├── LICENSE ├── README.md ├── b50.txt ├── c21.txt ├── create_matrix.m ├── draw_convergence.m ├── draw_distribution.m ├── draw_net.m ├── draw_pf.m ├── example.txt ├── execute re-encoding.bat ├── extract_value.m ├── fitness.m ├── floyd_algo.m ├── main.m ├── pareto_front.m ├── re-encoding.ps1 ├── read_dataset.m ├── reorganize.m ├── test.m ├── validate.m └── 说明 ├── 优化MOPSO算法流程图.jpeg ├── 优化MOPSO算法流程图.pos ├── 优化MOPSO算法流程图.svg ├── 函数依赖图.png ├── 函数依赖图.pptx ├── 数据集说明.docx └── 算法的若干细节.docx /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # 用改进后的多目标粒子群优化（MOPSO）算法解决带有风险矩阵的多辆车配送旅行商问题（TSP） 2 | 3 | - [用改进后的多目标粒子群优化（MOPSO）算法解决带有风险矩阵的多辆车配送旅行商问题（TSP）](#用改进后的多目标粒子群优化mopso算法解决带有风险矩阵的多辆车配送旅行商问题tsp) 4 | - [1. 项目说明](#1-项目说明) 5 | - [2. 资源](#2-资源) 6 | - [2.1. 本文件夹的文件结构](#21-本文件夹的文件结构) 7 | - [2.2. “说明”文件夹的文件结构](#22-说明文件夹的文件结构) 8 | - [2.3. 其他资源](#23-其他资源) 9 | - [3. 使用](#3-使用) 10 | - [3.1. 步骤](#31-步骤) 11 | - [3.2. 出现乱码？](#32-出现乱码) 12 | - [3.3. 在 MATLAB 2022a 下运行失败？](#33-在-matlab-2022a-下运行失败) 13 | - [4. 算法](#4-算法) 14 | - [4.1. 问题情景](#41-问题情景) 15 | - [4.2. 算法思路](#42-算法思路) 16 | - [4.3. 流程图与依赖图](#43-流程图与依赖图) 17 | - [4.4. 时间复杂度](#44-时间复杂度) 18 | - [4.5. 算法优缺点](#45-算法优缺点) 19 | - [优点](#优点) 20 | - [缺点](#缺点) 21 | - [4.6. 了解更多](#46-了解更多) 22 | - [5. 数据集](#5-数据集) 23 | - [引用](#引用) 24 | 25 | ## 1. 项目说明 26 | 27 | 此代码是河南财经政法大学硕士项目的一部分，受 GPL-3.0-only 开源协议保护。GitHub 地址：https://github.com/Ki-Seki/MOPSO-for-Distribution 28 | 29 | This code is a part of a HUEL master degree project under the protection of GPL-3.0-only license. GitHub Link: https://github.com/Ki-Seki/MOPSO-for-Distribution 30 | 31 | ## 2. 资源 32 | 33 | ### 2.1. 本文件夹的文件结构 34 | 35 | |名称或后缀|包含文件数|作用| 36 | |--|--|--| 37 | |`README.md`|1|本文档| 38 | |`*.m`|14|实现本算法的核心代码、测试文件等| 39 | |`*.txt`|3|给出的三个样例数据集| 40 | |`re-encoding.ps1`|1|用于编码格式转换的 PowerShell 脚本| 41 | |`execute re-encoding.bat`|1|用于执行上述脚本的 Batch 脚本| 42 | |`LICENSE`|1|GPL-3.0-only 开源协议| 43 | |`说明`|6|关于此项目算法、数据集的一系列辅助说明文件| 44 | 45 | ### 2.2. “说明”文件夹的文件结构 46 | 47 | |名称|类型|作用| 48 | |--|--|--| 49 | |`优化MOPSO算法流程图.png`|PNG 图片|描述了该算法的流程图| 50 | |`优化MOPSO算法流程图.pos`|POS 源文件|上述文件的源文件，在 [ProcessOn](https://www.processon.com/) 打开即可重新编辑| 51 | |`函数依赖图.png`|PNG 图片|描述了该算法各个模块间的相互依赖关系| 52 | |`函数依赖图.pptx`|PPT 源文件|上述文件的源文件，可重新编辑| 53 | |`算法的若干细节.docx`|WORD 文档|讲解了算法的四个细节：位置的编码与解的编码，速度与位置的重编码，适应度函数的设计，用帕累托前沿来替代粒子群优化中的全局最优| 54 | |`数据集说明.docx`|WORD 文档|以 `example.txt` 为例，详细地对数据集进行了说明| 55 | 56 | ### 2.3. 其他资源 57 | 58 | |名称|类型|作用|链接| 59 | |--|--|--|--| 60 | |`MOPSO说明与使用`|在线视频|包含对 MOPSO 的使用、算法、数据集的介绍|[Loom](https://loom.com/share/folder/5ee40289950a4896a24e5c6392fdca02)| 61 | |`优化MOPSO算法流程图`|在线流程图|MOPSO 的 `main.m` 程序的流程图的在线查看版本|[ProcessOn](https://www.processon.com/view/link/6201fb816376890390d1dd07)| 62 | 63 | ## 3. 使用 64 | 65 | ### 3.1. 步骤 66 | 67 | 1. 选择性修改 `main.m` 中“%% 参数设置”部分的参数 68 | 2. 运行 `main.m` 程序 69 | 3. 在命令行窗口交互式地查看输出，在图片窗口中查看输出的图表 70 | 71 | ### 3.2. 出现乱码？ 72 | 73 | 如果打开代码文件出现乱码，请阅读本小节 74 | 75 | MATLAB 对文件的编码遵照系统默认编码格式（GB 2312）。而本项目包括本文件都是 UTF-8 编码的。为了解决这一冲突，提供如下方法（仅在 Windows 平台可用）： 76 | 77 | * 在文件管理器中打开本文件夹，双击运行 `execute re-encoding.m` 文件 78 | * 这会生成与本文件夹同级的文件夹 `encoded` ，它包含重新编码后的文件 79 | * 在 MATLAB 中打开 `encoded` 文件夹即可，其中的文件均采用系统默认编码格式 80 | 81 | ### 3.3. 在 MATLAB 2022a 下运行失败？ 82 | 83 | 由于 MATLAB 2015b 固有的 Bug 及与 MATLAB 2022a 的版本兼容性问题，直接下载下来的代码运行时会报错。可根据下表按需修改： 84 | 85 | |文件名|行数|原内容|修改后内容| 86 | |--|--|--|--| 87 | |`extract_value.m`|16|`matchsize-field2size-2`|`matchsize-field2size-1`| 88 | |`draw_convergence.m`|8|`suptitle`|`sgtitle`| 89 | 90 | ## 4. 算法 91 | 92 | ### 4.1. 问题情景 93 | 94 | 疫情下不同节点风险等级不同，车辆跨异风险区运输需要相应的消杀成本，如何在此约束下解决含有多辆车及多目标的应急物资配送问题？ 95 | 96 | ### 4.2. 算法思路 97 | 98 | 本算法 = 普通粒子群优化 + 多目标优化 + 帕累托前沿 + 针对 TSP 的速度位置重编码 99 | 100 | ### 4.3. 流程图与依赖图 101 | 102 | 有三个地方可以查看该算法的流程图，分别是在线的 [ProcessOn](https://www.processon.com/view/link/6201fb816376890390d1dd07)，离线的图片 [优化MOPSO算法流程图.png](.\说明\优化MOPSO算法流程图.png) 和离线的 POS 文件 [优化MOPSO算法流程图.pos](.\说明\优化MOPSO算法流程图.pos). 其中，POS 文件是流程图绘制平台 ProcessOn 的源文件，从其官网打开即可对该文件再做修改。 103 | 104 | 在 `说明` 文件夹下，有函数依赖图，方便查看该算法代码各个模块间的相互依赖关系。 105 | 106 | ### 4.4. 时间复杂度 107 | 108 | 算法核心部分循环 loop_cnt 次；每次都要遍历粒子群中所有粒子，共 particle_cnt 个粒子；算法的瓶颈在于 fitness() 函数，此函数的算法复杂度与 NODE_COUNT 呈正相关。因此最终算法时间复杂度为 O(loop_cnt × particle_cnt × NODE_COUNT). 109 | 110 | 令 N = max{loop_cnt, particle_cnt,NODE_COUNT}, 则算法时间复杂度也可表示为 O(N³). 111 | 112 | ### 4.5. 算法优缺点 113 | 114 | #### 优点 115 | 116 | * 多目标粒子群优化（Multi-Objective PSO）算法：运用多目标优化的理论将单目标的粒子群优化算法改为支持多目标问题的求解 117 | * 风险矩阵：解决疫情下应急物资配送的一个强大数学工具 118 | * 适应度矩阵：构造这一矩阵，大大方便了从单目标到多目标问题的过渡 119 | * 速度与位置的重编码：问题情景为含有多辆车配送的 TSP（旅行商问题），其解的编码是离散的，而普通的粒子群优化算法处理的是连续的值，因此需要速度与位置的重编码 120 | * 帕累托前沿：使用帕累托前沿，也就是非支配解集来表现该多目标问题的解 121 | * 算法通用性非常强：解决 TSP 问题时，普通算法往往直接假设任意两个结点之间都存在直接边相连；而本算法不对此做要求。这更能有效解决现实问题 122 | 123 | #### 缺点 124 | 125 | * 复杂度：达到三次方级别，对于特大型问题的处理效率有待提升 126 | * 两个帕累托前沿的比较方法，用的是平均数比较方法，较为简单 127 | 128 | ### 4.6. 了解更多 129 | 130 | 可以在 [算法的若干细节.docx](./说明/算法的若干细节.docx) 文档中获取对算法的深入理解。该文档重点讲解了该算法的四个部分：“位置的编码与解的编码”，“速度与位置的重编码”，“适应度函数的设计”，“用帕累托前沿来替代粒子群优化中的全局最优”。 131 | 132 | ## 5. 数据集 133 | 134 | 网上并无现成的数据集，需要自己制作数据集。本文件夹提供了三个数据集，其文件名分别为：`example.txt`, `b50.txt`, `c21.txt`。其中，`example.txt` 是一个示例测试数据集，仅有 7 个结点，其他两个数据集后缀的数字均为其中结点数量。 135 | 136 | 在 [数据集说明.docx](./说明/数据集说明.docx) 文档中以 `example.txt` 为例，详细地对数据集进行了说明。 137 | 138 | ## 引用 139 | 140 | BibTex 格式： 141 | 142 | ```bibtex 143 | @unpublished{MOPSOfD, 144 | author = "宋世超", 145 | title = "用改进后的多目标粒子群优化（MOPSO）算法解决带有风险矩阵的多辆车配送旅行商问题（TSP）", 146 | year = 2022 147 | } 148 | ``` 149 | 150 | GB/T 7714-2015 格式： 151 | 152 | ``` 153 | [1]宋世超.用改进后的多目标粒子群优化（MOPSO）算法解决带有风险矩阵的多辆车配送旅行商问题（TSP）[CP].GitHub[2022].https://github.com/Ki-Seki/MOPSO-for-Distribution. 154 | ``` -------------------------------------------------------------------------------- /b50.txt: -------------------------------------------------------------------------------- 1 | DATASET: b50 2 | NODE_COUNT: 50 3 | NODE: 4 | 0 43.18910733 48.68496758 5 | 1 74.03560176 17.41722795 6 | 2 125.7439126 143.5916782 7 | 3 140.016796 5.344924045 8 | 4 18.25020376 120.3795128 9 | 5 77.95325814 27.03274968 10 | 6 29.30449854 56.84136166 11 | 7 11.26073045 32.37145736 12 | 8 30.9385556 58.42743871 13 | 9 8.755975858 16.04662356 14 | 10 131.1052359 12.60021853 15 | 11 134.4875199 98.72766559 16 | 12 43.20808881 50.85688846 17 | 13 136.9954985 17.82868691 18 | 14 23.60570096 40.79206412 19 | 15 124.603527 36.81747663 20 | 16 84.91428948 96.53574847 21 | 17 129.5572659 61.61933058 22 | 18 123.032034 25.53016795 23 | 19 55.43766008 142.4755682 24 | 20 93.80290391 18.39590335 25 | 21 85.62230688 5.636814291 26 | 22 27.76091392 144.2453693 27 | 23 10.25910481 34.56350472 28 | 24 24.87597187 4.65699853 29 | 25 110.7448036 70.55987018 30 | 26 39.54489908 105.3060982 31 | 27 138.5843442 101.9007672 32 | 28 57.50907925 58.62505869 33 | 29 96.47439966 144.6719615 34 | 30 61.90305644 120.7535193 35 | 31 120.8667781 139.257295 36 | 32 142.3590472 56.65623923 37 | 33 66.05658002 113.6901494 38 | 34 132.5369473 108.2634774 39 | 35 39.22559072 121.3254865 40 | 36 69.22794391 6.873900375 41 | 37 31.68178188 133.3757189 42 | 38 54.85587776 88.49858359 43 | 39 73.15156968 81.39174643 44 | 40 83.14156962 40.28216636 45 | 41 117.9253207 41.93434527 46 | 42 127.4919982 116.5495159 47 | 43 54.65097084 4.99302941 48 | 44 136.4635619 104.8809513 49 | 45 146.4918511 42.27021611 50 | 46 68.33451684 112.1124349 51 | 47 53.0752936 60.05557318 52 | 48 91.57856363 90.59027994 53 | 49 110.5025817 108.5734289 54 | EDGE_COUNT: 51 55 | EDGE: 56 | 0 28 57 | 0 27 58 | 1 29 59 | 1 28 60 | 2 30 61 | 2 29 62 | 3 31 63 | 3 30 64 | 4 32 65 | 4 31 66 | 5 38 67 | 6 27 68 | 7 33 69 | 7 32 70 | 8 34 71 | 8 33 72 | 9 35 73 | 9 34 74 | 10 36 75 | 10 35 76 | 11 37 77 | 11 36 78 | 12 38 79 | 12 37 80 | 13 39 81 | 13 38 82 | 14 40 83 | 14 39 84 | 15 41 85 | 15 40 86 | 16 42 87 | 16 41 88 | 17 26 89 | 18 43 90 | 18 42 91 | 19 44 92 | 19 43 93 | 20 45 94 | 20 44 95 | 21 46 96 | 21 45 97 | 22 47 98 | 22 46 99 | 23 48 100 | 23 47 101 | 23 26 102 | 23 25 103 | 24 49 104 | 24 48 105 | 24 27 106 | 24 26 107 | VEHICLE_COUNT: 100 108 | VEHICLE_CAPACITY: 1735 109 | VEHICLE_SHIPPING_COST: 0.53 110 | VEHICLE_FIXED_COST: 100 111 | VEHICLE_DISINFECTION_COST: 300 112 | VEHICLE_VELOCITY: 80 113 | DEMAND: 114 | 1 519 115 | 2 602 116 | 3 917 117 | 4 562 118 | 5 59 119 | 6 761 120 | 7 373 121 | 8 956 122 | 9 610 123 | 10 692 124 | 11 249 125 | 12 895 126 | 13 795 127 | 14 591 128 | 15 320 129 | 16 556 130 | 17 576 131 | 18 135 132 | 19 724 133 | 20 543 134 | 21 225 135 | 22 53 136 | 23 633 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1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 199 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 200 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 201 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 202 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 203 | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 204 | 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 205 | 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 206 | 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 207 | 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 208 | 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 209 | 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 210 | 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 211 | 1 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 1 1 212 | 1 0 0 0 0 0 1 1 0 1 1 0 1 1 0 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 213 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 214 | EOF -------------------------------------------------------------------------------- /c21.txt: -------------------------------------------------------------------------------- 1 | DATASET: c21 2 | NODE_COUNT: 21 3 | NODE: 4 | 0 68.18250552 52.23756662 5 | 1 56.7263866 32.28742038 6 | 2 15.2350627 143.1505891 7 | 3 64.66491217 111.6610127 8 | 4 143.014375 87.50969998 9 | 5 41.03674743 32.23180419 10 | 6 31.87945314 26.22635449 11 | 7 115.9354515 73.62541245 12 | 8 142.2641418 40.15753628 13 | 9 25.44411033 16.89728301 14 | 10 74.30479648 104.5248395 15 | 11 31.19534741 3.272164183 16 | 12 14.68894782 45.71133773 17 | 13 125.9543362 49.4473015 18 | 14 119.1362749 149.2005003 19 | 15 111.5566357 107.0289025 20 | 16 74.09200024 91.59433617 21 | 17 15.51536768 12.82820252 22 | 18 110.4402347 135.0419069 23 | 19 19.09493919 23.97566252 24 | 20 27.83652742 81.30996107 25 | EDGE_COUNT: 32 26 | EDGE: 27 | 0 1 28 | 0 3 29 | 1 2 30 | 1 4 31 | 2 5 32 | 3 4 33 | 3 6 34 | 4 5 35 | 4 7 36 | 5 8 37 | 6 7 38 | 6 9 39 | 7 8 40 | 7 10 41 | 8 11 42 | 9 10 43 | 9 12 44 | 10 11 45 | 10 13 46 | 11 14 47 | 12 13 48 | 12 15 49 | 13 14 50 | 13 16 51 | 14 17 52 | 15 16 53 | 15 18 54 | 16 17 55 | 16 19 56 | 17 20 57 | 18 19 58 | 19 20 59 | VEHICLE_COUNT: 30 60 | VEHICLE_CAPACITY: 1735 61 | VEHICLE_SHIPPING_COST: 0.53 62 | VEHICLE_FIXED_COST: 100 63 | VEHICLE_DISINFECTION_COST: 300 64 | VEHICLE_VELOCITY: 80 65 | DEMAND: 66 | 1 1408 67 | 2 1380 68 | 3 484 69 | 4 450 70 | 5 409 71 | 6 1013 72 | 7 638 73 | 8 180 74 | 9 1409 75 | 10 202 76 | 11 1332 77 | 12 59 78 | 13 1101 79 | 14 123 80 | 15 96 81 | 16 1387 82 | 17 864 83 | 18 950 84 | 19 139 85 | 20 1302 86 | RISK_MATRIX: 87 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 88 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 89 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 90 | 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 91 | 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 92 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 93 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 94 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 95 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 96 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 97 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 98 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 99 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 100 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 101 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 102 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 103 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 104 | 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 1 1 105 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 106 | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 107 | 1 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 108 | EOF -------------------------------------------------------------------------------- /create_matrix.m: -------------------------------------------------------------------------------- 1 | % 根据结点集和边集创建邻接矩阵 2 | function m = create_matrix(n, e, default) 3 | % n 结点集，三列（结点编号，横坐标，纵坐标）的矩阵 4 | % e 边集，两列（起点，终点）的矩阵 5 | % default 用 0 还是 Inf 来填充无边相连的点 6 | % m 邻接矩阵 7 | 8 | n_cnt = size(n, 1); 9 | e_cnt = size(e, 1); 10 | m = repmat(default, n_cnt); % 初始化邻接矩阵 11 | 12 | % 对角线清 0 13 | for i = 1 : n_cnt 14 | m(i, i) = 0; 15 | end 16 | 17 | for i = 1 : e_cnt 18 | n1 = e(i, 1) + 1; % 起始节点的索引编号 19 | n2 = e(i, 2) + 1; % 结束节点的索引编号 20 | x1 = n(n1, 2); % 起始节点的横坐标 21 | x2 = n(n2, 2); % 结束节点的横坐标 22 | y1 = n(n1, 3); % 起始节点的纵坐标 23 | y2 = n(n2, 3); % 结束节点的纵坐标 24 | m(n1, n2) = sqrt(power(x1-x2,2) + power(y1-y2,2)); 25 | m(n2, n1) = m(n1, n2); % 对称操作 26 | end 27 | end -------------------------------------------------------------------------------- /draw_convergence.m: -------------------------------------------------------------------------------- 1 | % 绘制 PSO 收敛过程图 2 | function draw_convergence(f, conv, field) 3 | % f 记录迭代：每行包括两目标每次在帕累托前沿中的平均值 4 | % conv 两目标收敛时分别的迭代次数 5 | % field 数据集 6 | 7 | figure('Name','MOPSO 收敛过程','NumberTitle','off') 8 | suptitle(['MOPSO 两目标收敛过程图（数据集：', field.DATASET, '）']); 9 | 10 | %% 绘制 T 的收敛过程 11 | 12 | subplot(2, 1, 1); 13 | plot(f(:, 1), '- .r'); 14 | hold on; 15 | pt = plot(conv, f(conv, 1), 'or'); 16 | labelt = [' (' num2str(conv) ', ' num2str(f(conv, 1)) ')']; % 收敛点的标签 17 | 18 | xlabel('迭代次数'); 19 | ylabel('平均时间（小时）'); 20 | legend(pt, ['收敛点' labelt]); 21 | hold off; 22 | 23 | %% 绘制 Z 的收敛过程 24 | 25 | subplot(2, 1, 2); 26 | plot(f(:, 2), '- .r'); 27 | hold on; 28 | pz = plot(conv, f(conv, 2), 'or'); 29 | labelz = [' (' num2str(conv) ', ' num2str(f(conv, 2)) ')']; % 收敛点的标签 30 | 31 | xlabel('迭代次数'); 32 | ylabel('平均成本（元）'); 33 | legend(pz, ['收敛点' labelz]); 34 | hold off; 35 | end -------------------------------------------------------------------------------- /draw_distribution.m: -------------------------------------------------------------------------------- 1 | % 绘制某个粒子代表的配送方案 2 | function draw_distribution(p, v, field) 3 | % p 最优粒子 4 | % v 车辆配送方案，行向量，每个元素代表一辆车，元素值是该车服务需求点数 5 | % field 数据集 6 | 7 | g = graph(create_matrix(field.NODE, field.EDGE, 0)); % 创建图对象 8 | st = 1; % 某辆车起始服务点，p(st) 是服务点编号 9 | for i = 1 : size(v, 2) % 遍历每辆车 10 | ed = st + v(i) - 1; % 某辆车终止服务点，p(ed) 是服务点编号 11 | 12 | %注意：下面常出现 p()，一般要令其 +1，是因为 matrix 是包括原点的 13 | 14 | %% 获得被该车辆服务的需求点的坐标，以便绘图 15 | 16 | servee = zeros(v(i), 2); 17 | for j = st : ed 18 | x = field.NODE(p(j) + 1, 2); 19 | y = field.NODE(p(j) + 1, 3); 20 | servee(j - st + 1, 1) = x; 21 | servee(j - st + 1, 2) = y; 22 | end 23 | 24 | %% 计算路径 25 | 26 | full_path = [shortestpath(g, 0+1, p(st)+1)]; % 加上原点到第一服务点路径 27 | for j = st+1 : ed % 遍历每辆车服务的点 28 | path = shortestpath(g, p(j-1)+1, p(j)+1); 29 | full_path = [full_path path(2:end)]; 30 | end 31 | path = shortestpath(g, p(ed)+1, 0+1); 32 | full_path = [full_path path(2:end)]; 33 | path_size = size(full_path, 2); 34 | 35 | %% 字符串化路径方便展示 36 | 37 | % 注意：需要 -1，因为 Matlab 下标从 1 开始 38 | 39 | txt_path = num2str(full_path(1)-1); 40 | for j = 2 : path_size 41 | txt_path = [txt_path '→' num2str(full_path(j)-1)]; 42 | end 43 | 44 | %% 绘图 45 | 46 | figure('Name',['第' num2str(i) '辆车配送方案图'],'NumberTitle','off'); 47 | 48 | % 绘制散点图 49 | scatter(field.NODE(:,2), field.NODE(:,3), 'b'); 50 | hold on; 51 | scatter(servee(:, 1), servee(:, 2), 'filled', 'b'); 52 | 53 | % 添加标签 54 | for j = 1 : field.NODE_COUNT 55 | x = field.NODE(j, 2); % 横坐标 56 | y = field.NODE(j, 3); % 纵坐标 57 | label = [num2str(j-1) ' (' num2str(x) ',' num2str(y) ') ']; 58 | if j > 1 % 如果是需求点 59 | label = [label num2str(field.DEMAND(j-1,2))]; 60 | end 61 | offset = 3; % 防止标签被 marker 挡住 62 | text(x+offset, y+offset, label); % 写标签 63 | end 64 | 65 | % 绘制路径 66 | X = zeros(path_size); 67 | Y = zeros(path_size); 68 | for j = 1 : path_size 69 | X(j) = field.NODE(full_path(j), 2); 70 | Y(j) = field.NODE(full_path(j), 3); 71 | end 72 | plot(X, Y, '-r'); 73 | title(['第' num2str(i) '辆车配送方案图（数据集：' field.DATASET '）']); 74 | xlabel('横坐标（千米）'); 75 | ylabel('纵坐标（千米）'); 76 | legend('途径点（编号 坐标 需求量）', '服务点（编号 坐标 需求量）', ['路径：' txt_path]); 77 | hold off; 78 | 79 | %% 更新 st 80 | 81 | st = ed + 1; 82 | end 83 | end -------------------------------------------------------------------------------- /draw_net.m: -------------------------------------------------------------------------------- 1 | % 绘制结点网络图 2 | function draw_net(field, graph_option) 3 | % field 数据集 4 | % graph_option 绘图选项，定义在 main.m 中 5 | 6 | node = field.NODE; 7 | 8 | %% 结点网络路径图 9 | 10 | figure('Name','结点网络路径图','NumberTitle','off') 11 | scatter(node(:,2), node(:,3), 'filled'); 12 | 13 | % 添加标签 14 | for i = 1 : field.NODE_COUNT 15 | x = node(i, 2); % 横坐标 16 | y = node(i, 3); % 纵坐标 17 | label = [num2str(i-1) ' (' num2str(x) ',' num2str(y) ') ']; % 结点标签 18 | if i > 1 % 如果是需求点 19 | label = [label num2str(field.DEMAND(i-1,2))]; % 结点标签加上需求量 20 | end 21 | offset = 3; % 防止标签被 marker 挡住 22 | text(x+offset, y+offset, label); % 写标签 23 | end 24 | 25 | % 如果要求详细绘图，添加边 26 | if graph_option.detail == true 27 | hold on; 28 | for i = 1 : field.EDGE_COUNT 29 | n1 = field.EDGE(i, 1) + 1; % 起始点编号 30 | n2 = field.EDGE(i, 2) + 1; % 结束点编号 31 | x = [node(n1,2), node(n2,2)]; 32 | y = [node(n1,3), node(n2,3)]; 33 | plot(x, y, 'red'); % 连接两个点 34 | end 35 | hold off; 36 | end 37 | 38 | 39 | % 添加说明 40 | xlabel('横坐标（千米）'); 41 | ylabel('纵坐标（千米）'); 42 | title(['结点网络路径图（数据集：', field.DATASET, '）']); 43 | if graph_option.detail == true 44 | legend('结点（编号 坐标 需求量）' ,'边'); 45 | else 46 | legend('结点（编号 坐标 需求量）'); 47 | end 48 | 49 | %% 结点网络拓扑图 50 | 51 | g = graph(create_matrix(field.NODE, field.EDGE, 0)); 52 | figure('Name','结点网络拓扑图','NumberTitle','off') 53 | plot(g, 'NodeLabel', 0:field.NODE_COUNT-1, 'EdgeLabel', g.Edges.Weight); 54 | title(['结点网络拓扑图（数据集：', field.DATASET, '）']); 55 | set(gca,'xtick',[],'xticklabel',[]); % 隐藏坐标轴，因为无实际含义，下同 56 | set(gca,'ytick',[],'yticklabel',[]); 57 | end -------------------------------------------------------------------------------- /draw_pf.m: -------------------------------------------------------------------------------- 1 | % 绘制帕累托前沿图 2 | function draw_pf(fit, pf, field, graph_option) 3 | % fit 适应度矩阵，每行表示一个粒子的适应度，包含 T 总时间和 Z 总成本两个元素 4 | % pf 帕累托前沿解集，是一个逻辑索引，每个元素为布尔值，若为 1 表示对应粒子在帕累托前沿上 5 | % field 数据集 6 | % graph_option 绘图选项，定义在 main.m 中 7 | 8 | figure('Name','帕累托前沿','NumberTitle','off'); 9 | 10 | %% 绘制非支配解散点图 11 | 12 | scatter(fit(pf, 1), fit(pf, 2), 'r'); 13 | xlabel('目标 1：T（小时）'); 14 | ylabel('目标 2：Z（元）'); 15 | title(['帕累托前沿图（数据集：', field.DATASET, '）']); 16 | 17 | %% 为非支配解添加标签 18 | 19 | p = fit(pf, :); % 获取非支配解解集 20 | cnt = size(p, 1); 21 | for i = 1 : cnt 22 | t = num2str(round(p(i, 1), 2)); % 保留两位小数，转换为字符串 23 | z = num2str(round(p(i, 2), 2)); 24 | label = ['(' t ',' z ') ']; 25 | offset = 1.005; % 为了不让标签盖住坐标点，添加偏置 26 | text(p(i, 1)*offset, p(i, 2)*offset, label); 27 | end 28 | 29 | %% 绘制帕累托前沿曲线 30 | 31 | p = sortrows(p, 1); % 按首列（时间）进行升序排序 32 | hold on, plot(p(:,1), p(:,2)), hold off; 33 | 34 | %% 选择性详细绘图 35 | 36 | if graph_option.detail == true 37 | hold on, scatter(fit(~pf, 1), fit(~pf, 2), 'r.'), hold off; % 绘制被支配解 38 | legend('非支配解（时间，成本）', '帕累托前沿', '被支配解'); 39 | else 40 | legend('非支配解（时间，成本）', '帕累托前沿'); 41 | end 42 | end -------------------------------------------------------------------------------- /example.txt: -------------------------------------------------------------------------------- 1 | DATASET: example 2 | NODE_COUNT: 7 3 | NODE: 4 | 0 345 184 5 | 1 21 99 6 | 2 200 190 7 | 3 150 200 8 | 4 177 37 9 | 5 76 211 10 | 6 75 64 11 | EDGE_COUNT: 7 12 | EDGE: 13 | 0 2 14 | 0 4 15 | 1 2 16 | 1 5 17 | 2 3 18 | 3 6 19 | 5 6 20 | VEHICLE_COUNT: 10 21 | VEHICLE_CAPACITY: 450 22 | VEHICLE_SHIPPING_COST: 0.5 23 | VEHICLE_FIXED_COST: 100 24 | VEHICLE_DISINFECTION_COST: 10 25 | VEHICLE_VELOCITY: 80 26 | DEMAND: 27 | 1 345 28 | 2 134 29 | 3 200 30 | 4 365 31 | 5 220 32 | 6 44 33 | RISK_MATRIX: 34 | 1 0 0 1 1 0 0 35 | 1 1 0 1 1 0 0 36 | 1 1 1 1 1 0 0 37 | 0 0 0 1 1 0 0 38 | 0 0 0 0 1 0 0 39 | 1 1 1 1 1 1 0 40 | 1 1 1 1 1 1 1 41 | EOF 42 | -------------------------------------------------------------------------------- /execute re-encoding.bat: -------------------------------------------------------------------------------- 1 | powershell .\re-encoding.ps1 -------------------------------------------------------------------------------- /extract_value.m: -------------------------------------------------------------------------------- 1 | % 将数据集中第 field_num 个字段值提取成字符串 value 2 | function value = extract_value(datatext, field, field_num) 3 | % datatext 数据集字符串 4 | % field 字段名数组 5 | % field_num 要提取的字段的序号 6 | % value 字符串返回值 7 | 8 | field1 = field{field_num}; 9 | field2 = field{field_num + 1}; 10 | regex = [field1, '.+', field2]; 11 | matches = regexp(datatext, regex, 'match'); 12 | match = matches{1}; 13 | matchsize = size(match, 2); 14 | field1size = size(field1, 2); 15 | field2size = size(field2, 2); 16 | value = match(field1size+1 : matchsize-field2size-2); 17 | end -------------------------------------------------------------------------------- /fitness.m: -------------------------------------------------------------------------------- 1 | % 多目标适应度函数，计算粒子群 particle 的配送总时间和总成本 2 | function [fit, vehicle, dist, risk] = fitness(particle, field, matrix) 3 | % particle 粒子群，每行是一个粒子（允许只有一个粒子） 4 | % field 数据集 5 | % matrix 邻接矩阵 6 | % fit 适应度矩阵，每行表示一个粒子的适应度，包含 T 总时间和 Z 总成本两个元素 7 | % 以下返回值按需取用 8 | % vehicle 元胞数组，每行是一个车辆使用情况数组，其中每个元素代表一辆车，元素值是该车服务需求点数 9 | % dist 总运距数组，每行代表一个粒子的总运距 10 | % risk 总消杀次数数组，每行代表一个粒子的总消杀次数 11 | 12 | [m, n] = size(particle); % 获取粒子个数和需求点个数 13 | 14 | % 返回值初始化 15 | fit = zeros(m, 2); 16 | vehicle = cell(m, 1); 17 | dist = zeros(m, 1); 18 | risk = zeros(m, 1); 19 | 20 | for i = 1 : m % 遍历每一个粒子 21 | 22 | p = particle(i, :); % 当前粒子 23 | 24 | %% 求车辆使用情况 25 | 26 | k = 1; % 车辆使用数量 27 | v = [0]; % 车辆使用情况数组 28 | load = 0; % 当前载重 29 | for j = 1 : n % 遍历每一个需求点，其编号为 p(j) 30 | demand = field.DEMAND(p(j), 2); % 需求点需求量 31 | if load + demand > field.VEHICLE_CAPACITY % 若车载不足 32 | k = k + 1; % 车数加一 33 | v = [v 0]; % 车数加一 34 | load = 0; % 载重清空 35 | end 36 | v(k) = v(k) + 1; % 第 k 辆车服务数量加一 37 | load = load + demand; % 增加载重 38 | end 39 | 40 | %% 计算总运距和总消杀成本 41 | 42 | d = 0; % 总运距 43 | r = 0; % 总消杀次数 44 | st = 1; % 某辆车起始服务点，p(st) 是服务点编号 45 | for j = 1 : k % 遍历每一辆车 46 | ed = st + v(j) - 1; % 某辆车终止服务点，p(ed) 是服务点编号 47 | 48 | % 注意：下面常出现 p()，一般要令其 +1，是因为 matrix 是包括原点的 49 | 50 | d = d + matrix(1, p(st)+1); % 加上原点到第一服务点距离 51 | r = r + field.RISK_MATRIX(1, p(st)+1); % 加上原点到第一服务点的风险 52 | for l = st+1 : ed % 遍历第 j 辆车服务的需求点 53 | d = d + matrix(p(l-1)+1, p(l)+1); 54 | r = r + field.RISK_MATRIX(p(l-1)+1, p(l)+1); 55 | end 56 | d = d + matrix(p(ed)+1, 1); % 加上最后服务点到原点距离 57 | r = r + field.RISK_MATRIX(p(ed)+1, 1); % 加上最后服务点到原点风险 58 | 59 | st = ed + 1; % 更新 st 60 | end 61 | 62 | %% 计算当前粒子的总时间和总成本 63 | 64 | t = d / field.VEHICLE_VELOCITY; % 小时 65 | z = d * field.VEHICLE_SHIPPING_COST + ... 66 | k * field.VEHICLE_FIXED_COST + ... 67 | r * field.VEHICLE_DISINFECTION_COST; % 元 68 | 69 | %% 更新返回值 70 | 71 | fit(i, :) = [t, z]; 72 | vehicle{i} = v; 73 | dist(i) = d; 74 | risk(i) = r; 75 | end 76 | end -------------------------------------------------------------------------------- /floyd_algo.m: -------------------------------------------------------------------------------- 1 | % 用弗洛伊德算法求邻接矩阵 2 | function matrix = floyd_algo(node, edge) 3 | % node 点集，三列（结点编号，横坐标，纵坐标）的矩阵 4 | % edge 边集，两列（起点，终点）的矩阵 5 | % matrix 邻接矩阵 6 | 7 | node_cnt = size(node, 1); 8 | matrix = create_matrix(node, edge, Inf); 9 | 10 | for k = 1 : node_cnt % 遍历所有中介点 11 | for i = 1 : node_cnt 12 | for j = 1 : node_cnt 13 | if (matrix(i, k) ~= Inf && matrix(k, j) ~= Inf && ... 14 | matrix(i, k) + matrix(k, j) < matrix(i, j)) 15 | matrix(i, j) = matrix(i, k) + matrix(k, j); % 松弛操作 16 | end 17 | end 18 | end 19 | end 20 | end -------------------------------------------------------------------------------- /main.m: -------------------------------------------------------------------------------- 1 | % 用改进后的多目标粒子群优化（MOPSO）算法解决带有风险矩阵的多辆车配送旅行商问题（TSP） 2 | 3 | % -*- coding: utf-8 -*- 4 | % @Time: 2022/02/09 20:57 5 | % @Author: Song Shichao 6 | % @Email: song.shichao@outlook.com 7 | % @Software: Matlab R2015b 8 | % @Platform: Windows11 64x 21H2 9 | % @CPU: Intel(R) Core(TM) i5-10210U CPU @ 1.60GHz 2.11 GHz 10 | % @RAM: 16.0 GB 11 | % @Notice: This code is a part of a HUEL master degree project 12 | % under the protection of GPL-3.0-only license. 13 | % @Link: https://github.com/Ki-Seki/MOPSO-for-Distribution 14 | 15 | % 算法特色 16 | % 多目标粒子群优化（MOPSO）、风险矩阵、适应度矩阵、速度与位置的重编码、帕累托前沿 17 | 18 | % 算法的输入与输出 19 | % 输入：在“参设设置”节 20 | % 输出：命令行输出结果、结点网络路径图、结点网络拓扑图、PSO 收敛过程图、每辆车的配送路径图 21 | 22 | % 注意事项 23 | % 结点从 0 开始编号，但是 MATLAB 是从 1 开始编号的； 24 | % TSP 背景下，适应度值即为路径长度、成本等，适应度值越小越好； 25 | % 邻接矩阵、风险矩阵的下标从配送原点（0 号结点）开始算起； 26 | % MOPSO 中群体最优 g_best 也是粒子群，学术上叫做 repository， 27 | % 本情景中输入的全排列是相当离散的数据，因此 repository 大小基本在 10 个以内， 28 | % 所以其帕累托前沿从观感上，不像是一个曲线 29 | 30 | clear; 31 | clc; 32 | close all; 33 | 34 | %% 参数设置 35 | 36 | rand_type = 'state'; % 随机数类型（无须动） 37 | rand_seed = 1; % 随机数种子（无须动） 38 | 39 | dataset = 'c21'; % 数据集名称（本程序所解决的对象，文件必须存在，不包括文件后缀名） 40 | 41 | loop_cnt = 150; % 进化次数（任意正整数，越小越好） 42 | particle_cnt = 200; % 粒子数目（任意正整数，越小越好） 43 | w = 1.5; % 惯性权重（可以不动，值小于 5，越小越好） 44 | c1 = 4; % 自我学习因子（两个学习因子建议相等，值在 1 到 5 之间） 45 | c2 = 4; % 群体学习因子 46 | 47 | graph_option.detail = false; % 是否详细绘图（合法值：true，false） 48 | % 由于绘图量比较大，所以预留 graph_option 为结构体，方便未来增加字段 49 | 50 | %% 初始化 51 | 52 | rand(rand_type, rand_seed); % 随机数生成器初始化 53 | field = read_dataset(dataset); % 读数据集到 field 结构体，它包含数据集中所有字段值 54 | draw_net(field, graph_option); % 绘制结点网络图 55 | 56 | matrix = floyd_algo(field.NODE, field.EDGE); % 用弗洛伊德算法求邻接矩阵 57 | particle = zeros(particle_cnt, field.NODE_COUNT-1); % 创建粒子种群 58 | for i = 1 : particle_cnt 59 | particle(i, :) = randperm(field.NODE_COUNT-1); % 为每个粒子生成随机的路径序列 60 | end 61 | velocity = rands(particle_cnt, field.NODE_COUNT-1); % 初始化粒子速度 62 | 63 | fit = fitness(particle, field, matrix); % 适应度是一个两列（T 和 Z）的矩阵 64 | pf = pareto_front(fit); % 得到当前帕累托前沿解集，是一个逻辑索引 65 | 66 | p_best = particle; % 个体最优对应的粒子群 67 | g_best = particle(pf, :); % 全局最优对应的粒子，pf 是逻辑索引 68 | p_best_fit = fit; % 个体最优值 69 | g_best_fit = fit(pf, :); % 全局最优值 70 | 71 | best_history = zeros(loop_cnt, 2); % 记录迭代：每行包括两目标每次在帕累托前沿中的平均值 72 | convergence = 0; % 结果收敛时的迭代次数 73 | 74 | %% 粒子群算法核心循环 75 | 76 | for i = 1 : loop_cnt 77 | for j = 1 : particle_cnt 78 | %% 计算速度与位置 79 | 80 | v = velocity(j, :); % 当前粒子速度 81 | x = particle(j, :); % 当前粒子位置 82 | 83 | v = w * v + c1 * rand * (p_best(j, :)-x) + c2 * rand * ... 84 | (g_best(randi(size(g_best, 1)), :)-x); % 速度更新公式 85 | x = x + v; % 位置更新公式 86 | 87 | [velocity(j, :), particle(j, :)] = validate(v, x); % 速度与位置冲编码 88 | 89 | %% 更新个体最优 90 | 91 | tmp = fitness(particle(j, :), field, matrix); 92 | if sum(tmp < p_best_fit(j, :)) == 2 % 如果新解是占优的才更新 93 | p_best(j, :) = particle(j, :); 94 | p_best_fit(j, :) = tmp; 95 | end 96 | end 97 | 98 | %% 更新群体最优：策略是把新粒子全部加入后，再求一遍帕累托前沿 99 | g_best = [g_best; p_best]; 100 | g_best_fit = [g_best_fit; p_best_fit]; 101 | 102 | pf = pareto_front(g_best_fit); % 帕累托前沿的逻辑索引 103 | if i == loop_cnt % 仅绘制最后一次的帕累托前沿 104 | draw_pf(g_best_fit, pf, field, graph_option); % 绘制帕累托前沿 105 | end 106 | g_best = g_best(pf, :); 107 | g_best_fit = g_best_fit(pf, :); 108 | 109 | %% 记录迭代 110 | 111 | avg_fit = mean(g_best_fit); 112 | best_history(i, :) = avg_fit; 113 | if i==1 || sum(best_history(i, :) 7 | 8 | mkdir ..\encoded; # 新建与当前文件夹同级的重编码后的文件夹 9 | Get-ChildItem | ForEach-Object -Process{ # 遍历当前文件夹中的所有文件 10 | if($_ -is [System.IO.FileInfo]){ 11 | $new_name = -join ("..\encoded\", $_.name); # 新文件名 12 | & {get-content $_.name -encoding utf8 | set-content $new_name -encoding Default}; # 编码转换为系统默认编码 13 | } 14 | } -------------------------------------------------------------------------------- /read_dataset.m: -------------------------------------------------------------------------------- 1 | % 从 .txt 数据集中读取数据到结构体数组 field 中 2 | function field = read_dataset(dataset) 3 | % dataset 数据集的名称，不含后缀 .txt 4 | % field 返回值，包含提取出来的数据值 5 | 6 | field_name = { % 数据集的各字段名 7 | 'DATASET: ' 8 | 'NODE_COUNT: ' 9 | 'NODE: ' 10 | 'EDGE_COUNT: ' 11 | 'EDGE: ' 12 | 'VEHICLE_COUNT: ' 13 | 'VEHICLE_CAPACITY: ' 14 | 'VEHICLE_SHIPPING_COST: ' 15 | 'VEHICLE_FIXED_COST: ' 16 | 'VEHICLE_DISINFECTION_COST: ' 17 | 'VEHICLE_VELOCITY: ' 18 | 'DEMAND: ' 19 | 'RISK_MATRIX: ' 20 | 'EOF'}; 21 | 22 | datatext = fileread([dataset '.txt']); % 读取数据集文件为字符串 23 | 24 | field.DATASET = extract_value(datatext, field_name, 1); 25 | field.NODE_COUNT = str2num(extract_value(datatext, field_name, 2)); 26 | field.NODE = str2num(extract_value(datatext, field_name, 3)); 27 | field.EDGE_COUNT = str2num(extract_value(datatext, field_name, 4)); 28 | field.EDGE = str2num(extract_value(datatext, field_name, 5)); 29 | field.VEHICLE_COUNT = str2num(extract_value(datatext, field_name, 6)); 30 | field.VEHICLE_CAPACITY = str2num(extract_value(datatext, field_name, 7)); 31 | field.VEHICLE_SHIPPING_COST = str2num(extract_value(datatext, field_name, 8)); 32 | field.VEHICLE_FIXED_COST = str2num(extract_value(datatext, field_name, 9)); 33 | field.VEHICLE_DISINFECTION_COST = str2num(extract_value(datatext, field_name, 10)); 34 | field.VEHICLE_VELOCITY = str2num(extract_value(datatext, field_name, 11)); 35 | field.DEMAND = str2num(extract_value(datatext, field_name, 12)); 36 | field.RISK_MATRIX = str2num(extract_value(datatext, field_name, 13)); 37 | end -------------------------------------------------------------------------------- /reorganize.m: -------------------------------------------------------------------------------- 1 | % 将粒子中多余的和缺失的元素熨平，使其成为一个全排列 2 | function x = reorganize(x) 3 | % x 是一个非法的粒子，其最大最小值确实为全排列里的最值，但中间的元素存在冗余和缺失 4 | % 返回值 x 是一个经过变换后合法的粒子 5 | 6 | %% 判定是否是全排列，如果是，直接返回即可 7 | % 判定定理：n 维全排列的求和与求积值是一定的，且不可能有 n 维非全排列和、积与其相同 8 | 9 | n = numel(x); 10 | if prod(x)==prod(1:n) && sum(x)==sum(1:n) 11 | return; 12 | end 13 | 14 | %% 找多余的和缺失的元素 15 | 16 | dup = []; % 重复出现的元素所在位置 17 | miss = []; % 缺少出现的元素的值 18 | for i = 1 : size(x, 2) 19 | occur = find(x == i); 20 | if size(occur, 2) == 0 % 若缺失 21 | miss = [miss i]; 22 | elseif size(occur, 2) > 1 % 若冗余 23 | dup = [dup occur(2:end)]; 24 | end 25 | end 26 | 27 | %% 将缺失的元素回填至冗余元素出现的位置 28 | 29 | for i = 1 : size(dup, 2) 30 | x(dup(i)) = miss(i); 31 | end 32 | end -------------------------------------------------------------------------------- /test.m: -------------------------------------------------------------------------------- 1 | % 测试程序以 example 数据集为例 2 | 3 | %% 一些先行过程 4 | 5 | clear; 6 | clc; 7 | close all; 8 | dataset = 'test'; % 数据集名称 9 | coeff.t = 0.95; % 目标 T 的权重 10 | coeff.z = 0.05; % 目标 Z 的权重 11 | field = read_dataset(dataset); % 读数据集到 field 结构体，它包含数据集中所有字段值 12 | matrix = floyd_algo(field.NODE, field.EDGE); % 用弗洛伊德算法求邻接矩阵 13 | 14 | %% 暴力搜索方法找到最优解 15 | 16 | all_particle = perms(1:field.NODE_COUNT-1); % 生成所有可能的解 17 | fit = fitness(all_particle, field, matrix); % 适应度是一个两列（T 和 Z）的矩阵 18 | [~, index] = min(weighted(fit, coeff)); % 找群体最优值对应下标 19 | disp(all_particle(index, :)); % 输出最好的粒子 20 | 21 | %% 测试几个适应度相似的粒子 22 | 23 | disp(fitness([1 3 2 5 6 4], field, matrix)) 24 | disp(fitness([1 2 3 5 6 4], field, matrix)) 25 | disp(fitness([3 4 2 5 6 1], field, matrix)) 26 | 27 | %% 测试需要五辆车时，图会不会正常地被画出来 28 | 29 | p = [3,4,6,2,1,5]; % 这个粒子需要 5 辆车 30 | [fit, vehicle, dist, risk] = fitness(p, field, matrix); 31 | draw_distribution(p, vehicle, field); % 绘制最佳配送方案 32 | -------------------------------------------------------------------------------- /validate.m: -------------------------------------------------------------------------------- 1 | % 在 TSP 问题背景下，使 PSO 中的速度与位置合法化，也就是使生成的解是有效解 2 | function [v, x] = validate(v, x) 3 | % v 速度向量 4 | % x 位置向量 5 | 6 | n = size(x, 2); 7 | m = min(x); 8 | M = max(x); 9 | 10 | x_old = round(x - v); % 复原原来位置，为避免浮点数计算影响，加上四舍五入运算 11 | x_new = (n-1) / (M-m) * (x-m) + 1; % 坐标变换：[m, M] → [1, n] 12 | x_new = round(x_new); % 变换为整数 13 | x_new = reorganize(x_new); % 熨平粒子 14 | 15 | v = x_new - x_old; 16 | x = x_new; 17 | end -------------------------------------------------------------------------------- /说明/优化MOPSO算法流程图.jpeg: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Ki-Seki/MOPSO-for-Distribution/fe3e78ca7694f69f0204f99e41772c750f1bb942/说明/优化MOPSO算法流程图.jpeg -------------------------------------------------------------------------------- /说明/优化MOPSO算法流程图.svg: -------------------------------------------------------------------------------- 1 | 开始i ≤ loop_cnt是普通 PSO 算法中的速度与位置的更新是否否结束MOPSO初始化：Floyd 算法更新邻接矩阵、计算初始个体最优和群体最优（帕累托前沿）...超参数设置j ≤ particle_cnt使用 validate() 对速度与位置重编码调用 fitness() 计算粒子 j 的适应度 fit新的 fit 更优是更新个体最优否所有粒子放入同一集合，计算当前帕累托前沿调用 fitness() 计算非支配解集中所有粒子 fit 的平均值新的 fit 更优是更新群体最优否记录算法迭代、收敛情况输出结果、图像 -------------------------------------------------------------------------------- /说明/函数依赖图.png: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/Ki-Seki/MOPSO-for-Distribution/fe3e78ca7694f69f0204f99e41772c750f1bb942/说明/函数依赖图.png -------------------------------------------------------------------------------- /说明/函数依赖图.pptx: -------------------------------------------------------------------------------- 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