粒子群算法源码及论文_算法_arm_其他

<html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta charset="utf-8"> <meta name="generator" content="pdf2htmlEX"> <meta http-equiv="X-UA-Compatible" content="IE=edge,chrome=1"> <link rel="stylesheet" href="https://static.pudn.com/base/css/base.min.css"> <link rel="stylesheet" href="https://static.pudn.com/base/css/fancy.min.css"> <link rel="stylesheet" href="https://static.pudn.com/prod/directory_preview_static/624b7bb5fc37f87c247ceca0/raw.css"> <script src="https://static.pudn.com/base/js/compatibility.min.js"></script> <script src="https://static.pudn.com/base/js/pdf2htmlEX.min.js"></script> <script> try{ pdf2htmlEX.defaultViewer = new pdf2htmlEX.Viewer({}); }catch(e){} </script> <title></title> </head> <body> <div id="sidebar" style="display: none"> <div id="outline"> </div> </div> <div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/624b7bb5fc37f87c247ceca0/bg1.jpg"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls0 ws0">池元成，方杰，蔡国飙：基于差分进化和粒子群优化算法的混合优化算法 2009,30</div><div class="t m0 x2 h2 y2 ff2 fs0 fc0 sc0 ls2 ws0">(</div><div class="t m0 x3 h2 y1 ff2 fs0 fc0 sc0 ls0 ws0">12</div><div class="t m0 x4 h2 y2 ff2 fs0 fc0 sc0 ls2 ws0">)</div><div class="t m0 x5 h2 y1 ff2 fs0 fc0 sc0 ls0 ws0">2963</div><div class="t m0 x1 h3 y3 ff3 fs0 fc0 sc0 ls0 ws0">0 引 言</div><div class="t m0 x6 h4 y4 ff4 fs1 fc0 sc0 ls0 ws0">差分进化</div><div class="t m0 x7 h5 y5 ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 x8 h5 y4 ff2 fs1 fc0 sc0 ls0 ws0">differential evolution，DE</div><div class="t m0 x9 h5 y5 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 xa h6 y6 ff2 fs2 fc0 sc0 ls8 ws0">[</div><div class="t m0 xb h6 y7 ff2 fs2 fc0 sc0 ls0 ws0">1</div><div class="t m0 xc h6 y6 ff2 fs2 fc0 sc0 ls8 ws0">]</div><div class="t m0 xd h4 y4 ff4 fs1 fc0 sc0 ls0 ws0">和粒子群优化算法</div><div class="t m0 x1 h5 y8 ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 xe h5 y9 ff2 fs1 fc0 sc0 ls0 ws0">particle swarm optimization，PSO</div><div class="t m0 xf h5 y8 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 x10 h6 ya ff2 fs2 fc0 sc0 ls8 ws0">[</div><div class="t m0 x11 h6 yb ff2 fs2 fc0 sc0 ls0 ws0">2</div><div class="t m0 x12 h6 ya ff2 fs2 fc0 sc0 ls8 ws0">]</div><div class="t m0 x13 h4 y9 ff4 fs1 fc0 sc0 ls0 ws0">作为目前应用较为广泛的全</div><div class="t m0 x1 h4 yc ff4 fs1 fc0 sc0 ls0 ws0">局优化算法，受到了很多学者的关注。这两个算法都是基于</div><div class="t m0 x1 h4 yd ff4 fs1 fc0 sc0 ls0 ws0">群体智能和随机策略、并且依据各自的搜索机制进行寻优，已</div><div class="t m0 x1 h4 ye ff4 fs1 fc0 sc0 ls0 ws0">经成功应用很多领域的优化问题中</div><div class="t m0 x14 h6 yf ff2 fs2 fc0 sc0 ls8 ws0">[</div><div class="t m0 x15 h6 y10 ff2 fs2 fc0 sc0 ls0 ws0">3-6</div><div class="t m0 x16 h6 yf ff2 fs2 fc0 sc0 ls8 ws0">]</div><div class="t m0 x17 h4 ye ff4 fs1 fc0 sc0 ls0 ws0">。</div><div class="t m0 x6 h5 y11 ff2 fs1 fc0 sc0 ls6 ws0">DE 最初是由 Storn 和 Price 提出的一种进化类算法。它</div><div class="t m0 x1 h4 y12 ff4 fs1 fc0 sc0 ls0 ws0">使用与遗传算法相类似的算术操作</div><div class="t m0 x18 h5 y13 ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 x19 h4 y12 ff4 fs1 fc0 sc0 ls0 ws0">包括变异、交叉和选择算</div><div class="t m0 x1 h4 y14 ff4 fs1 fc0 sc0 ls0 ws0">子</div><div class="t m0 x1a h5 y15 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 x1b h4 y14 ff4 fs1 fc0 sc0 ls0 ws0">来更新随机产生的初始群体或父代群体，通过多代进化来</div><div class="t m0 x1 h4 y16 ff4 fs1 fc0 sc0 ls0 ws0">实现对求解空间的全局搜索，以便找到待求解问题的最优解。</div><div class="t m0 x1 h5 y17 ff2 fs1 fc0 sc0 ls6 ws0">DE 操作简单，性能强大，可以并行求解。然而，对于不同的问</div><div class="t m0 x1 h5 y18 ff4 fs1 fc0 sc0 ls0 ws0">题，DE 都需要相应地调节自身参数；并且当群体迭代收敛到</div><div class="t m0 x1 h4 y19 ff4 fs1 fc0 sc0 ls0 ws0">某一区域时，由于差异性的减少，容易陷入局部最优。</div><div class="t m0 x6 h5 y1a ff2 fs1 fc0 sc0 lsa ws0">PSO 是由 Kennedy 和 Eberhart 提出的一种群智能算法。</div><div class="t m0 x1 h5 y1b ff4 fs1 fc0 sc0 ls0 ws0">作为非线性优化技术，PSO基于群体搜索策略，将粒子随机分</div><div class="t m0 x1 h4 y1c ff4 fs1 fc0 sc0 ls0 ws0">布于搜索空间，一个粒子即代表一个空间点。在搜索过程中，</div><div class="t m0 x1c h4 y1d ff4 fs1 fc0 sc0 ls0 ws0">每个粒子的运动轨迹取决于整个种群的历史最好位置及其个</div><div class="t m0 x1c h4 y1e ff4 fs1 fc0 sc0 ls0 ws0">体所经历的最好位置。该算法早期收敛速度较快，然而当不</div><div class="t m0 x1c h4 y1f ff4 fs1 fc0 sc0 ls0 ws0">再有更好的个体更新历史最好位置时，所有的粒子会快速聚</div><div class="t m0 x1c h4 y20 ff4 fs1 fc0 sc0 ls0 ws0">集到当前历史最好位置的区域，出现早熟停滞现象。此外，该</div><div class="t m0 x1c h4 y21 ff4 fs1 fc0 sc0 ls0 ws0">算法对自身参数也较为敏感，不同的参数设置对算法性能的</div><div class="t m0 x1c h4 y22 ff4 fs1 fc0 sc0 ls0 ws0">影响较大。</div><div class="t m0 x1d h5 y23 ff4 fs1 fc0 sc0 ls0 ws0">为了改进算法的性能，已经发展了若干混合 DE 和 PSO</div><div class="t m0 x1c h4 y24 ff4 fs1 fc0 sc0 ls0 ws0">的算法。例如，文献</div><div class="t m0 x1e h5 y25 ff2 fs1 fc0 sc0 ls3 ws0">[</div><div class="t m0 x1f h5 y24 ff2 fs1 fc0 sc0 ls0 ws0">7</div><div class="t m0 x20 h5 y25 ff2 fs1 fc0 sc0 ls3 ws0">]</div><div class="t m0 x21 h5 y24 ff4 fs1 fc0 sc0 ls0 ws0">利用 DE 对 PSO 的个体历史最好值进</div><div class="t m0 x1c h4 y26 ff4 fs1 fc0 sc0 ls0 ws0">行变异操作，将新产生的个体历史最好值用于指导粒子的飞</div><div class="t m0 x1c h4 y27 ff4 fs1 fc0 sc0 ls0 ws0">行；文献</div><div class="t m0 x22 h5 y28 ff2 fs1 fc0 sc0 ls3 ws0">[</div><div class="t m0 x23 h5 y27 ff2 fs1 fc0 sc0 ls0 ws0">8</div><div class="t m0 x24 h5 y28 ff2 fs1 fc0 sc0 ls3 ws0">]</div><div class="t m0 x25 h5 y27 ff4 fs1 fc0 sc0 ls0 ws0">将种群分为并行的 DE 群和 PSO 群，比较两个子群</div><div class="t m0 x1c h4 y29 ff4 fs1 fc0 sc0 ls0 ws0">得到的种群最优值作为下一代的进化依据；文献</div><div class="t m0 x26 h5 y2a ff2 fs1 fc0 sc0 ls3 ws0">[</div><div class="t m0 x27 h5 y29 ff2 fs1 fc0 sc0 ls0 ws0">9</div><div class="t m0 x28 h5 y2a ff2 fs1 fc0 sc0 ls3 ws0">]</div><div class="t m0 x29 h4 y29 ff4 fs1 fc0 sc0 ls0 ws0">依据随机</div><div class="t m0 x1c h5 y2b ff4 fs1 fc0 sc0 ls0 ws0">概率大小选择 DE 或 PSO 作为产生临时群体的方式，然后通</div><div class="t m0 x1c h4 y2c ff4 fs1 fc0 sc0 ls0 ws0">过对父代群体和临时群体使用选择算子来产生子代群体。</div><div class="t m0 x1d h5 y2d ff4 fs1 fc0 sc0 ls0 ws0">本文结合 DE和PSO 提出了一种新的混合优化算法</div><div class="t m0 x2a h5 y2e ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 x2b h4 y2d ff4 fs1 fc0 sc0 ls0 ws0">简称</div><div class="t m0 x1c h5 y2f ff2 fs1 fc0 sc0 ls6 ws0">DPA</div><div class="t m0 x2c h5 y30 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 x1d h4 y2f ff4 fs1 fc0 sc0 ls0 ws0">。该算法可以分为两个阶段：第一阶段为“变异—选择”</div><div class="t m0 x1c h5 y31 ff4 fs1 fc0 sc0 ls0 ws0">操作，即通过比较由DE变异算子生成的群体和父代群体来选</div><div class="t m0 x1c h5 y32 ff4 fs1 fc0 sc0 ls0 ws0">择更新进入下一阶段的父代群体；第二阶段为“PSO—交叉—</div><div class="t m0 x1 h7 y33 ff4 fs3 fc0 sc0 ls0 ws0">收稿日期：</div><div class="t m0 x2d h8 y34 ff2 fs3 fc0 sc0 ls1 ws0">2008-07-10</div><div class="t m0 x2e h7 y33 ff4 fs3 fc0 sc0 ls0 ws0">；修订日期：</div><div class="t m0 x11 h8 y34 ff2 fs3 fc0 sc0 ls1 ws0">2009-02-24</div><div class="t m0 xc h7 y33 ff4 fs3 fc0 sc0 ls0 ws0">。</div><div class="t m0 x1 h7 y35 ff4 fs3 fc0 sc0 ls0 ws0">作者简介：池元成</div><div class="t m0 x2f h8 y36 ff2 fs3 fc0 sc0 lsb ws0">(</div><div class="t m0 x30 h8 y37 ff2 fs3 fc0 sc0 ls1 ws0">1981</div><div class="t m0 x31 h7 y35 ff4 fs3 fc0 sc0 ls0 ws0">－</div><div class="t m0 x32 h8 y36 ff2 fs3 fc0 sc0 lsb ws0">)</div><div class="t m0 x33 h7 y35 ff4 fs3 fc0 sc0 ls0 ws0">，男，黑龙江宁安人，博士研究生，研究方向为优化算法； 方杰，男，博士研究生，研究方向为多学科设计优化；</div><div class="t m0 x1 h7 y38 ff4 fs3 fc0 sc0 ls0 ws0">蔡国飙，男，教授，研究方向为多学科设计优化。</div><div class="t m0 x34 h8 y39 ff2 fs3 fc0 sc0 lsc ws0">E-mail</div><div class="t m0 x35 h7 y38 ff4 fs3 fc0 sc0 ls0 ws0">：</div><div class="t m0 x36 h8 y39 ff2 fs3 fc0 sc0 lse ws0">chiyuancheng@126.com</div><div class="t m0 x37 h9 y3a ff5 fs4 fc0 sc0 ls0 ws0">基于差分进化和粒子群优化算法的混合优化算法</div><div class="t m0 x38 ha y3b ff1 fs5 fc0 sc0 ls0 ws0">池元成， 方 杰， 蔡国飙</div><div class="t m0 x16 h2 y3c ff2 fs0 fc0 sc0 ls2 ws0">(</div><div class="t m0 x39 h2 y3d ff1 fs0 fc0 sc0 ls0 ws0">北京航空航天大学 宇航学院，北京 100191</div><div class="t m0 x3a h2 y3c ff2 fs0 fc0 sc0 ls2 ws0">)</div><div class="t m0 x1 h4 y3e ff4 fs1 fc0 sc0 ls0 ws0">摘 要：为了发挥差分进化和粒子群优化算法各自拥有的特点，并克服自身存在的问题，提出了一种混合优化算法</div><div class="t m0 x2a h5 y3f ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 x2b h4 y3e ff1 fs1 fc0 sc0 ls0 ws0">简称</div><div class="t m0 x1 h5 y40 ff2 fs1 fc0 sc0 ls6 ws0">DPA</div><div class="t m0 x3b h5 y41 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 x6 h4 y40 ff1 fs1 fc0 sc0 ls0 ws0">。该算法首先利用差分进化的变异和选择算子产生新的群体，然后通过使用粒子群优化算法和交叉、选择算子进行局</div><div class="t m0 x1 h5 y42 ff1 fs1 fc0 sc0 ls0 ws0">部搜索。在整个算法过程中，群体寻优范围先扩散再收缩，反复迭代渐进收敛。通过 3 个标准算例的测试表明，新的混合优</div><div class="t m0 x1 h4 y43 ff1 fs1 fc0 sc0 ls0 ws0">化算法与差分进化和粒子群优化算法相比，具有收敛速度快、搜索能力强、鲁棒性好的特点。</div><div class="t m0 x1 h5 y44 ff4 fs1 fc0 sc0 ls0 ws0">关键词：差分进化; 粒子群优化算法; 混合算法; 优化; 基准测试函数</div><div class="t m0 x1 h5 y45 ff4 fs1 fc0 sc0 ls0 ws0">中图法分类号：TP18 文献标识码：A 文章编号：1000-7024</div><div class="t m0 x1c h5 y46 ff2 fs1 fc0 sc0 ls3 ws0">(</div><div class="t m0 x3c h5 y45 ff2 fs1 fc0 sc0 ls0 ws0">2009</div><div class="t m0 x3d h5 y46 ff2 fs1 fc0 sc0 ls3 ws0">)</div><div class="t m0 x3e h5 y45 ff2 fs1 fc0 sc0 ls0 ws0">12-2963-03</div><div class="t m0 x3f hb y47 ff2 fs6 fc0 sc0 ls12 ws0">Hybrid optimization algorithm based on differential evolution and particle</div><div class="t m0 x40 hb y48 ff2 fs6 fc0 sc0 ls16 ws0">swarm optimization</div><div class="t m0 x41 hc y49 ff2 fs5 fc0 sc0 ls17 ws0">CHI Yuan-cheng, FANG Jie, CAI Guo-biao</div><div class="t m0 x42 h2 y4a ff2 fs0 fc0 sc0 ls2 ws0">(</div><div class="t m0 x43 h2 y4b ff2 fs0 fc0 sc0 ls1e ws0">School of Astronautics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China</div><div class="t m0 x4 h2 y4a ff2 fs0 fc0 sc0 ls2 ws0">)</div><div class="t m0 x1 hd y4c ff3 fs7 fc0 sc0 ls24 ws0">Abstract：To take advantage of different algorithms and overcome their limitations, a hybridoptimization algorithm</div><div class="t m0 x44 he y4d ff2 fs7 fc0 sc0 ls26 ws0">(</div><div class="t m0 x45 he y4c ff2 fs7 fc0 sc0 ls24 ws0">DPA</div><div class="t m0 x46 he y4d ff2 fs7 fc0 sc0 ls26 ws0">)</div><div class="t m0 x4 he y4c ff2 fs7 fc0 sc0 ls29 ws0">is proposed,</div><div class="t m0 x1 he y4e ff2 fs7 fc0 sc0 ls1 ws0">based on the combination of differential evolution</div><div class="t m0 x47 he y4f ff2 fs7 fc0 sc0 ls26 ws0">(</div><div class="t m0 x48 he y4e ff2 fs7 fc0 sc0 ls24 ws0">DE</div><div class="t m0 x49 he y4f ff2 fs7 fc0 sc0 ls26 ws0">)</div><div class="t m0 x4a he y4e ff2 fs7 fc0 sc0 ls27 ws0">and particle swarm optimization</div><div class="t m0 x4b he y4f ff2 fs7 fc0 sc0 ls26 ws0">(</div><div class="t m0 x4c he y4e ff2 fs7 fc0 sc0 ls25 ws0">PSO</div><div class="t m0 x4d he y4f ff2 fs7 fc0 sc0 ls26 ws0">)</div><div class="t m0 x4e he y4e ff2 fs7 fc0 sc0 ls11 ws0">. In the first step of DPA, differential</div><div class="t m0 x1 he y50 ff2 fs7 fc0 sc0 ls2a ws0">mutation and selection operators are employed to produce a new population for effective variation. Next, PSO is carried out for local</div><div class="t m0 x1 he y51 ff2 fs7 fc0 sc0 ls27 ws0">exploration with high efficiency, followed by crossover and selection operations. Thus, the extent of search region for the population</div><div class="t m0 x1 he y52 ff2 fs7 fc0 sc0 ls29 ws0">is increased and decreased sequently at each iteration of the DPA progress, and eventually resulted in convergence to an optimal solution.</div><div class="t m0 x1 he y53 ff2 fs7 fc0 sc0 ls24 ws0">Numerical tests on four benchmark functions are conducted for the algrithom evaluation. The results show the improvement in the con-</div><div class="t m0 x1 he y54 ff2 fs7 fc0 sc0 ls1 ws0">vergence speed, searching ability, and computation stability by comparison with the DE and PSO.</div><div class="t m0 x1 hd y55 ff3 fs7 fc0 sc0 ls2a ws0">Key words：differential evolution; particle swarm optimization; hybrid algorithm; optimization; benchmark function</div><div class="t m0 x4f ha y56 ff4 fs5 fc0 sc0 ls0 ws0">计算机工程与设计 Computer Engineering and Design</div><div class="t m0 x50 hf y57 ff6 fs8 fc0 sc0 ls0 ws0">人工智能</div></div><div class="pi" data-data='{"ctm":[1.613445,0.000000,0.000000,1.613445,0.000000,0.000000]}'></div></div> </body> </html>