设置为每个操作符<我>k</我>。每个操作符的分数区间是(<我>r</我><sub>最小值</sub>,<我>r</我><sub>马克斯</sub>];<我>r</我><sub>最小值</sub>和<我>r</我><sub>马克斯</sub>分别代表了最低和最高分数。操作员<我>k</我>这并不是禁忌列表中,选择得分最高的。如果它可以提高目标函数,运营商的分数<我>k</我>将加1。否则,分数减去1,将与固定禁忌禁忌列表的长度。运营商在禁忌列表在出豁免根据第一原则。</p> <h5 id="sec3.3">3.3。验收标准</h5> <p>验收标准是是否新的解处理后的操作符。如果新解决方案总是无条件地取代了父母的解决方案,优化时间会太长了。然而,HH将落入一个本地搜索如果只是保存改进解决方案和省略了劣质的解决方案。其他验收标准包括接受改进的解决方案完全和接受一定比例的劣等方案。</p> <p>在这项研究中,三个提出验收标准:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">改善和相等(IE):接受所有改善供水情况好于没有改进解决方案和拒绝解决方案。</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">所有动作(AM):接受所有解决方案。</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">动态验收标准(DA):如果当前最优解并不太多次更新,这意味着解决方案分为本地搜索,接受的概率应该增加较差的方案,以确保全球搜索。接受概率计算如下:<span class="equation_break" id="EEq29"><span class="left_break" id="L35"></span><span 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</g> <g transform="matrix(.0091,0,0,-0.0091,77.88,12.42)"> <use xlink:href="#g50-117"></use> </g> <rect height="0.65243" width="71.3227" x="23.8" y="14.625"></rect> <g transform="matrix(.013,0,0,-0.013,23.8,28.358)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.82,28.358)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.55,31.49)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.12,28.358)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.65,28.358)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,61.01,23.716)"> <use xlink:href="#g190-99"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,65.71,23.716)"> <path d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z" id="g190-102"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,69.58,23.716)"> <path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z" id="g190-116"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,72.87,23.716)"> <use xlink:href="#g190-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,59.38,31.797)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,76.2,28.358)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,83.48,28.358)"> <use xlink:href="#g113-48"></use> </g> <g transform="matrix(.013,0,0,-0.013,88.84,28.358)"> <use xlink:href="#g113-51"></use> </g> <g transform="matrix(.013,0,0,-0.013,99.22,18.279)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,110.96,9.536)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,123.18,12.668)"> <use xlink:href="#g50-50"></use> </g> <rect height="0.65243" width="17.2123" x="110.96" y="14.625"></rect> <g transform="matrix(.013,0,0,-0.013,113.14,27.504)"> <use xlink:href="#g113-78"></use> </g> <g transform="matrix(.013,0,0,-0.013,129.36,18.279)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="32.2967pt" id="I35" version="1.1" viewbox="0 0 132.33 32.2967" width="132.33pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B35-1"></use> </svg></span></span><span class="right_break" id="R35"> <svg class="label" height="11.44pt" id="M35-2" version="1.1" viewbox="0 0 21.388 11.44" width="21.388pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B35-2"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-193"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.89,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="32.2967pt" id="IL35" version="1.1" viewbox="0 0 21.47 32.2967" width="21.47pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 10.22)" xlink:href="#B35-2"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里<我>f</我><sub><i>t</我>−<我>1</我></sub>是解决方案,<我>f</我><sub><i>t</我></sub>孩子的解决方案,<svg height="16.1013pt" id="M36" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -12.1577 23.9549 16.1013" width="23.9549pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.352,-5.741)"> <use xlink:href="#g58-96"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.139,-5.741)"> <use xlink:href="#g58-99"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.061,-5.741)"> <use xlink:href="#g58-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.437,-5.741)"> <use xlink:href="#g58-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.721,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>是一代的最优解<我>t</我>,<我>米</我>是一个常数,然后呢<我>米</我><sub><i>1</我></sub>的次数<svg height="16.1013pt" id="M37" style="vertical-align:-3.9436pt" version="1.1" viewbox="-0.0498162 -12.1577 23.9549 16.1013" width="23.9549pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,0,0)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.352,-5.741)"> <use xlink:href="#g58-96"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.139,-5.741)"> <use xlink:href="#g58-99"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.061,-5.741)"> <use xlink:href="#g58-113"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,20.437,-5.741)"> <use xlink:href="#g58-114"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.721,3.784)"> <use xlink:href="#g50-117"></use> </g> </svg>还没有更新。</span></span></span></p> <h5 id="sec3.4">3.4。LLH池</h5> <p>本节介绍了九LLH运营商包括四个运营商操作在一个路线,三个运营商运营两个路线,和两个运营商操作仓库的选择:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">2-opt在一个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.001.svgz" name="1811689.fig-inline.001" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">还是选择在一个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.002.svgz" name="1811689.fig-inline.002" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">在一个牧师的路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.003.svgz" name="1811689.fig-inline.003" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(4)</span><span class="list-content">里面一个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.004.svgz" name="1811689.fig-inline.004" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(5)</span><span class="list-content">还是选择两个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.005.svgz" name="1811689.fig-inline.005" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(6)</span><span class="list-content">交换两个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.006.svgz" name="1811689.fig-inline.006" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(7)</span><span class="list-content">交换两个路线<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.007.svgz" name="1811689.fig-inline.007" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(8)</span><span class="list-content">得宝取代<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.008.svgz" name="1811689.fig-inline.008" type="image/svg+xml"></object></span></span><span class="list-item"><span class="list-label">(9)</span><span class="list-content">得宝交换<object data="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig-inline.009.svgz" name="1811689.fig-inline.009" type="image/svg+xml"></object></span></span></span></p> <h5 id="sec3.5">3.5。HH的伪代码</h5> <p>表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab3/" target="_blank">3</一个>列出了HH的伪代码,和图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig3/" target="_blank">3</一个>给出了流程图。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> HH的伪代码。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab3" target="_blank" aria-label="View full page"></a> </div> </div> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-22ec16169c88ee649a72b1bcf68d6b10"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.003.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-22ec16169c88ee649a72b1bcf68d6b10 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-22ec16169c88ee649a72b1bcf68d6b10 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> HH的流程图。</d我v> </div> </div> </div> <h4 id="simulation-experiment-and-analysis">4所示。仿真实验与分析</h4> <p>所有程序编码MATLAB R2018a和一台计算机上执行一个英特尔(R)的核心(TM) i5 - 5200 u CPU @2.20GHZ, 4 GB内存,Windows 7操作系统。</p> <h5 id="sec4.1">4.1。基准</h5> <p>实验数据来自[<一个href="#B8">8</一个>]。表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab4/" target="_blank">4</一个>显示详细的仓库数据和表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab5/" target="_blank">5</一个>包括所有仓库的时间窗口。表中,“本”是基准的名字,“帕拉”是参数的缩写,“盖”的能力,“作”是协调,“成本”是固定成本,开放和“TW”笔记的时间窗口。表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab6/" target="_blank">6</一个>显示车辆的数据。关于客户的数据来自所罗门基准。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 数据仓库。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab4" target="_blank" aria-label="View full page"></a> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab5"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表5</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 仓库的时间窗口。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab5" target="_blank" aria-label="View full page"></a> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab6"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表6</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 车辆的数据。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab6" target="_blank" aria-label="View full page"></a> </div> </div> <h5 id="sec4.2">4.2。时间的速度函数</h5> <p>loannou [<一个href="#B37">37</一个>)首次提出车辆旅行时间计算速度函数在他的研究中对车辆路径问题和旅行时间的道路段的长度和旅行速度,也就是说,旅行速度是一个时间函数。这时间速度函数可以避免跳跃旅行时间并确保的FIFO特性时变网络;即车辆离开第一个到达目的地。道路网络,它可以被认为符合FIFO特性没有超车。</p> <p>在这项研究中,模拟城市道路条件和高峰,我们把道路分成五种类型,把总服务时间分成四个相等的时间。表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab7/" target="_blank">7</一个>显示的值。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab7"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表7</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 时间的速度函数。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab7" target="_blank" aria-label="View full page"></a> </div> </div> <p>道路类型是通过方程(<一个href="#EEq30">30.</一个>),<我>年级</我>(<我>我</我>,<我>j</我>)是道路节点之间的类型<我>我</我>和<我>j</我>和国防部(<我>一个</我>,<我>b</我>剩余的数量<我>一个</我>除以<我>b</我>:<span class="equation_break" id="EEq30"><span class="left_break" id="L38"></span><span class="middle_break"><span class="center_break" id="M38"> <svg height="13.9281pt" id="M38-1" version="1.1" viewbox="0 0 76.684 13.9281" width="76.684pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B38-1"> <g transform="matrix(.013,0,0,-0.013,0,9.308)"> <path d="M861 0V28C774 35 771 41 768 147L759 509C756 612 762 614 851 622V650H681L449 149L221 650H57V622C148 613 153 609 144 479L130 271C123 166 117 123 111 88C104 46 85 34 26 28V0H259V28C192 35 169 42 167 90C166 130 166 173 170 256L185 541H187L411 7H431L675 555H679L683 147C683 41 680 35 598 28V0H861Z" id="g190-78"></path> </g> <g transform="matrix(.013,0,0,-0.013,11.24,9.308)"> <use xlink:href="#g190-112"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.99,9.308)"> <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> </g> <g transform="matrix(.013,0,0,-0.013,27.13,9.491)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.64,9.308)"> <use xlink:href="#g113-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.22,9.308)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,43.37,9.308)"> <use xlink:href="#g113-99"></use> </g> <g transform="matrix(.013,0,0,-0.013,49.47,9.491)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,56.94,9.308)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,67.48,9.308)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,73.72,9.308)"> <use xlink:href="#g113-47"></use> </g> </g> </svg></span></span><span class="right_break" id="R38"> <svg class="label" height="11.44pt" id="M38-2" version="1.1" viewbox="0 0 21.438 11.44" width="21.438pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B38-2"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.25)"> <use xlink:href="#g190-254"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.94,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg></span></span></p> <h5 id="sec4.3">4.3。参数设置</h5> <p>人口规模是100,该算法迭代号码是200,蚂蚁路径长度<我>LP</我>= 11,重量参数<我>α</我>= (0.6,0.7,0.8),<我>β</我>= (0.6,0.7,0.8)<我>γ</我>=(0.6,0.7,0.8),增强系数<我>ɛ</我>= 0.001,<我>σ</我>= 1.001。禁忌搜索算法参数最大分数rankingMax = 5,最低分数是rankingMin = 0,和禁忌长度是tabuLength = 4。</p> <h5 id="sec4.4">4.4。比较分析结合美国卫生和公众服务部的9个</h5> <p>三个高级算法(ACO, ABC和TS)和三个验收标准(点,即和DA)可以形成九个美国卫生和公众服务部叫ABC +点,美国广播公司(ABC) +即ABC + DA算法+点,ACO +,即算法+哒,TS +点,TS + IE, TS + DA这九HHs解决MOGTDLRP的基准。结果可以反映了算法的性能。相关数据如下:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">目标函数:<我>f</我><sub><i>1</我></sub>最低总成本。</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">实例:C1 (C101-C109)。</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">比较参数:偏差百分比<我>理查德·道金斯</我>获得,<span class="equation_break" id="EEq31"><span class="left_break" id="L39"></span><span class="middle_break"><span class="center_break" id="M39"> <svg height="30.9338pt" id="M39-1" version="1.1" viewbox="0 0 124.364 30.9338" width="124.364pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B39-1"> <g transform="matrix(.013,0,0,-0.013,0,18.279)"> <use xlink:href="#g113-83"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.5,18.279)"> <use xlink:href="#g113-69"></use> </g> <g transform="matrix(.013,0,0,-0.013,26.09,18.279)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,38.55,9.288)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.27,12.42)"> <path d="M722 32C646 41 636 48 622 116L544 496L509 667L472 658L153 123C106 45 93 42 27 32L18 0H259L268 32C178 40 172 48 204 107L272 233H509C523 180 533 137 540 96C548 50 546 39 466 32L457 0H714L722 32ZM502 283H299L448 547H450L502 283Z" id="g50-66"></path> </g> <g transform="matrix(.013,0,0,-0.013,55.17,9.288)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,65.7,9.288)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,72.43,12.42)"> <path d="M460 334C460 396 434 451 378 451C330 451 241 408 148 300H146L237 679C241 697 241 710 232 710C213 710 153 684 67 675L66 646H95C141 646 145 642 134 595L39 170C23 97 31 54 46 33C64 8 100 -12 137 -12C178 -12 234 3 298 43C391 101 460 222 460 334ZM371 320C371 204 316 89 248 51C230 41 208 37 192 37C143 37 102 72 119 166C124 194 129 215 135 235C202 323 298 392 335 392C353 392 371 372 371 320Z" id="g50-99"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,76.78,12.42)"> <path d="M398 365C398 411 356 451 297 451C250 451 198 430 151 397C65 336 24 230 24 139C24 14 97 -12 148 -12C198 -12 284 7 373 104L355 130C306 84 246 53 198 53C132 53 111 109 111 163V189C209 211 398 261 398 365ZM317 351C317 308 273 262 117 225C134 338 189 383 221 399C230 404 249 407 263 407C295 407 317 389 317 351Z" id="g50-102"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,80.62,12.42)"> <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> <g transform="matrix(.0091,0,0,-0.0091,84.25,12.42)"> <use xlink:href="#g50-117"></use> </g> <rect height="0.65243" width="49.4882" x="38.55" y="14.625"></rect> <g transform="matrix(.013,0,0,-0.013,52.15,27.504)"> <use xlink:href="#g113-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,58.87,30.636)"> <use xlink:href="#g50-99"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,63.23,30.636)"> <use xlink:href="#g50-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,67.07,30.636)"> <use xlink:href="#g50-116"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,70.7,30.636)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.013,0,0,-0.013,92.14,18.279)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,102.68,18.279)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.92,18.279)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,115.16,18.279)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,121.4,18.279)"> <use xlink:href="#g113-45"></use> </g> </g> </svg> <svg class="alt_equation" height="30.9338pt" id="I39" version="1.1" viewbox="0 0 124.36 30.9338" width="124.36pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B39-1"></use> </svg></span></span><span class="right_break" id="R39"> <svg class="label" height="11.44pt" id="M39-2" version="1.1" viewbox="0 0 19.078 11.44" width="19.078pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B39-2"> <g transform="matrix(.013,0,0,-0.013,0,9.25)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.25)"> <use xlink:href="#g190-232"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.19,9.25)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.58,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="30.9338pt" id="IL39" version="1.1" viewbox="0 0 19.16 30.9338" width="19.16pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 9.54)" xlink:href="#B39-2"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在哪里<我>f</我><sub><i>一个</我></sub>是最好的算法获得的结果<我>一个</我>和<我>f</我><sub>最好的</sub>结果的平均值的九个美国卫生和公众服务部。</span></span></span></p> <p>九流的美国卫生和公众服务部:<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">步骤1:由IMTT算法生成初始种群,计算目标函数得到初始S11父亲解决方案,S21、S31</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第二步:设置相关算法参数</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">步骤3:选择的运营商LLH根据通过计算目标函数得到孩子解决方案S12, S22, S32</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">步骤4:确定是否接受当前的孩子解决方案根据验收标准</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第五步:更新相关参数</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">第六步:如果算法终止条件满足,算法结束;否则,进入步骤3</span></span></span></p> <p>C101-C109通过九个美国卫生和公众服务部的结果表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab8/" target="_blank">8</一个>。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab8"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表8</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 结果C101-C109得到9美国卫生和公众服务部。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab8" target="_blank" aria-label="View full page"></a> </div> </div> <p>理查德·道金斯在表的最大价值<一个href="//www.newsama.com/journals/aor/2022/1811689/tab8/" target="_blank">8</一个>是1.95,这表明解决方案获得的这些九算法不是很不同。我们继续分析算法与博达算法的性能。每个HH有1到9的分数据RD的值。与最小的RD算法得到9分,与第二小的RD算法得到8分,等等。图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig4/" target="_blank">4</一个>显示了九个美国卫生和公众服务部的分数。图中的横坐标1 - 9对应9美国卫生和公众服务部。图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig4/" target="_blank">4</一个>是一个饼状图的数量9组合算法获得最优解的C1的例子;的次数<我>理查德·道金斯</我>等于0。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-cb244692b9c6985bd000da70d9f8cc20"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.004.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-cb244692b9c6985bd000da70d9f8cc20 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.004_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-cb244692b9c6985bd000da70d9f8cc20 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 美国卫生和公众服务部得分C1的条形图。</d我v> </div> </div> </div> <p>通过数据表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab8/" target="_blank">8</一个>和数字<一个href="//www.newsama.com/journals/aor/2022/1811689/fig4/" target="_blank">4</一个>和<一个href="//www.newsama.com/journals/aor/2022/1811689/fig5/" target="_blank">5</一个>,众所周知,美国广播公司+ DA组合算法以80分得分最高,其次是配电网+ DA = 69分,第三名是TS + DA以67的高分。饼图显示,美国广播公司(ABC)的次数+ DA算法获得最优解占47.06%;ACO +哒,占17.65%;TS + DA占23.53%;ABC + IE和ACO + IE占5.88%,分别和其他组合无法得到最优解。在美国广播公司高层战略下,总分是30 + 48 + 80 = 158;配电网高级策略是27 + 45 + 69 = 141分;TS高层战略是34 + 59 + 67 = 160分。是验收标准的得分30 + 27 + 34 + 91,即是48 + 45 + 59 = 152,达是80 + 69 + 67 = 16分。三种策略的得分几乎没有差异,但是差异解决方案的验收标准很大。 AE accepts all solutions, which is easy to cause too divergent search range and difficult to find the optimal solution. IE only accepts noninferior solutions, which is easy to fall into the trap of local optimization. DA accepts all noninferior solutions and conditionally selects inferior solutions. This method gets a higher score because of which it takes into account the advantages of AE and IE and avoid their shortcomings. In general, the ABC + DA is the best combined HH algorithm in the C1 case.</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-5567dae221ae655316ccf258027dc9c7"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.005.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-5567dae221ae655316ccf258027dc9c7 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.005_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-5567dae221ae655316ccf258027dc9c7 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 美国卫生和公众服务部得分C1的饼图。</d我v> </div> </div> </div> <h5 id="sec4.5">4.5。分析单目标优化问题</h5> <p>MOGTDLTP是一个多目标模型,其中包括三个目标:总成本,旅行时间和燃料消耗。不同的优化目标导致不同的配送路线。在本节中,区别不同的单目标优化问题的解决方案进行了探讨。<span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">实例:RC2 (RC201-RC208)。</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">算法:ABC-DA</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">单一的目的:<我>f</我><sub><i>1</我></sub>最低总成本,<我>f</我><sub><i>2</我></sub>,最低交货时间,<我>f</我><sub><i>3</我></sub>,最低燃油消耗。</span></span></span></p> <p>结果在表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab9/" target="_blank">9</一个>。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab9"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表9</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 三个优化目标的结果。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab9" target="_blank" aria-label="View full page"></a> </div> </div> <p>在表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab9/" target="_blank">9</一个>OBJ客观,TC是总成本,TI旅行时间,和FC燃料消耗;<我>理查德·道金斯</我><sub><i>我</我></sub>百分比计算的区别是<span 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</svg></span></span></p> <p>结果表明,不同优化目标下的最优解是不同的。相比<我>f</我><sub><i>2</我></sub>和<我>f</我><sub><i>3</我></sub>目标,与获得的总成本<我>f</我><sub><i>1</我></sub>目标是最低,但交货时间和燃料消耗最低。的值<我>理查德·道金斯</我>显示当前值之间的偏差百分比和最小值。值越大,误差越大。当以旅行时间为优化目标,<我>理查德·道金斯</我>价值获得最大的7倍,这表明当以旅行时间为优化目标,虽然总旅行时间得到了优化,总成本和燃料消耗很高。因此,它是不合适的旅行时间作为一个单独的优化目标。当<我>f</我><sub><i>1</我></sub>,总成本优化目标;的平均值<我>理查德·道金斯</我>是6.62,什么时候<我>f</我><sub><i>3</我></sub>,燃料消耗是优化目标;的平均值<我>理查德·道金斯</我>是5.30。因此,根据获得的解决方案<我>f</我><sub><i>3</我></sub>目的是更好的。</p> <h5 id="sec4.6">4.6。单目标和多目标之间的比较</h5> <span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content">实例:RC201 RC208</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">优化目标:<我>f</我><sub><i>1</我></sub>最低总成本,<我>f</我><sub>2</sub>旅行时间最小,<我>f</我><sub><i>3</我></sub>,最低油耗,<我>莫</我>多目标。</span></span><span class="list-item"><span class="list-label"></span><span class="list-content">算法:美国广播公司(ABC) +哒</span></span></span> <p>结果如表所示<一个href="//www.newsama.com/journals/aor/2022/1811689/tab10/" target="_blank">10</一个>。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab10"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表10</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 四的结果最优的目标。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab10" target="_blank" aria-label="View full page"></a> </div> </div> <p>在表<一个href="//www.newsama.com/journals/aor/2022/1811689/tab10/" target="_blank">10</一个>,MO-TC与最低总成本的解决方案,MO-TI是最低的解决方案交付时间,和MO-FC燃油消耗最小的解决方案在帕累托解集。</p> <p>单目标函数RC201,最低总成本是180116,最低旅行时间是2335.3,最低油耗是1548.9。RC201的多目标函数的最小总成本是180155 > 180116,偏差<我>理查德·道金斯</我>= 0.02,最低旅行时间是2332 < 2335.3,和偏差<我>理查德·道金斯</我>=−0.14;最低燃油消耗是1641 > 1548.9,和偏差<我>理查德·道金斯</我>= 5.95。单目标函数RC208,最低总成本是179485,最小的旅行时间是1604.1,最小的油耗是945.14。RC208的多目标函数的最小总成本是179439 < 179485,偏差<我>理查德·道金斯</我>旅行时间=−0.02,最低是1599 < 1604.1,偏差<我>理查德·道金斯</我>=−0.32;最低燃油消耗是915 < 945.14,偏差<我>理查德·道金斯</我>=−3.2。四个六<我>理查德·道金斯</我>值小于0,表明结合成本、时间和燃料消耗下多目标函数比,在单目标函数。图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig6/" target="_blank">6</一个>的曲线是RC201和RC208的价值观相结合,分别。在图中,实线是曲线通过单目标和多目标下的虚线是合并后的曲线。下面的虚线大多是实线,这也表明,合并后得到的多目标函数值更好。</p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-fafeb07f97807bc08968ca06face5acd"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.006.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-fafeb07f97807bc08968ca06face5acd partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/thumbnails/1811689.fig.006_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-fafeb07f97807bc08968ca06face5acd partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图6</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 合并后的值的曲线RC201 RC208。</d我v> </div> </div> </div> <h5 id="sec4.7">4.7。所有基准测试结果和分析</h5> <p>在本节中,我们使用ABC + DA算法来解决所有基准测试和分析结果。迭代的数量设置为200。所有的结果都在桌子上<一个href="//www.newsama.com/journals/aor/2022/1811689/tab11/" target="_blank">11</一个>“MC”的最低总成本,“太”是最小的旅行时间,“曼氏金融”是最低燃油消耗。“交流”、“对焦”和“在”,分别代表的平均成本、平均油耗,平均时间整个帕累托解集。“AV”意味着启动车辆的平均数量。</p> <div class="floats-partial-section partial-other-wrapper" data-section="tab11"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表11</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/tab11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> C1∼C2的结果。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/aor/2022/1811689/tab11" target="_blank" aria-label="View full page"></a> </div> </div> <p>表中的数据<一个href="//www.newsama.com/journals/aor/2022/1811689/tab11/" target="_blank">11</一个>显示如下:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">一般来说,由于高质量的解决方案,解决方案的数量每基准并不是一个巨大。</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">因为仓库的成本,MCs的值太大,表明仓库物流成本成本的比例大于燃料消耗和旅行时间成本的比率。然而,随着客户数量的增加,燃料消耗和旅行时间成本增加,主要的变化选择仓库。</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">更多的车辆需要启用参与分配以满足客户时间窗口的需要。以RC201案为例,所有客户的总需求是1724和车辆的容量是1000。从理论上讲,只有两辆车需要启用,但在MOGTDLRP,三辆车需要启用。由于使用大容量车辆数量的多目标最优解的C2, R2和RC2比相应的C1, R1, RC1。帕累托最优解决方案C1的平均数为5.78,虽然C2是10.75,这是关于C1的两倍。R1的帕累托最优解的平均数是6.42;而R2为6.72,大于6.42。的平均数为5.75 RC1是帕累托最优解;在RC2 7.5,大于5.75。从实用的角度来看,物流公司想使用更少的车辆,所以在设计算法时,汽车的数量是解决方案的优先条件。 On the contrary, using fleets of different capacities is also an effective way for logistic networks to achieve a low-carbon economy.</span></span><span class="list-item"><span class="list-label">(4)</span><span class="list-content">数据<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(一)-<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(c)的二维投影C201总成本和旅行时间,旅行时间和燃料消耗、总成本和燃料消耗。图<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(d)的三维图C201的解决方案。成本和燃料消耗量之间的关系是线性的,因为燃料消耗总成本的一部分。数据<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(一),<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(b)<一个href="//www.newsama.com/journals/aor/2022/1811689/fig7/" target="_blank">7</一个>(d)溶液分布相对均匀,表明高质量的解决方案。</span></span></span></p> <div class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-d25f57364de56b6336e87d6c7605716f"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.007a.jpg"> <br> <strong>(一)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.007b.jpg"> <br> <strong>(b)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.007c.jpg"> <br> <strong>(c)</strong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)" src="https://static.hindawi.com/articles/aor/volume-2022/1811689/figures/1811689.fig.007d.jpg"> <br> <strong>(d)</strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-d25f57364de56b6336e87d6c7605716f partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" 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aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图7</span> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/aor/2022/1811689/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> C201的解决方案。</d我v> </div> </div> </div> <h4 id="conclusion-and-outlook">5。结论和展望</h4> <p>在这项研究中,我们提出了MOGTDLRP模型有三个目标,一个依赖于时间的速度函数将一天划分为四个时期五路类型和定义。五十六实例得到基于所罗门基准指相关的文献。在每个基准测试中,有100个客户的坐标,要求,和时间窗和10个仓库的坐标,也被认为是能力,和时间窗口。基准是由九个有效解决美国卫生和公众服务部IMTT获得的高质量的初始解。结果表明,MOGTDLRP能有效地减少燃料消耗和总成本。</p> <p>根据实验结果的分析,本研究可以得到以下结论和建议:<span class="list"><span class="list-item"><span class="list-label">(1)</span><span class="list-content">拟议的美国卫生和公众服务部在解决MOGTDLRP高精度模型,可以获得高质量的解决方案在合理的计算时间。MOGTDLRP模型可以有效地降低物流成本,燃料消耗和旅行时间。</span></span><span class="list-item"><span class="list-label">(2)</span><span class="list-content">因素如客户分销和客户时间窗口应该是一样的问题,物流公司需要注意仓库成本。</span></span><span class="list-item"><span class="list-label">(3)</span><span class="list-content">异构的舰队可以减少分销成本。</span></span><span class="list-item"><span class="list-label">(4)</span><span class="list-content">交通限速影响交货时间和车辆燃料消耗,所以最近的交货计划并不一定交货时间或燃料消耗。</span></span></span></p> <p>总之,时间依赖网络更接近现实交通网络比静态网络。然而,从节点到节点的独特之处在于时间依赖网络。然而,有多个路由节点之间在真实道路网络。此外,实际的城市道路网络是复杂的,在同一条公路上的车辆的速度在不同的时间段是随机波动的。同时,车辆从一个节点移动到另一个时,它往往通过多个节点,节点之间的路线并不是唯一的。因此,如何解决绿色位置路径的优化问题的随机道路网络和多节点道路网络是未来的研究方向。</p> <h4 id="data-availability">数据可用性</h4> <p>使用的数据来支持本研究的结果包括在本文中。</p> <h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者宣称没有利益冲突。</p> <h4 id="authors’-contributions">作者的贡献</h4> <p>张Hua-xing概念化的研究;Chun-miao张策划数据;Chun-miao张正式进行分析;Hua-xing张资金进行收购;张Hua-xing调查研究;张Chun-miao开发方法论;张Hua-xing管理项目;张Hua-xing收集资源;Chun-miao张先生与软件;Hua-xing张写了初稿;Hua-xing张审查和编辑。</p> <h4 id="acknowledgments">确认</h4> <p>这项工作是支持中国的浙江省自然科学基金,格兰特Y18F030036之下。</p> 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Prastacos“贪婪的先行的时间窗的车辆路径问题的启发式,”<我>运筹学学会》杂志上</我>,52卷,不。5,523 - 537年,2001页。</p>视图: <a href="https://doi.org/10.1057/palgrave.jors.2601113" target="_blank" rel="noreferrer">出版商的网站</一个> <span class="sep">|</span> <a href="https://scholar.google.com/scholar_lookup?title=A%20greedy%20look-ahead%20heuristic%20for%20the%20vehicle%20routing%20problem%20with%20time%20windows&author=G.%20Ioannou&author=M.%20Kritikos&author=G.%20Prastacos&publication_year=2001" target="_blank" rel="noreferrer">谷歌学术搜索</一个> </div></li> </ol> </div> <h4 class="copyright-title" id="copyright">版权</h4> <div class="copyright-body"> 版权©2022张花心和Chun-Miao张。这是一个开放的分布式下文章<一个rel="license" href="http://creativecommons.org/licenses/by/4.0/">知识共享归属许可</一个>,它允许无限制的使用、分配和复制在任何媒介,提供最初的工作是正确引用。</d我v> <div id="related-articles"></div> </div> </div> <div class="ant-col ThreeColumnLayout_rightColumn__b_MuL"> <div> <div> <div class="ArticleRightSection_articleRightSection__rG8Zh"> <div class="ArticleToolbar_articleToolbar__8fsAH"> <a 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