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class="articleHeader__authors_author">燕郊王<年代up>1</年代up></span> <span class="articleHeader__authors_author">和<年代trong>Jieru汉</年代trong><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/0000-0003-4577-7799" 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>1</年代up></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:</年代trong> <span>Fangqing温</年代pan> </div> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2021年9月01</年代pan> </div> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2021年9月30日</年代pan> </div> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>2021年10月15日</年代pan> </div> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4> <p>全面分析柔性工作车间调度问题的特点(FJSSP),需要等实际调度过程中的动态因素的到来和离开工作,机器的故障和恢复同时考虑进去,并建立一个新的动态多目标数学模型。松鼠搜索算法(SSA)为核心的发展战略,并结合多目标框架和动态处理技术解决建立数学模型。实验结果表明,本文提出的数学模型可以有效地解决柔性作业车间调度问题。与其他数学模型相比,本文建立的数学模型能保持更好的平衡之间的效率和稳定性。</p><年代pan class="end-abs"></span> <h4 id="introduction-to-flexible-job-shop-scheduling-problem">1。介绍柔性工作车间调度问题</h4> <p>柔性工作车间调度问题的目的(FJSSP)是合理分配机器到达工厂的所有流程处理,以实现一个或多个目标有关运行效率和系统的稳定性<a href="#B1">1</a>]。FJSSP是一个复杂的组合优化问题。增加的计算量成倍增加机器的数量和工作。智能进化算法不限制搜索空间的约束,不依赖于其他辅助知识,他们只需要确定优化目标和相应的适应度函数的搜索方向,适合求解大规模优化问题,如极化估计,估计,合作定位(<a href="#B2">2</a>- - - - - -<a href="#B6">6</a>]。许多学者已经使用群集智能进化算法,包括传统的智能优化算法,如遗传算法(<a href="#B7">7</a>),新的智能进化算法,如重组青蛙跳算法,蜂群蜘蛛优化算法,等等,来解决FJSSP大规模组合优化问题。调度计划的完成时间最小,FJSSP的初始优化目标,这是最常见的优化目标<a href="#B8">8</a>- - - - - -<a href="#B10">10</a>];然而,实际的工作环境往往是动态的,也就是说。,new events may occur at any time, such as the arrival of new jobs, the departure of completed jobs, and the sudden breakdown of machines. Obviously, the best scheduling scheme matching the original system state is unsuitable for the new working environment. Rescheduling the jobs in the new environment is necessary. For the scheduling scheme in the new environment, if the highest efficiency is the goal, the machine with the highest efficiency for the process to be chosen may cause the load imbalance of the system, and the new scheduling scheme may have a great difference from the historical scheduling scheme, which will affect the system stability. If the system stability is the optimization objective, the gap between new and old scheduling schemes can be reduced, but the processes needed may not be performed by the most efficient machines corresponding to them, resulting in low operation efficiency. In summary, flexible job shop scheduling should consider the efficiency and stability of the system at the same time to ensure the scheduling efficiency after changing the working environment, and a mutual exclusion relationship exists between the two. Scholars have proposed new flexible job shop scheduling methods after environmental change.</p><p>例如,Lei,詹森,分别针对完成最短的时间和最好的鲁棒性,和解决机器故障的任务调度问题<a href="#B11">11</a>,<a href="#B12">12</a>]。Chryssolouris和张完成时间和延迟时间的加权和作为生产调度方案的优化目标(<a href="#B13">13</a>,<a href="#B14">14</a>),虽然运行效率和系统的稳定性被认为是在优化过程;解决问题时,多个目标可以转化为单一目标通过使用加权求和方法,和合理的体重值不能设置依照实际情况的环境;因此,最合适的调度方案很难生成,普遍性是弱。黄Zhiqing等人FJSSP问题建立一个能源消耗模型和改进遗传算法与粒子群优化和模拟退火算法。完成时间和能源消耗是作为优化目标,同时优化和效率和稳定性。然而,该模型忽略了区别新旧调度方案之前和之后的机器故障,在故障时系统的稳定性是可怜的(<a href="#B15">15</a>]。FJSSP史等人解决问题通过使用离散multi-population入侵杂草优化算法、自适应变异和域搜索策略以提高算法的搜索能力和使用滚动窗口的概念来安排系统运行在特定的时间。从本质上讲,静态FJSSP问题分为几个时期,并不适用于动态情况的任务序列随时离开<a href="#B16">16</a>]。陈et al .,延迟和偏差作为效率指标和稳定性指标,分别。他们用NSGA-II同时优化两个目标。偏差度的评估是重新安排计划的时候失败。系统的稳定性在一定程度上改善了之前和之后的机器故障,但它并不适用于动态环境中操作到达任何时间(<a href="#B17">17</a>]。</p><p>总之,首先,FJSSP自然动力学。当建立柔性工作车间调度模型,工作效率通常是衡量处理任务的完成时间,以及系统的稳定性是衡量机器车间的负荷状态。尽管现有的数学模型可以应付一些工作环境的变化,他们仍然不能处理任务序列的随机到达,完成任务的离开,突然机器故障和修复失败的机器在同一时间。其次,灵活的车间的效率和稳定系统是互相排斥的;因此,在数学的本质,FJSSP是一个动态的多目标优化问题(<a href="#B18">18</a>]。相比之下的方法将多目标转化为单目标通过加权求和,多目标进化算法可以同时考虑效率和稳定性,这是解决柔性作业车间调度的主要方法。因此,多目标算法的性能也是解决DJSSP的关键。为了得到一个调度方案的效率和稳定在动态环境下,有必要建立一个数学模型符合DFJSSP的动态特性和动态多目标进化算法具有优良的性能。</p><p>基于上述分析,本文提出了一种基于动态多目标柔性车间调度方法松鼠算法。的主要创新如下:首先,在考虑一个实际的车间环境的变化,包括任务序列的随机到达、出发完成任务,突然机器故障,和失败的修复机,提出了一种新的动态多目标柔性车间调度模型,完成时间,负载平衡(磅),和故障延期偏差为目标函数,以解决工作效率和系统的稳定性。第二,为了有效地解决上述建立的数学模型,一种改进的动态多目标松鼠搜索算法提出了基于分解。采用操作和机器编码个体编码和提高个人进化策略的SSA根据FJSSP的特点。此外,一个新的动态处理技术包括建立和更新外部人口和人口的初始化的时候重新安排,提出了再生可以快速响应变化的初始种群在重新安排时间。</p><p>其余部分安排如下:部分<a href="#sec2">2</a>介绍了数学模型的建立过程的动态多目标柔性车间调度问题;第三部分介绍了柔性车间调度方法的原理基于动态多目标松鼠搜索算法;第四部分给出了实验结果和分析;第五部分总结了整个论文。</p><h4 id="the-establishment-of-a-mathematical-model-for-dynamic-multi-objective-flexible-job-shop-scheduling-problem">2。建立一个数学模型对动态多目标柔性作业车间调度问题</h4> <h5 id="sec2.1">2.1。柔性工作车间调度问题的描述</h5> <p>柔性工作车间调度问题可以描述为:<我>n</我>工作<我>J</我>={<我>J</我><年代ub>1</年代ub>,<我>J</我><年代ub>2</年代ub><i>,…</我>,<我>J</我><年代ub><i>n</我></年代ub>},每个操作<我>J</我><年代ub><i>我</我></年代ub>是由<我>n</我><年代ub><i>我</我></年代ub>流程和多目标的数量每操作步骤<我>n</我><年代ub><i>我</我></年代ub>。的处理时间<我>t</我><年代ub><i>ij</我></年代ub>每个进程有一定的分布。FJSSP的目的是为每个进程分配操作机器,所以到达车间的过程在一定的顺序加工,加工完成后,操作机器离开车间。一个新的数学模型建立了柔性工作车间调度问题,实现柔性工作车间动态调度。首先,介绍了变量参与柔性工作车间调度问题如下:<年代pan class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>t</我><年代ub>1</年代ub>:延期偿还周期时间<我>t</我>=<我>nt</我><年代ub><i>l</我></年代ub>(<我>n</我>是一个正整数),更新车间的状态,包括新任务,机器空闲时间等。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>t</我><年代ub><i>b</我></年代ub>:机器坏了的时候。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>t</我><年代ub><i>r</我></年代ub>:从机械故障中恢复的时间。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>平均故障间隔</我>:平均故障时间。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>Mttr</我>:平均恢复时间。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>J</我><年代ub><i>我</我></年代ub>:任务<我>我</我>到达工厂。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>N</我><年代ub><i>l</我></年代ub>:数量的任务的时间之前到达工厂<我>nt</我><年代ub>l</年代ub>。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>n</我><年代ub>我</年代ub>:数量的过程。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>O (i, j)</我>:<我>j</我>任务的过程<我>J</我><年代ub><i>我</我></年代ub><i>。</我></年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>米</我>:在车间机器的总数。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>米</我>:在车间的机器,<我>米</我>={<我>米</我><年代ub>1</年代ub>,<我>米</我><年代ub>2</年代ub>、…<我>米</我><年代ub>米</年代ub>}。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>M (i, j)</我>:一组机器可以处理<我>O(我,j)。</我></年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>F (i, j)</我>:机器替代机组中包含的数量<我>米(我,j)</我>的<我>O(我,j)</我>、灵活程度。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>t (i, j, k)</我>的处理时间<我>O(我,j)</我>在机<我>米</我><年代ub>k</年代ub>。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>年代</我><年代ub><i>我</我></年代ub>:工作的开始时间<我>我</我>。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>C</我><年代ub><i>我</我></年代ub>:工作的完成时间<我>我</我>。<我>年代(我,j)</我>:开始时间的过程<我>O(我,j)</我>。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>C (i, j)</我>:过程的完成时间<我>O(我,j)</我>。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>C</我><年代ub>k_last</年代ub>:<我>O(我,j)</我>处理<我>米</我><年代ub>k</年代ub>最后的完成时间过程的<我>米</我><年代ub>k</年代ub>前处理<我>O(我,j)</我>就开始了。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>S (i, j)</我><年代pan class="nowrap"> <svg height="10.1524pt" id="M1" style="vertical-align:-0.04990005pt" version="1.1" viewbox="-0.0498162 -10.1025 6.17869 10.1524" width="6.17869pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.0091,0,0,-0.0091,0,-5.741)"> <path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 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class="list-content"><i>我</我><年代ub><i>k</我></年代ub>:最早的机器可用时间<我>米</我><年代ub><i>k</我></年代ub>;</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>l</我><年代ub><i>k</我></年代ub>:机器的总工作时间<我>米</我><年代ub><i>k</我></年代ub>;</年代pan></span></span></p> <p>柔性工作车间任务调度要求:<年代pan class="list"><span class="list-item"><span class="list-label">(1)</年代pan><span class="list-content">在最初的时候,所有的机器都是可用的,例如,<我>t</我>=0,<我>我</我><年代ub>k</年代ub>= 0。</年代pan></span><span class="list-item"><span class="list-label">(2)</年代pan><span class="list-content">这一过程只能由一台机器处理,也就是说,<我>O(我,j)</我>只能处理一台机器<我>米(我,j)</我>在一个时间。</年代pan></span><span class="list-item"><span class="list-label">(3)</年代pan><span class="list-content">一台机器一次只能处理一个进程。</年代pan></span><span class="list-item"><span class="list-label">(4)</年代pan><span class="list-content">之间不存在优先约束不同的任务。</年代pan></span><span class="list-item"><span class="list-label">(5)</年代pan><span class="list-content">流程在同一任务没有优先级,也就是说,<我>O(我,j- 1)</我>只能处理<我>O(我,j)</我>后加工。</年代pan></span><span class="list-item"><span class="list-label">(6)</年代pan><span class="list-content">所有进程没有优先考虑同一台机器上,也就是说,这台机器之前必须处理当前进程可以处理下一个过程。</年代pan></span><span class="list-item"><span class="list-label">(7)</年代pan><span class="list-content">机器没有故障时,操作系统将在一个固定的周期根据操作的完成和到达。当机器坏了,无论执行过程的故障机还是要执行的过程很快,在重新安排计划,所有剩下的过程对应于故障机由nonfault安排执行机器。修理机器故障后是固定的,可以继续执行作业调度。</年代pan></span></span></p> <p>nt的周期重新安排时间<年代ub><i>l</我></年代ub>重新安排时间<我>t</我><年代ub><i>b</我></年代ub>和要处理的任务延期的恢复时间<我>t</我><年代ub><i>r</我></年代ub>,如果程序<我>O(我,j)</我>是上处理机器<我>米</我><年代ub><i>k</我></年代ub>,然后开始时间<我>年代(我,j)</我>和结束时间<我>C(我,j)</我>的<我>O(我,j)</我>分别是公式所示(<a href="#EEq1">1</a>)和(<a href="#EEq2">2</a>)。如果一开始时间和结束时间<我>C</我><年代ub><i>我</我></年代ub>的<我>J</我><年代ub><i>我</我></年代ub>所示公式(<a href="#EEq2">3</a>)和(<a href="#EEq2">4</a>),分别。<年代pan class="equation_break" id="EEq1"><span class="left_break" id="L3"></span><span class="middle_break"><span class="center_break" id="M3"> <svg height="36.3978pt" id="M3-1" 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style="vertical-align:-3.29107pt" version="1.1" viewbox="99.07918380000001 -9.28833 34.298 12.5794" width="34.298pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,99.129,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,107.748,3.132)"> <use xlink:href="#g50-108"></use> </g> <rect height="0.3985" width="2.74024" x="112.928" y="2.73319"></rect> <g transform="matrix(.0091,0,0,-0.0091,115.668,3.132)"> <path d="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g190-109"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,117.998,3.132)"> <path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 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transform="matrix(.013,0,0,-0.013,158.28,57.468)"> <use xlink:href="#g119-8"></use> </g> <g transform="matrix(.013,0,0,-0.013,165.54,57.468)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="61.4457pt" id="I5" version="1.1" viewbox="0 0 170.75 61.4457" width="170.75pt" 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="#B5-1"></use> <use transform="matrix(1 0 0 1 0 0)" xlink:href="#B5-3"></use> <use transform="matrix(1 0 0 1 2.17 0)" xlink:href="#B5-5"></use> </svg></span></span><span class="right_break" id="R5"> <svg class="label" height="11.44pt" id="M5-2" version="1.1" viewbox="0 0 15.038 11.44" width="15.038pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B5-2"> <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)"> <path d="M411 139C381 76 368 73 314 73H129L267 224C351 317 400 380 400 469C400 574 322 635 233 635C176 635 128 610 98 576L40 495L63 476C89 515 130 568 198 568C274 568 316 519 316 436C316 347 251 264 191 192C142 134 85 76 30 21V0H403C415 45 425 89 438 131L411 139Z" id="g190-243"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.54,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M5-4" version="1.1" viewbox="0 0 14.868 11.44" width="14.868pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B5-4"> <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)"> <path d="M269 381C298 400 325 421 340 436C360 455 370 476 370 504C370 579 313 635 223 635H222C170 635 123 610 95 579L52 516L72 497C95 533 136 577 193 577C245 577 286 546 286 482C286 408 218 369 127 339L133 314C149 319 174 325 197 325C254 325 324 285 324 192C325 83 266 39 201 39C143 39 103 68 78 91C70 98 62 97 54 91C45 84 33 71 32 58C30 46 34 35 48 22C61 10 102 -12 148 -12C216 -12 410 57 410 225C410 298 357 362 269 379V381Z" id="g190-232"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.37,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="label" height="11.44pt" id="M5-6" version="1.1" viewbox="0 0 15.458 11.44" width="15.458pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B5-6"> <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)"> <path d="M465 179V225H369V632H330C227 497 124 346 29 205V179H289V107C289 37 284 33 198 26V0H454V26C374 33 369 37 369 107V179H465ZM289 225H92C156 335 222 430 287 520H289V225Z" id="g190-166"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.96,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="61.4457pt" id="IL5" version="1.1" viewbox="0 0 15.52 61.4457" width="15.52pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 1.35)" xlink:href="#B5-2"></use> <use transform="matrix(1 0 0 1 0 24.79)" xlink:href="#B5-4"></use> <use transform="matrix(1 0 0 1 0 48.22)" xlink:href="#B5-6"></use> </svg></span></span></p> <p>调度的例子(<a href="#B19">19</a>]说明有一个增强的柔性工作车间调度规则的理解。如表所示<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>,“/”意味着这个过程不能在相应的机器上执行。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>是一个甘特图对应于一个特定的调度计划数据表<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>。</p><d我v 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 6个任务调度的例子。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2021/6062689/tab1" 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-705f41a699e543a4f16e4ba0140b597f"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-705f41a699e543a4f16e4ba0140b597f partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-705f41a699e543a4f16e4ba0140b597f 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 调度计划1所示。</d我v> </div> </div> </div> <p>如图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>,当<我>t</我>=0,<我>O</我><年代ub>31日</年代ub>,<我>O</我><年代ub>41</年代ub>,<我>O</我><年代ub>21</年代ub>被使用<我>米</我><年代ub>1</年代ub>,<我>米</我><年代ub>3</年代ub>,<我>米</我><年代ub>5</年代ub>,分别。考虑到<我>O</我><年代ub>31日</年代ub>,<我>O</我><年代ub>41</年代ub>,<我>O</我><年代ub>21</年代ub>第一个过程吗<我>J</我><年代ub>3</年代ub>,<我>J</我><年代ub>4</年代ub>,<我>J</我><年代ub>2</年代ub>分别所有的机器都空闲时<我>t</我>=0;因此,<我>年代</我><年代ub>31日</年代ub>=<我>年代</我><年代ub>41</年代ub>=<我>年代</我><年代ub>21</年代ub>= 0。<我>O</我><年代ub>11</年代ub>选择治疗使用吗<我>米</我><年代ub>1</年代ub>。虽然<我>O</我><年代ub>11</年代ub>的第一步吗<我>J</我><年代ub>1</年代ub>,没有优先级约束在不同的任务中,<我>米</我><年代ub>1</年代ub>已经开始加工<我>O</我><年代ub>31日</年代ub>当<我>t</我>=0。<我>O</我><年代ub>11</年代ub>后就可以开始<我>O</我><年代ub>31日</年代ub>结束;因此,<我>年代</我><年代ub>11</年代ub>=<我>我</我><年代ub>1</年代ub>=<我>C</我><年代ub>31日</年代ub>=<我>年代</我><年代ub>31日</年代ub>+<我>t</我><年代ub>311年</年代ub>= 5。<我>O</我><年代ub>12</年代ub>处理使用<我>米</我><年代ub>4</年代ub>。考虑到流程在同一任务没有优先级,<我>O</我><年代ub>12</年代ub>只能开始后<我>O</我><年代ub>11</年代ub>结束,<我>O</我><年代ub>11</年代ub>结束<我>t</我>=<我>C</我><年代ub>11</年代ub>=<我>年代</我><年代ub>11</年代ub>+<我>t</我><年代ub>111年</年代ub>= 7。然而,当<我>t</我>=7,<我>米</我><年代ub>4</年代ub>处理<我>O</我><年代ub>32</年代ub>,<我>米</我><年代ub>4</年代ub>后闲置<我>O</我><年代ub>32</年代ub>完成后,即<我>我</我><年代ub>4</年代ub>=<我>C</我><年代ub>32</年代ub>=<我>年代</我><年代ub>32</年代ub>+<我>t</我><年代ub>324年</年代ub>= 8;因此,<我>年代</我><年代ub>12</年代ub>=<我>我</我><年代ub>4</年代ub>= 8。<我>O</我><年代ub>13</年代ub>处理使用<我>米</我><年代ub>2</年代ub>。虽然<我>米</我><年代ub>2</年代ub>一直在空闲<我>t</我>=5时<我>O</我><年代ub>22</年代ub>结束后,<我>O</我><年代ub>12</年代ub>还没有开始的时候吗<我>t</我>=5,流程在同一任务没有优先级。因此,<我>年代</我><年代ub>13</年代ub>=<我>C</我><年代ub>12</年代ub>=<我>年代</我><年代ub>12</年代ub>+<我>t</我><年代ub>124年</年代ub>= 10。</p><h5 id="sec2.2">2.2。FJSSP特点分析</h5> <p>柔性工作车间调度问题的,甚至完全相同的调度任务,往往存在多个调度方案。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" target="_blank">2</a>甘特图对应表吗<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>和另一个调度方案不同于图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-5b4d1b776792184278d86c571adfdfc4"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-5b4d1b776792184278d86c571adfdfc4 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-5b4d1b776792184278d86c571adfdfc4 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 调度计划2。</d我v> </div> </div> </div> <p>对于FJSSP,通常被认为是效率和系统的稳定性。在此基础上,比较和分析数据的调度方案<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>和<a href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" target="_blank">2</a>从这两个观点。在表的任务<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>,最后两个调度方案的完成时间是17日,表明两个调度方案的效率是等价的。然而,在相对应的调度方案图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>、所有机器参与调度过程和机器的负载平衡。调度方案图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" target="_blank">2</a>,<我>米</我><年代ub>6</年代ub>没有参与调度过程。完成所有进程使用<我>米</我><年代ub>1</年代ub>- - - - - -<我>米</我><年代ub>5</年代ub>和机器的磅差。机器在车间的不平衡负荷可能导致一些机器闲置和其他人在工作状态很长时间了。机器的工作状态很长一段时间很容易失败,从而影响系统的稳定性。因此,相比之下,在图的调度方案<a href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" target="_blank">2</a>,调度方案图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>同时确保效率和考虑系统稳定性要好。</p><p>上面提到的机器故障的重要因素之一,影响系统稳定性,并具体分析如下。当机器在车间分解,过程在同一任务没有优先级,除了过程实施失败的机器上或尚未实现。<我>O</我>(<我>我</我>,<我>j</我>)只能加工后<我>O</我>(<我>我</我>,<我>j</我>1)处理,流程安排在无过错机在原始的调度计划也将受到影响。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig2/" target="_blank">2</a>被认为是一个例子,即。,如果<我>米</我><年代ub>4</年代ub>分解在<我>t</我>=9。过程<我>O</我>(1、2)处理<我>米</我><年代ub><i><u>4</u></i></sub>和过程<我>O</我>(4,2)尚未处理<我>米</我><年代ub><i>4</我></年代ub>需要重新安排。<我>O</我>(1、3)<我>O</我>(4,3)无法按照原来的调度计划执行的变化造成的<我>O</我>(1、2)<我>O</我>(4,2),虽然<我>O</我>(2、3)原调度方案是失败的影响机器,机器故障系统状态变化,调度<我>O</我>(2,3)也将有一个新的对系统状态的影响。尽管如此,车间仍然保持一个高效稳定运行时失败。除了流程已经开始无过错机的过程已经完成故障机器上的,所有其他进程需要改期。复苏的时候,所有剩余的未经处理的流程需要改期,除了已经完成,开始的过程。重新安排计划之间的偏差越小原调度方案,系统变化越小,稳定性越好。相反,新老之间的差异越大调度方案,系统的稳定性将会越糟糕。</p><p>总之,如果我们想要确保运行效率,最有效的机器在所有进程可能导致一些机器被闲置了很长一段时间,虽然一些机器的工作很长一段时间,导致不平衡负载。如果我们想确保机器的磅,有些工作可能不是最有效的处理机器,导致低效率。有些流程不匹配最有效的机器,和机器的效率仍有可能减少。如果要保证工作效率,新的调度方案可能比历史上的调度方案,但系统的稳定性将会更糟。</p><h5 id="sec2.3">2.3。FJSSP的动态多目标数学模型</h5> <p>分段<a href="#sec2.2">2。2</a>表明,运行效率和系统的稳定性是矛盾的。考虑车间的效率和稳定的同时,本文把完成时间,磅,和重新安排偏差为目标函数,建立了多目标优化数学模型。完成时间是用来评估车间效率,而磅和故障延期偏差用于测量系统的稳定性。细节如下:</p><h6 id="sec2.3.1">2.3.1。工作效率</h6> <p>完成时间短,意味着工作效率较高。确保车间工作效率,本文把完成时间最短为优化目标,以及目标函数公式所示(<a href="#EEq5">5</a>)。<年代pan class="equation_break" 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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="#B8-1"></use> <use transform="matrix(1 0 0 1 2.17 -10.93)" xlink:href="#B8-2"></use> <use transform="matrix(1 0 0 1 3.63 23.42)" xlink:href="#B8-3"></use> </svg></span></span><span class="right_break" id="R8"> <svg class="label" height="11.44pt" id="M8-4" version="1.1" viewbox="0 0 15.028 11.44" width="15.028pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B8-4"> <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)"> <path d="M430 623H48C43 580 39 534 30 478H57C80 544 84 550 152 550H369C286 366 187 178 74 -1L81 -12L156 -2C249 201 343 408 438 611L430 623Z" id="g190-223"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.53,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="109.388pt" id="IL8" version="1.1" viewbox="0 0 15.09 109.388" width="15.09pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 48.76)" xlink:href="#B8-4"></use> </svg></span></span></p> <p>磅是越小,系统将更加平衡。<年代pan class="equation_break" id="EEq8"><span class="left_break" id="L9"></span><span class="middle_break"><span class="center_break" id="M9"> <svg height="37.2414pt" id="M9-1" version="1.1" viewbox="0 0 42.598 37.2414" width="42.598pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B9-1"> <g transform="matrix(.013,0,0,-0.013,0,24.743)"> <use xlink:href="#g121-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.65,24.743)"> <use xlink:href="#g121-103"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.13,24.743)"> <use xlink:href="#g121-108"></use> </g> <g transform="matrix(.013,0,0,-0.013,23.5,24.743)"> <path d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 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xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,191.19,12.744)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,194.74,12.744)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,199.88,12.744)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,205.38,12.744)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,213.36,12.744)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,223.89,12.744)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,232.58,7.002)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.013,0,0,-0.013,240.84,12.744)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,245.86,12.744)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,249.41,12.744)"> <use xlink:href="#g113-45"></use> </g> <g transform="matrix(.013,0,0,-0.013,254.55,12.744)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,260.05,12.744)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,265.12,6.076)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,265.12,9.677)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,265.12,13.279)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,265.12,16.88)"> <use xlink:href="#g119-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,268.64,12.744)"> <use xlink:href="#g119-6"></use> </g> <rect height="0.65243" width="261.239" x="12.46" y="21.09"></rect> <g transform="matrix(.013,0,0,-0.013,134.33,33.969)"> <use xlink:href="#g113-111"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,140.79,37.1)"> <use xlink:href="#g190-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,144.05,37.1)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,147.92,37.1)"> <use xlink:href="#g190-116"></use> </g> <g transform="matrix(.013,0,0,-0.013,274.89,24.743)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="59.2566pt" id="I9" version="1.1" viewbox="0 0 281.53 59.2566" width="281.53pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -15.56)" xlink:href="#B9-1"></use> <use transform="matrix(1 0 0 1 1.45 22.02)" xlink:href="#B9-2"></use> </svg></span></span><span class="right_break" id="R9"> <svg class="label" height="11.44pt" id="M9-3" version="1.1" viewbox="0 0 15.168 11.44" width="15.168pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B9-3"> <g transform="matrix(.013,0,0,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <path d="M246 635C138 635 67 554 67 471C67 401 116 348 178 315C143 296 103 268 87 252C65 231 42 203 42 157C42 50 128 -12 234 -12C319 -12 432 52 432 169C432 256 370 303 299 344C347 376 373 399 381 408C399 430 408 459 408 487C408 569 341 635 246 635ZM235 603C284 603 334 567 334 483C334 420 306 383 273 358C202 393 142 427 142 503C142 552 173 603 235 603ZM245 21C179 21 122 70 122 163C122 219 155 270 204 300C279 263 352 219 352 144C352 66 308 21 245 21Z" id="g190-152"></path> </g> <g transform="matrix(.013,0,0,-0.013,10.67,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="59.2566pt" id="IL9" version="1.1" viewbox="0 0 15.23 59.2566" width="15.23pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 23.7)" xlink:href="#B9-3"></use> </svg></span></span></p> <p>在(<a href="#EEq8">8</a>),<我>n</我><年代ub>res</年代ub>操作的总数是改期;的操作,已经开始或完成的工作机器,<年代pan class="inline_break"> <svg height="13.532pt" id="M10" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -10.1025 17.148 13.532" width="17.148pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.311,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,12.81,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.359,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="21.4521838 -10.1025 21.261 13.532" width="21.261pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,21.502,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.002,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.132,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="46.3451838 -10.1025 23.226 13.532" width="23.226pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,46.395,0)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,52.531,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.61,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,63.108,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.657,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="71.7501838 -10.1025 10.327 13.532" width="10.327pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,71.8,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,77.301,0)"> <use xlink:href="#g113-42"></use> </g> </svg></span>和<年代pan class="inline_break"> <svg height="13.532pt" id="M11" style="vertical-align:-3.4295pt" version="1.1" viewbox="-0.0498162 -10.1025 19.696 13.532" width="19.696pt" 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="#g113-68"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.684,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.182,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,16.732,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="21.8251838 -10.1025 21.261 13.532" width="21.261pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,21.875,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,27.375,0)"> <use xlink:href="#g113-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,35.505,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="46.7181838 -10.1025 25.774 13.532" width="25.774pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,46.768,0)"> <use xlink:href="#g113-68"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,55.452,-5.741)"> <use xlink:href="#g50-43"></use> </g> <g transform="matrix(.013,0,0,-0.013,61.531,0)"> <use xlink:href="#g113-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,66.029,0)"> <use xlink:href="#g113-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,69.578,0)"> <use xlink:href="#g113-45"></use> </g> </svg><span class="ipunc"></span><span class="nowrap"> <svg height="13.532pt" style="vertical-align:-3.4295pt" version="1.1" viewbox="74.67118380000001 -10.1025 10.346 13.532" width="10.346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,74.721,0)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.221,0)"> <use xlink:href="#g113-42"></use> </g> </svg>。</年代pan></span></p> <p>总之,考虑系统的效率和稳定性,建立了FJSSP动态多目标数学模型:<年代pan class="equation_break" id="EEq9"><span class="left_break" id="L12"></span><span class="middle_break"><span class="center_break" id="M12"> <svg height="102.261pt" id="M12-1" version="1.1" viewbox="0 0 354.664 102.261" width="354.664pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B12-1"> <g transform="matrix(.013,0,0,-0.013,0,17.335)"> <path d="M660 1109V1150C557 1150 406 1122 406 886V0H513V923C513 1011 529 1089 660 1109Z" id="g119-47"></path> </g> <g 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version="1.1" viewbox="0 0 15.4 102.261" width="15.4pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 45.2)" xlink:href="#B12-2"></use> </svg></span></span></p> <p>在上面的数学模型中,第一个目标函数保证所有任务的完成时间最短到达时间<我>nt</我><年代ub>l</年代ub>;第二目标函数保证所有机器都将尽可能均匀,直到加载<我>nt</我><年代ub>l</年代ub>;第三个目标函数确保机器分解或回去工作时,重新安排计划之间的偏差和原调度方案是最小的。当没有机器分解或一台机器不是恢复,只有1和2被认为是目标函数,以供应点和数学模型是优化问题。如果一台机器坏了或者有缺陷的机器恢复,这三个目标都需要优化,并被视为three-objective优化问题的数学模型。</p><p>与现有FJSSP的数学模型相比,本文建立的数学模型考虑完成任务的动态特性出发,新任务的到来,车间机器的故障,修理机器故障。调整优化数学模型目标自动按照国家机器,这将缩短机器的工作时间和平衡负载时不机分解或机不是恢复。与此同时,建立数学模型,将新老的偏差最小化调度计划当一台机器分解或错误的恢复,使考虑工作效率和系统的稳定性。</p><h4 id="dynamic-multi-objective-ssa-for-solving-fjssp">3所示。为解决动态多目标SSA FJSSP</h4> <p>解决动态多目标优化问题时,动态环境分为几个瞬态环境;动态处理技术用于处理环境变化,以及多目标算法是用来解决静态瞬态环境中的多目标优化问题。松鼠搜索算法(SSA)是一种新的群集智能进化算法(<a href="#B20">20.</a>]。与传统的进化算法相比,SSA具有较高的收敛速度和精度。王等人提出一种改进的松鼠全球函数优化搜索算法(ISSA),提高了SSA的收敛。此外,张等人提出MOEA / D,可以解决多目标优化问题在瞬态环境中,具有较高的求解速度和效率<a href="#B21">21</a>]。因此,为了扩大SSA在工程领域的应用,本文认为伊萨为核心的进化策略,认为MOEA / D的多目标框架,集成了一个动态处理技术来解决FJSSP。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig3/" target="_blank">3</a>是解决动态多目标SSA FJSSP的流程图。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-deaf5734e78ee91835f6ae39293744f4"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-deaf5734e78ee91835f6ae39293744f4 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.003_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-deaf5734e78ee91835f6ae39293744f4 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 为解决FJSSP流程图。</d我v> </div> </div> </div> <p>图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig3/" target="_blank">3</a>说明在每个瞬态环境,最终的调度方案在当前环境nondominated解集应该选择,和新环境下的调度是基于所选择的调度方案。在这项研究中,TOPSIS (<a href="#B22">22</a>)是用来确定最终的调度方案为每个瞬态环境。此外,考虑到FJSSP是一个离散的优化问题,本研究采用个体编码方法(<a href="#B23">23</a>]。按照FJSSP的特点,动态处理技术与进化策略FJSSP设计如下。</p><h5 id="sec3.1">3.1。个体编码方法</h5> <p>个体编码方法包括两个部分:操作和机器代码。确定操作编码使用数量在重新安排时间处理工作。操作<我>O(我,j)</我>由其任务是几号<我>J</我><年代ub><i>我</我></年代ub>。第一次出现的<我>J</我><年代ub><i>我</我></年代ub>对应于操作<我>O(1)我</我>,第二次出现<我>J</我><年代ub><i>我</我></年代ub>对应于操作<我>O(我,2)</我>,等等。的<我>j</我>发生的<我>J</我><年代ub><i>我</我></年代ub>对应于操作<我>O(我,j)</我>;因此,发生的频率<我>J</我><年代ub><i>我</我></年代ub>总操作数是一样的<我>J</我><年代ub><i>我</我></年代ub>。每个操作代码对应一台机器代码。一组机器从候选人中选择机器的<我>O(我,j)</我>随机,所选的机器的数量相对应的机器代码<我>O(我,j)</我>。</p><p>任务表中的数据<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>被认为是一个例子。完整的代码对应的调度方案如图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig1/" target="_blank">1</a>是342133221144/135145264243,即。阿,<年代ub>31日</年代ub>⟶米<年代ub>1</年代ub>阿,<年代ub>41</年代ub>⟶米<年代ub>3</年代ub>阿,<年代ub>21</年代ub>⟶米<年代ub>5</年代ub>阿,<年代ub>11</年代ub>⟶米<年代ub>1</年代ub>阿,<年代ub>32</年代ub>⟶米<年代ub>4</年代ub>阿,<年代ub>33</年代ub>⟶米<年代ub>5</年代ub>阿,<年代ub>22</年代ub>⟶米<年代ub>2</年代ub>阿,<年代ub>23</年代ub>⟶米<年代ub>6</年代ub>阿,<年代ub>12</年代ub>⟶米<年代ub>4</年代ub>阿,<年代ub>13</年代ub>⟶米<年代ub>2</年代ub>阿,<年代ub>42</年代ub>⟶米<年代ub>4</年代ub>阿,<年代ub>43</年代ub>⟶米<年代ub>3</年代ub>。</p><h5 id="sec3.2">3.2。动态处理技术</h5> <h6 id="sec3.2.1">3.2.1之上。建立和更新的外来人口</h6> <p>MOEA / D的解决方案原理表明,当后代个体<年代vg height="14.8655pt" id="M13" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="M556 393C556 426 537 448 514 448C496 448 478 435 471 420C468 414 462 401 466 394C473 382 480 368 480 346C480 268 392 143 338 67H336C329 163 319 253 309 330S286 448 254 448C215 448 160 383 127 337L143 311C167 344 200 373 208 373S222 365 229 320C246 214 264 66 268 -20C219 -83 131 -171 17 -239L25 -261L137 -235C248 -110 273 -79 335 8C384 77 481 215 520 287C544 332 556 363 556 393Z" id="g113-122"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z" id="g50-31"></path> </g> </svg>不能取代任何个人在附近,<年代vg height="14.8655pt" id="M14" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>是直接放弃了。因此,本研究建立了一个外部人口<我>莎莉</我>为每个单独的放弃了<年代vg height="14.8655pt" id="M15" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>参与进化。具体方法如下。外部人口大小设置相同的社区<我>T</我>。num_alt用于记录的个人社区所取代<年代pan class="nowrap"> <svg height="14.8655pt" id="M16" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>。</年代pan><span class="nowrap"> <svg height="14.8655pt" id="M17" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>,</年代pan>的num_alt = 0,进入外部人口。</p><p>当的规模<我>莎莉</我>小于上限吗<我>T</我>如果num_alt = 0,相应的<年代vg height="14.8655pt" id="M18" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>进入<我>莎莉</我>;如果0<我><</我>num_alt<年代vg height="8.89449pt" id="M19" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -7.77468 7.75925 8.89449" width="7.75925pt" 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="M531 71V127L115 310L531 494V550L57 335V285L531 71ZM531 -40V10H57V-40H531Z" id="g117-93"></path> </g> </svg><i>T /</我>2,<我>莎莉</我>保持不变;如果num_alt<我>></我><我>T/</我>2,<我>莎莉</我>清空,因为当前的子问题和其邻国子问题最优解。</p><p>当的规模<我>莎莉</我>到上限吗<我>T</我>,如果num_alt<我>=</我><我>0</我>,人口已经进化到一定程度上,当前个人接近其邻国个人。保持种群的多样性,个人的最小欧氏距离当前的个人<我>莎莉</我>被删除,<年代vg height="14.8655pt" id="M20" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -11.4361 11.4504 14.8655" width="11.4504pt" 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="#g113-122"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.529,-5.741)"> <use xlink:href="#g50-31"></use> </g> </svg>进入<我>莎莉</我>。</p><h6 id="sec3.2.2">3.2.2。代的初始种群在重新安排时间</h6> <p>两种情况需要重新安排任务被认为是。第一个车间工作时间有关,即周期性的重新安排。第二个是有关机器的状态,包括故障和故障恢复重新安排。考虑到上述两种情况中,两个不同的动态处理技术设计,细节如下。</p><p>在周期性的重新安排<我>nt</我><年代ub><i>l</我></年代ub>,新任务记录,机器状态更新,新时期下的初始种群生成按照分段编码方法<a href="#sec3.1">3.1</a>。</p><p>如果机器坏了或再次运行,也就是说,<我>t</我>=<我>t</我><年代ub><i>b</我></年代ub>或<我>t</我>=<我>t</我><年代ub><i>r</我></年代ub>,新的人口<我>t</我><年代ub><i>b</我></年代ub>或<我>t</我><年代ub><i>r</我></年代ub>生成按照原调度方案的实现。细节如下。如果<我>t</我>=<我>t</我><年代ub><i>b</我></年代ub>,在目前的调度方案,操作调度包含所有未完成的操作安排在破碎的机器,所有的操作都才开始<我>t</我><年代ub><i>b</我></年代ub>。如果<我>t</我>=<我>t</我><年代ub><i>r</我></年代ub>在当前的调度方案,操作调度包含所有的操作才开始<我>t</我><年代ub><i>r</我></年代ub>。所有操作的集合被重新命名<我>O</我><年代ub>再保险</年代ub>。当<我>t</我>=<我>t</我><年代ub><i>b</我></年代ub>或<我>t</我>=<我>t</我><年代ub><i>r</我></年代ub>为每个单独的原始人群,如果<我>莎莉</我>=∅,所有操作<我>O</我><年代ub><i>再保险</我></年代ub>应该被重新初始化新的个人在新环境中按照上面的编码方法;如果<我>莎莉</我>≠∅,对于每个调度计划<我>莎莉</我>操作的集合,需要重新记录和命名<我>O</我><年代ub>莎莉</年代ub>;如果内存和完全相同的个体<我>O</我><年代ub>莎莉</年代ub>和<我>O</我><年代ub>再保险</年代ub>存在,一个是随机选择的,所有操作的调度顺序保存在<我>O</我><年代ub>莎莉</年代ub>,和相应的机器代码是突变,视为初始个体在新环境中。高相似性调度方案在内存中人口和当前执行的调度方案,生成的新个体使用内存的人更适合当前工作状态,有利于系统稳定。</p><h5 id="sec3.3">3.3。核心进化策略</h5> <p>每个瞬态环境的调度过程中,核心的进化策略SSA用于更新人口。个体包含操作和机器代码,但机器代码是由操作码。因此,人口的更新策略是只针对操作的代码,而不是机器代码。具体的更新过程描述如下。</p><h6 id="sec3.3.1">3.3.1。相关的变量</h6> <p><span class="list"><span class="list-item"><span class="list-label"></span><span class="list-content"><i>F</我><年代ub><i>d</我></年代ub>:学习目标按照标准SSA;详细介绍了在文献[<a href="#B20">20.</a>]。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>n</我>_年代ame:当操作的代码<我>F年代</我><年代ub><i>我</我></年代ub>和<我>F</我><年代ub><i>d</我></年代ub>匹配一个接一个地<我>n</我>_年代ame的总数是一样的操作规范。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>n</我>_<我>j</我><年代ub><i>l</我></年代ub>:新工作的总数<我>t</我><年代ub><i>l</我></年代ub><i>。</我></年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>Fr</我><年代ub>1</年代ub>,<我>Fr</我><年代ub>2</年代ub>:如果<我>莎莉</我>=∅,<我>Fr</我><年代ub>1</年代ub>和<我>Fr</我><年代ub>2</年代ub>两个人不同的来自哪里<我>F</我><年代ub><i>d</我></年代ub>和<我>F年代</我><年代ub><i>我</我></年代ub>随机选择在他们的邻居;如果<我>莎莉</我>≠∅,<我>Fr</我><年代ub>1</年代ub>在周边国家的任何个人不同吗<我>F年代</我><年代ub><i>我</我></年代ub>,<我>Fr</我><年代ub>2</年代ub>是随机选择的<我>莎莉。</我></年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content"> <svg height="13.8999pt" id="M21" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 12.0363 13.8999" width="12.0363pt" 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="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.136,-5.741)"> <path d="M554 433L549 437C539 437 513 441 503 443C481 447 456 451 436 451C354 451 268 415 216 368C150 308 99 205 99 106C99 24 136 -12 165 -12C196 -12 243 14 268 33C318 70 374 118 415 181H419L395 39C374 -84 332 -149 295 -175C269 -193 245 -197 212 -197C137 -197 93 -156 76 -102C71 -87 61 -87 51 -96C36 -110 24 -130 24 -147C24 -183 76 -257 171 -257C226 -257 285 -227 323 -200C387 -155 455 -76 480 94C499 225 538 391 554 433ZM460 386C457 361 438 287 426 254C408 218 373 176 332 133C294 93 246 61 217 61C198 61 186 80 186 122C186 167 206 250 231 294C262 349 288 375 317 387C334 394 358 400 381 400C413 400 439 393 460 386Z" id="g50-104"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,6.071,3.784)"> <path d="M387 400C387 425 348 451 303 451C247 451 176 414 132 376C69 322 24 228 24 148C24 43 74 -12 147 -12C211 -12 301 33 363 103L346 128C319 99 249 51 193 51C148 51 112 84 112 165C112 230 130 287 154 330C170 359 199 400 243 400C277 400 304 383 326 354C333 345 343 343 354 348C378 360 387 382 387 400Z" id="g50-100"></path> </g> </svg>和<年代vg height="11.8174pt" id="M22" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 21.9089 11.8174" width="21.9089pt" 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="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,6.071,3.132)"> <path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,13.66,3.132)"> <path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 422 40 414V386C101 378 104 372 104 311V109C104 41 97 35 33 30V0H257Z" id="g58-103"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,16.163,3.132)"> <path d="M532 0V30C473 38 467 38 467 107V298C467 395 416 451 336 451C307 451 279 439 251 420C226 404 205 389 185 374V453C142 434 94 422 43 413V386C98 378 104 373 104 309V107C104 41 100 38 31 30V0H251V30C191 35 185 40 185 107V337C216 364 255 389 295 389C360 389 386 347 386 276V110C386 44 380 35 321 30V0H532Z" id="g58-108"></path> </g> </svg>计算根据文献[<a href="#B20">20.</a>),冬季时选择搜索策略<年代pan class="inline_break"> <svg height="13.8999pt" id="M23" style="vertical-align:-3.94351pt" version="1.1" viewbox="-0.0498162 -9.95639 23.177 13.8999" width="23.177pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,2.175,0)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.311,-5.741)"> <use xlink:href="#g50-104"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,8.246,3.784)"> <use xlink:href="#g50-100"></use> </g> <g transform="matrix(.013,0,0,-0.013,17.721,0)"> <use xlink:href="#g117-92"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="13.8999pt" style="vertical-align:-3.94351pt" version="1.1" viewbox="28.934183800000003 -9.95639 21.96 13.8999" width="21.96pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,28.984,0)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,35.055,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,42.644,3.132)"> <use xlink:href="#g58-103"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,45.147,3.132)"> <use xlink:href="#g58-108"></use> </g> </svg>。</年代pan></span><span class="list"><span class="list-item"><span class="list-label">(1)</年代pan><span class="list-content">冬天的搜索策略<年代pan class="list"><span class="list-item"><span class="list-label">①</年代pan><span class="list-content">不存在任何食肉动物时<年代pan class="inline_break"> <svg height="14.1101pt" id="M24" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 16.751 14.1101" width="16.751pt" 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="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(.013,0,0,-0.013,9.12,0)"> <use xlink:href="#g117-92"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.1101pt" style="vertical-align:-5.4742pt" version="1.1" viewbox="20.3331838 -8.6359 17.346 14.1101" width="17.346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.383,0)"> <path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,27.039,3.132)"> <path d="M538 684C542 703 539 710 529 710C512 710 455 682 363 674L361 644H396C444 644 448 642 438 594L405 438C373 450 347 451 336 451C288 451 200 416 147 374C69 312 24 207 24 113C24 29 60 -12 94 -12C126 -12 156 4 196 30C231 53 296 100 346 166H348L328 81C311 10 325 -12 348 -12C380 -12 450 24 512 98L495 125C466 97 431 70 417 70C408 70 408 80 411 98L538 684ZM390 373L361 240C336 196 210 56 145 56C132 56 113 73 113 131C113 216 156 338 220 379C243 394 266 402 303 402C331 402 375 388 390 373Z" id="g50-101"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,31.587,3.132)"> <path d="M573 302C573 402 527 451 414 451C386 451 343 446 313 437L330 513L320 522C295 508 261 484 243 463L230 415C194 400 159 383 126 359L131 330C159 344 187 357 222 368L109 -147C96 -204 80 -214 18 -223L13 -255L256 -244L259 -212L236 -210C184 -205 180 -195 191 -141L219 -1C240 -10 268 -12 284 -12C352 4 431 48 484 104C543 166 573 240 573 302ZM481 290C481 165 381 37 305 37C280 37 249 56 235 71L302 395C328 399 353 402 372 402C427 402 481 378 481 290Z" id="g50-113"></path> </g> </svg>。</年代pan></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">跳时选择搜索方法<我>n</我>_年代ame ><我>n</我>_<我>j</我><年代ub><i>l</我></年代ub>/ 2,逐步搜索方法是决定的时候<我>n</我>_年代ame<年代vg height="8.89449pt" id="M25" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -7.77468 7.75925 8.89449" width="7.75925pt" 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="#g117-93"></use> </g> </svg><i>n</我>_<我>j</我><年代ub><i>l</我></年代ub>/ 2。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content">跳的搜索方法:<我>F年代</我><年代ub><i>我</我></年代ub>和<我>F</我><年代ub><i>d</我></年代ub>有很高的相似性,<我>n</我>_年代ame ><我>n</我>_<我>j</我><年代ub><i>l</我></年代ub>更新/ 2,个人使用公式(<a href="#EEq10">10</a>)。<年代pan class="equation_break" id="EEq10"><span class="left_break" id="L26"></span><span class="middle_break"><span class="center_break" id="M26"> <svg height="18.5793pt" id="M26-1" version="1.1" viewbox="0 0 29.162 18.5793" width="29.162pt" 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,-0.013,0,12.749)"> <path d="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path> </g> <g transform="matrix(.013,0,0,-0.013,7.77,12.749)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.91,5.85)"> <use xlink:href="#g50-104"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.17,5.85)"> <path d="M556 236V289H337V504H275V289H56V236H275V-4H337V236H556Z" id="g54-36"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,24.73,5.85)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.84,16.79)"> <use xlink:href="#g50-106"></use> </g> </g> </svg> <svg height="18.5793pt" id="M26-2" version="1.1" viewbox="0 0 30.43 18.5793" width="30.43pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B26-2"> <g transform="matrix(.013,0,0,-0.013,0,12.749)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,12.749)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,19.03,12.749)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,25.17,5.85)"> <use xlink:href="#g50-104"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,25.1,16.79)"> <use xlink:href="#g50-106"></use> </g> </g> </svg> <svg height="18.5793pt" id="M26-3" version="1.1" viewbox="0 0 134.524 18.5793" width="134.524pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B26-3"> <g transform="matrix(.013,0,0,-0.013,0,12.749)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.54,12.749)"> <path d="M335 -404V-369L312 -368C205 -360 203 -355 203 -249V751C203 895 206 900 312 908L335 909V944H138V-404H335Z" id="g119-129"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.9,12.749)"> <path d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z" id="g113-101"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,23.05,15.88)"> <use xlink:href="#g50-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.73,12.749)"> <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,-0.013,42.27,12.749)"> <path d="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 467 666C201 666 23 502 23 278C23 90 156 -16 339 -16C410 -16 501 6 569 24C566 43 567 70 573 101L589 183C604 259 607 262 667 271L673 297Z" id="g113-72"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,51.1,15.88)"> <use xlink:href="#g50-100"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.26,12.749)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.79,12.749)"> <path d="M378 -385C239 -253 158 0 158 271S238 795 378 927L356 953C165 798 79 550 79 272V271C79 -10 165 -259 356 -411L378 -385Z" id="g119-133"></path> </g> <g transform="matrix(.013,0,0,-0.013,74.57,12.749)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,82.47,6.485)"> <path d="M329 433H203L239 587L230 596L147 534L123 433H57L30 395L34 388H115L61 129C37 16 59 -12 85 -12C147 -12 222 58 260 98L241 125C212 95 160 62 144 62C132 62 127 71 138 126L192 386L305 394L329 433Z" id="g50-117"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,81.36,16.533)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,89.91,12.749)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,100.45,12.749)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,108.21,12.749)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,114.35,6.485)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,114.29,16.533)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,118.02,12.749)"> <path d="M364 271V272C364 550 278 798 87 953L65 927C205 795 285 542 285 271S204 -253 65 -385L87 -411C278 -259 364 -10 364 271Z" id="g119-134"></path> </g> <g transform="matrix(.013,0,0,-0.013,123.9,12.749)"> <path d="M273 -404V944H76V909L99 908C205 900 208 895 208 751V-249C208 -355 206 -360 99 -368L76 -369V-404H273Z" id="g119-130"></path> </g> <g transform="matrix(.013,0,0,-0.013,131.56,12.749)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="68.313pt" id="I26" version="1.1" viewbox="0 0 162.35 68.313" width="162.35pt" 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="#B26-1"></use> <use transform="matrix(1 0 0 1 13.59 24.18)" xlink:href="#B26-2"></use> <use transform="matrix(1 0 0 1 27.79 49.73)" 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 19.728 11.44" width="19.728pt" 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,-0.013,0,9.26)"> <use xlink:href="#g190-41"></use> </g> <g transform="matrix(.013,0,0,-0.013,4.5,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.82,9.26)"> <path d="M248 635C97 635 43 457 43 311C43 153 97 -12 247 -12S450 166 450 312C450 466 397 635 248 635ZM246 603C337 603 361 452 361 312S337 20 248 20S132 172 132 313C132 452 156 603 246 603Z" id="g190-254"></path> </g> <g transform="matrix(.013,0,0,-0.013,15.23,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="68.313pt" id="IL26" version="1.1" viewbox="0 0 19.81 68.313" width="19.81pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 28.23)" xlink:href="#B26-4"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在上面的公式中,”。”意味着进行舍入操作,确保每个维度的个人代码是一个正整数。<年代vg height="14.8173pt" id="M27" style="vertical-align:-5.52897pt" version="1.1" viewbox="-0.0498162 -9.28833 13.0541 14.8173" width="13.0541pt" 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="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,7.15,3.132)"> <use xlink:href="#g50-104"></use> </g> </svg>和<我>G</我><年代ub><i>c</我></年代ub>介绍了在文献[<a href="#B20">20.</a>]。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content">先进的搜索方法:<我>F年代</我><年代ub><i>我</我></年代ub>和<我>F</我><年代ub><i>d</我></年代ub>相似度较低时<我>n_</我>相同<年代vg height="8.89449pt" id="M28" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -7.77468 7.75925 8.89449" width="7.75925pt" 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="#g117-93"></use> </g> </svg><i>n_j</我><年代ub><i>l</我></年代ub><i>/</我>2<我>。</我>保持种群多样性,<我>r</我><年代ub><i>ds</我></年代ub>维随机选择按照公式(<a href="#EEq11">11</a>),然后重新安排也随机。<年代pan class="equation_break" id="EEq11"><span class="left_break" id="L29"></span><span class="middle_break"><span class="center_break" id="M29"> <svg height="14.5707pt" id="M29-1" version="1.1" viewbox="0 0 143.594 14.5707" width="143.594pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B29-1"> <g transform="matrix(.013,0,0,-0.013,0,10.593)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,4.9,13.725)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,10.03,13.725)"> <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(.013,0,0,-0.013,17.66,10.593)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,28.92,10.593)"> <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,-0.013,33.78,10.593)"> <use xlink:href="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.17,10.593)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,52.71,10.593)"> <use xlink:href="#g119-5"></use> </g> <g transform="matrix(.013,0,0,-0.013,57.73,10.593)"> <use xlink:href="#g113-111"></use> </g> <rect height="0.3985" width="3.91466" x="65.04" y="10.195"></rect> <g transform="matrix(.013,0,0,-0.013,68.95,10.593)"> <use xlink:href="#g113-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,74.13,13.725)"> <use xlink:href="#g50-109"></use> </g> <g transform="matrix(.013,0,0,-0.013,80.01,10.593)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,90.54,10.593)"> <use xlink:href="#g113-111"></use> </g> <rect height="0.3985" width="3.91466" x="97.85" y="10.195"></rect> <g transform="matrix(.013,0,0,-0.013,101.77,10.593)"> <use xlink:href="#g190-116"></use> </g> <g transform="matrix(.013,0,0,-0.013,106.62,10.593)"> <use xlink:href="#g190-98"></use> </g> <g transform="matrix(.013,0,0,-0.013,112.21,10.593)"> <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="g190-110"></path> </g> <g transform="matrix(.013,0,0,-0.013,122.8,10.593)"> <use xlink:href="#g190-102"></use> </g> <g transform="matrix(.013,0,0,-0.013,128.43,10.593)"> <use xlink:href="#g119-6"></use> </g> <g transform="matrix(.013,0,0,-0.013,133.55,10.593)"> <path d="M244 -259V799H63V768H72C178 759 181 755 181 616V-109C181 -215 179 -219 72 -228H63V-259H244Z" id="g119-2"></path> </g> <g transform="matrix(.013,0,0,-0.013,140.63,10.593)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="14.5707pt" id="I29" version="1.1" viewbox="0 0 143.59 14.5707" width="143.59pt" 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="#B29-1"></use> </svg></span></span><span class="right_break" id="R29"> <svg class="label" height="11.44pt" id="M29-2" version="1.1" viewbox="0 0 17.788 11.44" width="17.788pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B29-2"> <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="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.9,9.26)"> <use xlink:href="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,13.29,9.26)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="14.5707pt" id="IL29" version="1.1" viewbox="0 0 17.85 14.5707" width="17.85pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 1.35)" xlink:href="#B29-2"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">在上面的公式中,<我>r</我>是一个0到1之间的随机数;之间的相似度越低<我>F年代</我><年代ub><i>我</我></年代ub>和<我>F</我><年代ub><i>d</我></年代ub>可以重新安排更多的维度,和搜索空间可以开发更加充分。</年代pan></span><span class="list-item"><span class="list-label">②</年代pan><span class="list-content">捕食者时<年代pan class="inline_break"> <svg height="14.1101pt" id="M30" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 16.751 14.1101" width="16.751pt" 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="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.12,0)"> <use xlink:href="#g117-93"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.1101pt" style="vertical-align:-5.4742pt" version="1.1" viewbox="20.3331838 -8.6359 17.346 14.1101" width="17.346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.383,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.039,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.587,3.132)"> <use xlink:href="#g50-113"></use> </g> </svg>。</年代pan></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content"><i>FS</我><年代ub><i>我</我></年代ub>被认为是死亡,通过生成后代吗<我>F</我><年代ub><i>r1</我></年代ub>和<我>F</我><年代ub><i>r2</我></年代ub>按照痘了文献[<a href="#B24">24</a>]。</年代pan></span></span></span></span><span class="list-item"><span class="list-label">(2)</年代pan><span class="list-content">夏天的搜索策略<年代pan class="list"><span class="list-item"><span class="list-label">①</年代pan><span class="list-content">不存在任何食肉动物时<年代pan class="inline_break"> <svg height="14.1101pt" id="M31" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 16.751 14.1101" width="16.751pt" 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="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.12,0)"> <use xlink:href="#g117-92"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.1101pt" style="vertical-align:-5.4742pt" version="1.1" viewbox="20.3331838 -8.6359 17.346 14.1101" width="17.346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.383,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.039,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.587,3.132)"> <use xlink:href="#g50-113"></use> </g> </svg>。</年代pan></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">跳时选择搜索方法<我>n_</我>同样的><我>n_j</我><年代ub><i>l</我></年代ub><i>/</我>2,进步时选择搜索方法<我>n_</我>相同<年代vg height="8.89449pt" id="M32" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -7.77468 7.75925 8.89449" width="7.75925pt" 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="#g117-93"></use> </g> </svg><i>n_j</我><年代ub><i>l</我></年代ub><i>/</我>2<我>。</我></年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content">跳的搜索方法:<我>F年代</我><年代ub><i>我</我></年代ub>和<我>F</我><年代ub><i>d</我></年代ub>有很高的相似性,<我>n_</我>同样的><我>n_j</我><年代ub><i>l</我></年代ub><i>/</我>2,更新个人使用公式(<a href="#EEq12">12</a>)。<年代pan class="equation_break" id="EEq12"><span class="left_break" id="L33"></span><span class="middle_break"><span class="center_break" id="M33"> <svg height="18.3157pt" id="M33-1" version="1.1" viewbox="0 0 27.052 18.3157" width="27.052pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-1"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,7.77,12.485)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.9,6.222)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,17.06,6.222)"> <use xlink:href="#g54-36"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,22.62,6.222)"> <use xlink:href="#g50-50"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,13.84,16.269)"> <use xlink:href="#g50-106"></use> </g> </g> </svg> <svg height="18.3157pt" id="M33-2" version="1.1" viewbox="0 0 23.182 18.3157" width="23.182pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-2"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g117-34"></use> </g> <g transform="matrix(.013,0,0,-0.013,11.27,12.485)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,19.16,6.222)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,18.05,16.269)"> <use xlink:href="#g50-101"></use> </g> </g> </svg> <svg height="18.3157pt" id="M33-3" version="1.1" viewbox="0 0 134.524 18.3157" width="134.524pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-3"> <g transform="matrix(.013,0,0,-0.013,0,12.485)"> <use xlink:href="#g117-36"></use> </g> <g transform="matrix(.013,0,0,-0.013,10.53,12.485)"> <use xlink:href="#g119-129"></use> </g> <g transform="matrix(.013,0,0,-0.013,15.9,12.485)"> <use xlink:href="#g113-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,23.05,15.617)"> <use xlink:href="#g50-104"></use> </g> <g transform="matrix(.013,0,0,-0.013,31.73,12.485)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,42.27,12.485)"> <use xlink:href="#g113-72"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,51.09,15.617)"> <use xlink:href="#g50-100"></use> </g> <g transform="matrix(.013,0,0,-0.013,58.25,12.485)"> <use xlink:href="#g117-42"></use> </g> <g transform="matrix(.013,0,0,-0.013,68.79,12.485)"> <use xlink:href="#g119-133"></use> </g> <g transform="matrix(.013,0,0,-0.013,74.57,12.485)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.013,0,0,-0.013,82.33,12.485)"> <use xlink:href="#g113-84"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,88.47,6.222)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,88.4,16.269)"> <use xlink:href="#g50-106"></use> </g> <g transform="matrix(.013,0,0,-0.013,95.04,12.485)"> <use xlink:href="#g117-33"></use> </g> <g transform="matrix(.013,0,0,-0.013,105.58,12.485)"> <use xlink:href="#g113-71"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,113.47,6.222)"> <use xlink:href="#g50-117"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,112.36,16.269)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.013,0,0,-0.013,118.01,12.485)"> <use xlink:href="#g119-134"></use> </g> <g transform="matrix(.013,0,0,-0.013,123.9,12.485)"> <use xlink:href="#g119-130"></use> </g> <g transform="matrix(.013,0,0,-0.013,131.56,12.485)"> <use xlink:href="#g113-47"></use> </g> </g> </svg> <svg class="alt_equation" height="67.7847pt" id="I33" version="1.1" viewbox="0 0 162.35 67.7847" width="162.35pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 -0.37)" xlink:href="#B33-1"></use> <use transform="matrix(1 0 0 1 13.59 24.15)" xlink:href="#B33-2"></use> <use transform="matrix(1 0 0 1 27.79 49.47)" xlink:href="#B33-3"></use> </svg></span></span><span class="right_break" id="R33"> <svg class="label" height="11.44pt" id="M33-4" version="1.1" viewbox="0 0 19.468 11.44" width="19.468pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g id="B33-4"> <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="#g190-213"></use> </g> <g transform="matrix(.013,0,0,-0.013,8.93,9.25)"> <use xlink:href="#g190-243"></use> </g> <g transform="matrix(.013,0,0,-0.013,14.97,9.25)"> <use xlink:href="#g190-42"></use> </g> </g> </svg> <svg class="alt_label" height="67.7847pt" id="IL33" version="1.1" viewbox="0 0 19.55 67.7847" width="19.55pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <use transform="matrix(1 0 0 1 0 27.96)" xlink:href="#B33-4"></use> </svg></span></span></span></span><span class="list-item"><span class="list-label"></span><span class="list-content">公式(<a href="#EEq12">12</a>)的问候<我>F</我><年代ub><i>d</我></年代ub>为基本载体,提高收敛速度的环境变化,并深入发展后的搜索空间人口的发展在一定程度上。</年代pan></span><span class="list-item"><span class="list-label"></span><span class="list-content">进步的搜索方法是一样的,在冬天搜索方法。如果<我>n_</我>相同<年代vg height="8.89449pt" id="M34" style="vertical-align:-1.11981pt" version="1.1" viewbox="-0.0498162 -7.77468 7.75925 8.89449" width="7.75925pt" 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="#g117-93"></use> </g> </svg><i>n_j</我><年代ub><i>l</我></年代ub><i>/</我>2,<我>r</我><年代ub><i>ds</我></年代ub>维随机选择按照公式(<a href="#EEq10">10</a>),然后重新安排也随机。</年代pan></span><span class="list-item"><span class="list-label">②</年代pan><span class="list-content">捕食者时<年代pan class="inline_break"> <svg height="14.1101pt" id="M35" style="vertical-align:-5.4742pt" version="1.1" viewbox="-0.0498162 -8.6359 16.751 14.1101" width="16.751pt" 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="#g113-115"></use> </g> <g transform="matrix(.013,0,0,-0.013,9.12,0)"> <use xlink:href="#g117-93"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="14.1101pt" style="vertical-align:-5.4742pt" version="1.1" viewbox="20.3331838 -8.6359 17.346 14.1101" width="17.346pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,20.383,0)"> <use xlink:href="#g113-81"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,27.039,3.132)"> <use xlink:href="#g50-101"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,31.587,3.132)"> <use xlink:href="#g50-113"></use> </g> </svg>。</年代pan></span></span></span></span></span></span></span></span></span></span></p> <p><i>FS</我><年代ub><i>我</我></年代ub>被认为是死,生成后代使用吗<我>F</我><年代ub><i>r</我>1</年代ub>和<我>F</我><年代ub><i>r</我>2</年代ub>按照痘了文献[<a href="#B24">24</a>]。</p><p>FJ年代年代P要求每个维度的价值是工作号码对应操作,和每个作业的总出现时间应该是相同的总操作数。因此,操作码的后代获得使用上述更新策略应该被修改。任务表<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>被认为是一个例子来介绍修改过程,细节如下。</p><p>冗余工作数量确定和记录在向量”。“如果数量<我>我</我>的工作<我>J</我><年代ub><i>我</我></年代ub>发生<我>n</我><年代ub><i>我</我></年代ub><i>+</我><我>c</我>次,然后<我>我</我>发生在“更多”<我>c</我>次了。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig4/" target="_blank">4</a>被认为是一个例子。在表的问题<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>后代的操作码是134312214131,更多= {1 1}。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-d10bc5750664700b22eb79c904a40bd5"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-d10bc5750664700b22eb79c904a40bd5 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.004_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-d10bc5750664700b22eb79c904a40bd5 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 修改操作的代码。</d我v> </div> </div> </div> <p>失踪的就业数据标识和记录在向量”<我>更少。</我>“如果数量<我>我</我>的工作<我>J</我><年代ub><i>我</我></年代ub>发生<我>n</我><年代ub><i>我</我></年代ub><i>- c</我>次,然后<我>我</我>发生在“少”<我>c</我>次了。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig4/" target="_blank">4</a>被认为是一个例子。在表的问题<a href="//www.newsama.com/journals/ijap/2021/6062689/tab1/" target="_blank">1</a>后代的操作码是134312214131,莱斯<我>年代</我>={2、4}。</p><p>冗余就业数据出现在“更多”的后代选择随机替换丢失的工作数字”更少。“所有元素在“少”是随机分布的,修改完成。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig4/" target="_blank">4</a>被认为是一个例子,后代的5日维操作代码更改从1到4,和第十维度从1到2的变化。</p><p>随机选择一个操作机器的替代机组操作码后确定每一个后代,和操作代码构成一个完整的后代调度方案。</p><h4 id="experimental-simulation-and-result-analysis">4所示。实验仿真和结果分析</h4> <p>验证动态多目标的有效性SSA求解FJSSP数学模型建立了本文FJSSP模型和动态多目标SSA应用于解决一个实际的FJSSP。所有的测试在计算机上实现CPU:英特尔(R)的核心(TM) i5 - 7200 u, 4 G内存和2.70 GHz频率。程序中实现MATLAB R2016a。实验包括两个部分:有效性验证和先进的验证。</p><h5 id="sec4.1">4.1。有效性验证</h5> <p>本文探讨FJSSP建立数学模型和设计的调度方法的影响,以下FJSSPs测试:机器的数量<我>米</我>=6;重新安排周期是<我>t</我><年代ub><i>l</我></年代ub><i>=</我>1;两个相邻任务之间的时间间隔到达平均0.5的指数分布;工作/任务的数量<我>n</我><年代ub><i>j</我></年代ub>遵循(之间的均匀分布<我>米/</我>2,<我>米</我>];每个流程的灵活性受到之间均匀分布(<我>米/</我>2,<我>米</我>];每个流程的处理时间服从指数分布的平均值的1;<我>平均故障间隔</我>服从指数分布的意思<我>快艇</我>,<我>快艇</我>遵循(20、40)之间的均匀分布;<我>米TTR</我>服从指数分布的意思<我>地铁</我>,<我>地铁</我>遵循的均匀分布<a href="#B5">5</a>,<a href="#B10">10</a>),随机选择一个故障机器。要处理的任务的初始时间如表所示<a href="//www.newsama.com/journals/ijap/2021/6062689/tab2/" target="_blank">2</a>。算法参数设置如下:SSA的<我>N</我><年代ub><i>fs</我></年代ub>= 2;人口规模<我>N</我>=300;人口的上限附近大小和积极的内存大小是20;每个瞬态环境的最大迭代数<年代pan class="inline_break"> <svg height="11.7782pt" id="M36" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 34.927 11.7782" width="34.927pt" 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="M546 430L539 434C529 434 505 438 495 440C473 444 450 448 430 448C352 448 265 412 213 366C145 306 96 203 96 103C96 22 135 -12 160 -12C190 -12 238 14 262 32C310 68 368 120 411 184H413C403 117 396 75 384 21C353 -118 325 -158 291 -184C270 -200 241 -205 208 -205C133 -205 90 -164 74 -110C70 -98 58 -100 49 -107C34 -119 23 -140 23 -155C23 -190 74 -261 166 -261C219 -261 280 -233 314 -208C383 -157 446 -79 470 81C491 223 529 388 546 430ZM456 386C452 357 433 283 420 252C402 216 366 174 325 129C288 88 239 56 212 56C192 56 182 77 182 120C182 165 199 242 226 292C256 348 281 377 311 389C327 395 353 402 375 402C408 402 436 394 456 386Z" id="g113-104"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,7.072,3.132)"> <use xlink:href="#g58-107"></use> </g> <g transform="matrix(.0091,0,0,-0.0091,14.634,3.132)"> <path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z" id="g58-95"></path> </g> <g transform="matrix(.0091,0,0,-0.0091,18.72,3.132)"> <path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path> </g> <g transform="matrix(.013,0,0,-0.013,27.296,0)"> <use xlink:href="#g117-34"></use> </g> </svg><span class="irelop"></span><span class="nowrap"> <svg height="11.7782pt" style="vertical-align:-3.42938pt" version="1.1" viewbox="38.509183799999995 -8.34882 18.945 11.7782" width="18.945pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"> <g transform="matrix(.013,0,0,-0.013,38.559,0)"> <use xlink:href="#g113-50"></use> </g> <g transform="matrix(.013,0,0,-0.013,44.799,0)"> <use xlink:href="#g113-49"></use> </g> <g transform="matrix(.013,0,0,-0.013,51.039,0)"> <use xlink:href="#g113-49"></use> </g> </svg>;</年代pan></span>痘十字交叉概率模式<我>p</我><年代ub><i>c</我></年代ub>= 1;变异概率<我>p</我><年代ub><i>米</我></年代ub>= 1;当<我>N</我><年代ub><i>l</我></年代ub><sub><i>=</我></年代ub>100年,调度任务的总数是终止。</p><d我v 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 要处理的任务<我>t</我>=0。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2021/6062689/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <p>表<a href="//www.newsama.com/journals/ijap/2021/6062689/tab3/" target="_blank">3</a>是nondominated解决方案的一部分获得从断层的空闲时间吗<我>t</我>=5,第一次失败的时间<我>t</我>=15。7633,第一次故障修复时间<我>t</我>=23。7424或重新安排任务的优化。数据<a href="//www.newsama.com/journals/ijap/2021/6062689/fig5/" target="_blank">5</a>- - - - - -<a href="//www.newsama.com/journals/ijap/2021/6062689/fig7/" target="_blank">7</a>分别是nondominated图得到的任务处理或重新安排任务优化t = 52.1802失败的时候免费t = 30,第二个失败时间t = 43.6123,第二次故障修理时间。</p><d我v 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> Nondominated留存在不同时间的解决方案。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2021/6062689/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-b05d1052b17c9d6459a14016b045f26d"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-b05d1052b17c9d6459a14016b045f26d partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.005_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b05d1052b17c9d6459a14016b045f26d 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> Nondominated图的优化处理的任务<我>t</我>=30。</d我v> </div> </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-de8c7ee7411c5df32a77e0c22a8e6344"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.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-de8c7ee7411c5df32a77e0c22a8e6344 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.006_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-de8c7ee7411c5df32a77e0c22a8e6344 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig6/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> Nondominated图重新安排任务的优化<我>t</我>=43。6123。</d我v> </div> </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-a9db033fcb0f534393b52b94f4d788cc"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.007.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-a9db033fcb0f534393b52b94f4d788cc partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.007_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-a9db033fcb0f534393b52b94f4d788cc 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7</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig7/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> Nondominated图重新安排任务的优化<我>t</我>=52。1802。</d我v> </div> </div> </div> <p>从上面的图表中,本文提出的数学模型是一个以供应点优化问题当所有失败的机器在车间都是免费的。nondominated的解决方案是分布在同一个平面上。当故障发生或恢复时,数学模型是一个three-objective优化问题,nondominated的解决方案是分散在一个三维空间。</p><p>数据<a href="//www.newsama.com/journals/ijap/2021/6062689/fig8/" target="_blank">8</a>和<a href="//www.newsama.com/journals/ijap/2021/6062689/fig9/" target="_blank">9</a>的甘特图是车间调度计划在吗<我>t</我>=10- 30<我>t</我>分别为= -55。<我>J</我><年代ub><i>我</我></年代ub>任务数量。紫色,黄色,蓝色,橙色,青色,灰色代表每个任务的1 - 6的流程,分别。红色代表机器后重新安排过程失败,和绿色代表了重排过程机后无法恢复。当机器<我>米</我><年代ub>2</年代ub>分解在<我>t</我>=15。7633- -23.7424,故障机不执行任何操作。当机器<我>米</我>分解在<我>t</我>=43。6123- -52.1802,故障机不执行任何操作。机分解后,故障机器处于工作状态。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-37f25c38c25bfcebe8a22245f56fabe1"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.008.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-37f25c38c25bfcebe8a22245f56fabe1 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.008_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-37f25c38c25bfcebe8a22245f56fabe1 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8</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig8/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 甘特图的<我>t</我>=10- 30调度方案。</d我v> </div> </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-3b855b427e096da70f8d928a8f125f24"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.009.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-3b855b427e096da70f8d928a8f125f24 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.009_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-3b855b427e096da70f8d928a8f125f24 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9</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig9/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 甘特图的<我>t</我>=- 55调度方案。</d我v> </div> </div> </div> <p>为了进一步验证本文FJSSP数学模型建立和设计调度方法的影响,我们进行以下实验。机器的数量设置为8,重新安排时间<我>t</我><年代ub><i>l</我></年代ub>= 15;两个相邻的任务之间的时间间隔服从指数分布与平均为0.625。其他调度环境的参数设置和算法设置符合上面提到的这些。要处理的任务的初始时间如表所示<a href="//www.newsama.com/journals/ijap/2021/6062689/tab4/" target="_blank">4</a>。数据<a href="//www.newsama.com/journals/ijap/2021/6062689/fig10/" target="_blank">10</a>和<a href="//www.newsama.com/journals/ijap/2021/6062689/fig11/" target="_blank">11</a>的甘特图是车间调度计划在吗<我>t</我>=15- 25<我>t</我>=30- 40,分别。</p><d我v 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 要处理的任务<我>t</我>=0。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2021/6062689/tab4" 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-6675e5fabbdac12f5172fe296133330e"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0010.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-6675e5fabbdac12f5172fe296133330e partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0010_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-6675e5fabbdac12f5172fe296133330e 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10</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig10/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 甘特图的<我>t</我>=15∼<我>t</我>=25调度方案。</d我v> </div> </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-95593222172d8bff318ab028d7b38287"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0011.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-95593222172d8bff318ab028d7b38287 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0011_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-95593222172d8bff318ab028d7b38287 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11</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig11/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 甘特图的<我>t</我>=30∼<我>t</我>=40调度方案。</d我v> </div> </div> </div> <p>从数据可以看出<a href="//www.newsama.com/journals/ijap/2021/6062689/fig10/" target="_blank">10</a>和<a href="//www.newsama.com/journals/ijap/2021/6062689/fig11/" target="_blank">11</a>,当机<我>米</我><年代ub><i>1</我></年代ub>分解在<我>t</我>=15。5810-<我>t</我>=17。7670,故障机不执行任何操作。当机器<我>米</我><年代ub><i>2</我></年代ub>分解在<我>t</我>=33。9251-<我>t</我>=39。2939,故障机不执行任何操作。机分解后,故障机器处于工作状态。</p><p>总之,FJSSP数学模型,本文建立的调度方法可以有效地应对变化的一个实际的车间环境,包括到达或离开的任务在任何时间和故障的发生。这个条件可以有效地解决FJSSP。</p><h5 id="sec4.2">4.2。先进的验证</h5> <p>动态多目标SSA用于优化本文建立的数学模型和文献[<a href="#B23">23</a>)解决FJSSP通过满足下列条件:机器的数量<我>米</我>=6;重新安排周期<我>t</我><年代ub><i>l</我></年代ub>= 30;之间的时间间隔两个相邻任务到达的意思是3的指数分布;工作/任务的数量<我>n</我><年代ub><i>j</我></年代ub>遵循(之间的均匀分布<我>米</我>/2,<我>米</我>];每个过程遵循的程度的灵活性之间的均匀分布(<我>米</我>/2,<我>米</我>];每个流程的处理时间服从指数分布的意思是5;<我>平均故障间隔</我>服从指数分布的意思<我>快艇</我>,<我>快艇</我>服从均匀分布(100、200);<我>米TTR</我>服从指数分布的意思<我>地铁</我>,<我>地铁</我>服从均匀分布的(30、60)和随机选择一个故障机器的时候失败。其余的参数设置是与之前的一致。要处理的任务的初始时间如表所示<a href="//www.newsama.com/journals/ijap/2021/6062689/tab5/" target="_blank">5</a>。</p><d我v 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</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/tab5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 要处理的任务<我>t</我>=0。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/ijap/2021/6062689/tab5" target="_blank" aria-label="View full page"></a> </div> </div> <p>动态调度环境下的调度方案是不同的,和车间状态结束时每个瞬态环境是不同的。研讨会的初始状态,开始下一个新环境是不同的。比较不同数学模型的优化能力FJSSP需要相同的初始车间状态和相同的任务优化。以下部分在本研究中进行了测试。<年代pan class="list"><span class="list-item"><span class="list-label">(1)</年代pan><span class="list-content">数学模型在文献[<a href="#B23">23</a>)用于动态环境不断优化。车间状态记录每个新的调度周期的开始。几种不同的初始状态和瞬态调度周期。要处理的新任务在每个调度周期记录,本文建立的数学模型是用来优化初始状态对应的车间。完成时间和最大机器负载两个调度指标的文献[<a href="#B23">23</a>)进行了比较。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig12/" target="_blank">12</a>是最大的调度时间的对比图获得优化的两个模型。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig13/" target="_blank">13</a>最大的是一个比较图机负载从两个模型获得。</年代pan></span><span class="list-item"><span class="list-label">(2)</年代pan><span class="list-content">图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig12/" target="_blank">12</a>显示,当数学模型在文献[<a href="#B23">23</a>)是用于优化FJSSP不断,完成时间增加而增加的数量要处理的任务。在最初的时候,数学模型在文献[<a href="#B23">23</a>)达到第四周期调度完成时间短,但最小差异之间存在两个数学模型在第九调度周期。在调度周期的其余部分,本文数学模型实现完成时间短。因此,相比之下,数学模型在文献[<a href="#B23">23</a>),本文的数学模型是更有效的解决FJSSP。在图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig13/" target="_blank">13</a>机器负载的增加,最大数量的增加要处理的任务。第一调度周期和第七调度期在文献中最大产量较小的机器负荷。两个数学模型的优化结果在第五调度周期相似。在调度周期的其余部分,本文提出的数学模型实现最大机载荷较小。因此,相比之下,数学模型在文献[<a href="#B23">23</a>),本文的数学模型解决FJSSP时具有更好的稳定性。</年代pan></span><span class="list-item"><span class="list-label">(3)</年代pan><span class="list-content">本文建立的数学模型用于上述动态环境不断优化。车间状态记录每个新的调度周期的开始。几种不同的初始状态和瞬态调度周期。要处理的新任务在每个调度周期记录,以及数学模型在文献[<a href="#B23">23</a>)优化的初始状态对应的车间。完成时间、磅和偏差度的三个调度索引优化本文进行了比较。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" target="_blank">14</a>显示了最大的调度时间的比较从两个模型的优化,获得和图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig15/" target="_blank">15</a>描绘了一个磅所得的比较两个模型的优化。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" target="_blank">14</a>显示了两个模型的故障或恢复(<我>米</我><年代ub>2</年代ub>分解在<我>t</我>=85。7705,108.0616;<我>米</我><年代ub>5</年代ub>分解在<我>t</我>=137。4366和复苏<我>t</我>=196。8504;<我>米</我><年代ub>6</年代ub>分解在<我>t</我>=253。2210和复苏<我>t</我>=261。4715)。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig16/" target="_blank">16</a>是最后的甘特图得到的调度方案优化的数学模型建立。</年代pan></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-bd12c6c582a988be331120a03b777d95"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0012.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-bd12c6c582a988be331120a03b777d95 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0012_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-bd12c6c582a988be331120a03b777d95 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12</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig12/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较每个调度周期的最大完工时间。</d我v> </div> </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-6d5a965269467122e8b48d32c7ddcf16"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0013.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-6d5a965269467122e8b48d32c7ddcf16 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0013_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-6d5a965269467122e8b48d32c7ddcf16 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13</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig13/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较的最大负载的机器在每个调度周期。</d我v> </div> </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-da782a50eb94397ccc83c8074bae9bb3"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0014.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-da782a50eb94397ccc83c8074bae9bb3 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0014_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-da782a50eb94397ccc83c8074bae9bb3 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14</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较每个调度周期的最大完工时间。</d我v> </div> </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-fea199c9fa31d229c75cb1888ae2ce17"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0015.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-fea199c9fa31d229c75cb1888ae2ce17 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0015_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-fea199c9fa31d229c75cb1888ae2ce17 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15</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig15/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较每个调度周期的磅。</d我v> </div> </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-b4849f7746f3e2e81154a97571a93778"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0016a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0016b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0016c.jpg"> <br> <strong>(c)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-b4849f7746f3e2e81154a97571a93778 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0016a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0016b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0016c_th.jpg"><br><strong>(c)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-b4849f7746f3e2e81154a97571a93778 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16</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig16/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 最终的调度方案。(一)<我>t</我>=0- 3<我>t</我><年代ub>l</年代ub>。(b)<我>t</我>=4<我>t</我><年代ub>l</年代ub>6<我>t</我><年代ub>l</年代ub>。(c)<我>t</我>=7<我>t</我><年代ub>l</年代ub>9<我>t</我><年代ub>l</年代ub>。</d我v> </div> </div> </div> <p>图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" target="_blank">14</a>表明本文建立的数学模型时不断优化FJSSP,完成时间与任务要处理的数量增加。除了在第四调度周期,本文的数学模型实现一个更小的完成时间在调度周期的其余部分。因此,相比之下,数学模型在文献[<a href="#B23">23</a>),本文的数学模型是更有效的解决FJSSP。在图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig15/" target="_blank">15</a>调度过程的进度,车间的稳定性增强。除了在第六调度周期,本文的数学模型实现一个小磅的调度周期。因此,相比之下,数学模型在文献[<a href="#B23">23</a>),目前的模型解决FJSSP达到更好的系统稳定性。图<a href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" target="_blank">14</a>说明当时的失败和恢复的时间,本文建立的数学模型可以实现更小的新老方案的偏差。因此,本文提出的数学模型可以重新安排过程中保持更好的稳定后,车间机器故障或机器故障恢复。一个全面的观察数据<a href="//www.newsama.com/journals/ijap/2021/6062689/fig14/" target="_blank">14</a>- - - - - -<a href="//www.newsama.com/journals/ijap/2021/6062689/fig17/" target="_blank">17</a>表明,机<我>米</我><年代ub><i>5</我></年代ub>失败在第四调度周期。虽然最终的调度计划优化的数学模型建立在本文较长,最好保持系统稳定,特别是当机器故障延期实现较小的偏差;<我>米5</我>恢复在第六调度周期。虽然最终的调度计划优化的磅用本文建立的数学模型是穷人,完成时间是短的,和一个较小的偏差度达到在机器故障延期。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-1936390db485f124e0c2ac9f5f6c3999"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0017a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0017b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/figures/6062689.fig.0017c.jpg"> <br> <strong>(c)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-1936390db485f124e0c2ac9f5f6c3999 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0017a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0017b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)" src="https://static.hindawi.com/articles/ijap/volume-2021/6062689/thumbnails/6062689.fig.0017c_th.jpg"><br><strong>(c)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-1936390db485f124e0c2ac9f5f6c3999 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17</年代pan> <a aria-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/ijap/2021/6062689/fig17/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 比较新旧调度计划之间的偏差在机器故障和故障恢复。(一)M2失败。(b) M5失败。(c) M6失败。</d我v> </div> </div> </div> <p>总之,本文建立的数学模型具有更高的效率和更好的解决FJSSP时系统的稳定性。此外,在车间机器故障或故障恢复,它可以同时关注效率和稳定性。它为FJSSP优化有一定的优势。</p><h4 id="conclusions">5。结论</h4> <p>在这项研究中,FJSSP特点和研究现状的综合分析。一个新的数学模型的基础上建立了三个目标:完成时间,磅,和广告新老之间的调度方案。一个动态的多目标SSA用于建立优化模型。实验结果表明,动态多目标SSA可以用来解决FJSSP。在本文建立的数学模型在解决动态多目标FJSSP提高效率与稳定。尤其是车间机器分解或回到工作,建立模型可以提高效率之间的平衡与稳定。在未来,收敛速度应该改进柔性工作车间调度算法。</p><h4 id="data-availability">数据可用性</h4> <p>使用的数据来支持本研究的发现可以从相应的作者。</p><h4 id="conflicts-of-interest">的利益冲突</h4> <p>作者宣称没有利益冲突有关的出版。</p><h4 id="acknowledgments">确认</h4> <p>这项工作的部分支持由吉林在格兰特没有技术创新发展。20210103090。</p></d我v> </div> <div class="ArticleReferences_xmlContent__p_40j"> <h4 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</g> </svg></span></a> <div class="articleToolbarStatistics_articleToolbarStatistics__8_woN"> <div class="articleToolbarStatistics_column__R2GqD"> <div> <div> <span>的观点</年代pan> <div class="articleToolbarStatistics_amount__vJIDp"> 518年</d我v> </div> <div> <span>下载</年代pan> <div class="articleToolbarStatistics_amount__vJIDp"> 631年</d我v> </div> </div> </div> <div class="articleToolbarStatistics_column__R2GqD articleToolbarStatistics_dimensions__pe7pO"> <div> 引用</d我v> <span class="__dimensions_badge_embed__ articleToolbarStatistics_circle__p2dSc" data-doi="10.1155/2021/6062689" data-style="small_circle"></span> </div> </div> <ul class="articleToolbarSocials_articleToolbarSocials__g02HH"> <li><a href="https://twitter.com/share?url=https://doi.org/10.1155/2021/6062689&via=Hindawi" unselectable="on" title="" rel="noopener noreferrer" target="_blank"><span role="img" class="anticon"> <svg xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="126.444 2.281 589 589"> <circle 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