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结合聚类分解的增强蚁群算法求解复杂绿色车辆路径问题

胡蓉 李洋 钱斌 金怀平 向凤红

胡蓉, 李洋, 钱斌, 金怀平, 向凤红. 结合聚类分解的增强蚁群算法求解复杂绿色车辆路径问题. 自动化学报, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190872
引用本文: 胡蓉, 李洋, 钱斌, 金怀平, 向凤红. 结合聚类分解的增强蚁群算法求解复杂绿色车辆路径问题. 自动化学报, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190872
HU Rong, LI Yang, QIAN Bin, JIN Huai-Ping, XIANG Feng-Hong. An enhanced ant colony algorithm combined with clustering decomposition for solving complex green vehicle routing problem. Acta Automatica Sinica, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190872
Citation: HU Rong, LI Yang, QIAN Bin, JIN Huai-Ping, XIANG Feng-Hong. An enhanced ant colony algorithm combined with clustering decomposition for solving complex green vehicle routing problem. Acta Automatica Sinica, 2020, 46(x): 1−18 doi: 10.16383/j.aas.c190872

结合聚类分解的增强蚁群算法求解复杂绿色车辆路径问题

doi: 10.16383/j.aas.c190872
基金项目: 国家自然科学基金项目(61963022, 51665025); 云南省应用基础研究计划重点项目资助
详细信息
    作者简介:

    胡蓉:昆明理工大学信息工程与自动化学院副教授, 2004年获得清华大学自动化系硕士学位, 主要研究方向为调度理论与方法, 智能计算, 决策支持系统. E-mail: ronghu@vip.163.com

    李洋:昆明理工大学信息工程与自动化学院硕士研究生, 2009年获得昆明理工大学电力工程学院学士学位. 主要研究方向为调度理论与智能优化算法. E-mail: Yang.L.Liam@hotmail.com

    钱斌:昆明理工大学信息工程与自动化学院副教授, 2009年获得清华大学自动化系博士学位, 主要研究方向为调度理论与方法, 以及智能优化. E-mail: bin.qian@vip.163.com

    金怀平:昆明理工大学信息工程与自动化学院副教授, 2016年获得北京理工大学博士学位, 主要研究方向为智能计算和软测量方法

    向凤红:昆明理工大学信息工程与自动化学院教授, 2002年获得昆明理工大学博士学位, 主要研究方向为智能优化与控制

    通讯作者:

    昆明理工大学信息工程与自动化学院副教授, 2009年获得清华大学自动化系博士学位, 主要研究方向为调度理论与方法, 以及智能优化. E-mail: bin.qian@vip.163.com

  • 中图分类号: TP399

An enhanced ant colony algorithm combined with clustering decomposition for solving complex green vehicle routing problem

Funds: Supported by National Natural Science Foundation of China (61963022,51665025) and Applied Basic Research Key Project of Yunnan Province
More Information
    Corresponding author: QIAN Bin Professor at the School of Information Engineering and Automation, Kunming University of Science and Technology. He received his Ph.D. degree from Tsinghua University in 2009. His research interests include scheduling theory and method, and intelligent optimization. Corresponding author of this paper
  • 摘要: 本文针对带时间窗的低能耗多车场多车型车辆路径问题(low-energy-consumption multi-depot heterogeneous-fleet vehicle routing problem with time windows, LMHFVPR_TW), 提出一种结合聚类分解策略的增强蚁群算法(enhanced ant colony algorithm based on clustering decomposition, EACO_CD)进行求解. 首先, 由于该问题具有强约束、大规模和NP-Hard等复杂性, 为有效控制问题的求解规模并合理引导算法在优质解区域搜索, 根据问题特点设计两种基于K-means的聚类策略, 将LMHFVPR_TW合理分解为一系列带时间窗的低能耗单车场单车型车辆路径子问题(low-energy-consumption vehicle routing problem with time windows, LVRP_TW); 其次, 本文提出一种增强蚁群算法(enhanced ant colony optimization, EACO)求解分解后的各子问题(LVRP_TW), 进而获得原问题的解. EACO不仅引入信息素挥发系数控制因子进一步动态调节信息素挥发系数, 从而有效控制信息素的挥发以提高算法的全局搜索能力, 而且设计基于4种变邻域操作的两阶段变邻域局部搜索(two-stage variable neighborhood search, TVNS)来增强算法的局部搜索能力. 最后, 在不同规模问题上的仿真和对比实验验证了所提EACO_CD的有效性.
  • 图  1  EACO_CD(EACO_IBKA_HKMA)结构

    Fig.  1  Framework of EACO_CD

    图  2  4类客户平衡移动示意图

    Fig.  2  Diagram of balanced movement for four customer groups

    图  3  三车场K-means未平衡聚类与平衡聚类比较

    Fig.  3  The comparison of unbalanced K-means cluster and balanced K-means cluster of three depots

    图  4  HKMA工作机制

    Fig.  4  The HKMA’s running mechanism

    图  5  HKMA三维聚类效果

    Fig.  5  The 3D clustering results of HKMA

    图  6  HKMA二维结果

    Fig.  6  The 2D results of HKMA

    图  7  局部搜索策略

    Fig.  7  Local search strategy

    表  1  符号及定义

    Table  1  Symbols and definitions

    符号 释义 符号 释义
    $F_1$ 运输距离费用 $H_{PM}$ 表示车场 $Ρ$ $H_{PM}$ $M$ 类型的车
    $F_2$ 车辆固定成本 $r(A)$ 完成客户子集 $A$ 中所有客户的配送需要的最少车辆数
    $F_3$ 燃油消耗费用 $N$ 总共有 $N$ 个客户
    $F_4$ 时间窗惩罚费用 $V$ $V$ 表示客户编号集合{0,1,2,···, $N$ }(0表示车场)
    $C_{M1}$ $M$ 类型车的距离费用系数 $M_t$ 表示共有 $M_t$ 种类型的车
    $C_{M2}$ $M$ 种类型车的固定发车费用系数 $x_{PMijk}$ 表示车场 $P$ 车型 $M$ 的第 $k$ 辆车从客户 $i$ 到客户 $j$ 的决策变量
    $C_{M3}$ $M$ 种类型车的燃油费用系数 $k$ 表示辆车编号 $k$
    $C_1$ 配送车辆提前到达的单位惩罚费用 $d_{ij}$ $d_{ij}$ 表示客户 $i$ 到客户 $j$ 的距离
    $C_2$ 配送车辆迟到的单位惩罚费用 ${ET}_i$ 客户 $i$ 要求的最早到达时间
    $i$ 表示客户点 $i$ ${LT}_i$ 客户 $i$ 要求的最晚到达时间
    $j$ 表示客户点 $j$ $S_i$ 客户 $i$ 要求的卸货时间
    $P_s$ 表示全部车场集合{1,2,···, $P_t$ } $q_i$ 客户i要求的货物需求量
    $P_t$ 表示总共有 $P_t$ 个车场 $t_i$ 车辆到达客户 $i$ 的时间
    $P$ 表示车场编号 $P$ $Q_M$ $M$ 种车型的最大载重量
    $M_s$ 表示全部车型集合 $\{1,2,\cdots,\ M_t\}$ $M$ 表示车型编号 $M$
    $H_{PMS}$ 表示车场 $P$ 中车型 $M$ 的全部车辆集合 $\{1,2,\cdots,\ H_{PM}\}$ ${FU}_{Mij}$ 车型为 $M$ 的车辆从客户 $i$ 到客户 $j$ 之间的耗油量
    备注: 综合燃油消耗模型中的其他相关参数设定参考文[25]
    下载: 导出CSV

    表  2  目标函数中的相关系数

    Table  2  Coefficients in the object function

    符号 数值
    $C_{M1}$ 1.5元/kM
    $C_{M2}$ 300-800元/辆
    $C_{M3}$ 7.6元/L
    $C_{1}$ 15元/H
    $C_{2}$ 20元/H
    下载: 导出CSV

    表  3  主要参数与水平

    Table  3  Main parameters and level

    主要参数 水平设置
    1 2 3 4
    $\alpha$ 1.25 1.5 1.75 2.0
    $\beta$ 10 1.5 2.0 2.5
    $P_m$ 1.1 1.2 1.3 1.4
    $W$ 500 1000 1500 2000
    下载: 导出CSV

    表  4  参数设置的正交表

    Table  4  Orthogonal table of parameter settings

    组合编号 水平设置 AVR(元)
    $\alpha$ $\beta$ $P_m$ $W$
    1 1 1 1 1 9677
    2 1 2 2 2 9625
    3 1 3 3 3 9613
    4 1 4 4 4 9541
    5 2 1 2 3 9745
    6 2 2 1 4 9624
    7 2 3 4 1 9602
    8 2 4 3 2 9593
    9 3 1 3 4 9836
    10 3 2 4 3 9703
    11 3 3 1 2 9654
    12 3 4 2 1 9612
    13 4 1 4 2 9865
    14 4 2 3 1 9689
    15 4 3 2 4 9656
    16 4 4 1 3 9672
    下载: 导出CSV

    表  5  各参数不同水平下的平均响应值和影响力

    Table  5  Average response values and influences table at different levels of each parameter

    水平 水平设置
    $\alpha$ $\beta$ $P_m$ $W$
    1 9614 9780 9656 9645
    2 9641 9660 9659 9684
    3 9701 9631 9683 9683
    4 9720 9604 9677 9664
    极差 106 176 27 39
    影响力排名 2 1 4 3
    下载: 导出CSV

    表  7  EACO_IBKA与其他算法对比结果

    Table  7  Comparison results of EACO_IBKA with other algorithms

    N_Pt EACO_IBKA EACO_KM EACO_NNA EACO1 DHACO ${{T}}({{s}})$
    best average best average best average best average best average
    96_2 17483 18155 18037 18379 16768 17675 15371 17009 16011 17559 19
    192_2 27522 28546 28457 29482 28758 29560 28379 29838 28524 30863 38
    288_2 39217 41028 40412 42363 41179 42142 41283 43164 42606 43930 58
    360_2 53748 56268 54672 57402 55251 57847 56276 58653 56965 59409 72
    96_3 16638 17278 17066 17491 15957 16821 14627 16582 15236 17186 29
    192_3 26199 27175 27090 28066 27376 28140 27016 28405 27153 29381 58
    288_3 37337 39062 38476 40333 39205 41123 39305 41096 40565 41826 86
    360_3 51176 53576 52056 54656 52608 55080 53584 55848 54240 56568 108
    96_4 16062 16943 16810 17146 15871 16425 16012 16907 16391 16991 38
    192_4 25690 26612 26528 27235 26846 27620 26443 27896 26623 28850 77
    288_4 36519 38266 37624 39493 38365 39338 38442 40278 39692 40974 115
    360_4 50480 52904 51344 53960 51904 54392 52088 55184 53584 55904 144
    平均值 33173 34651 34048 35501 34174 35514 34069 35905 34799 36620 /
    下载: 导出CSV

    表  8  HKMA与其他划分算法的对比结果

    Table  8  Comparison results of HKMA and the other dividing algorithms

    $ {{N}}\_ {{M}}_{{t}}$ EACO_ HKMA EACO_ RDA EACO_ RAA EACO_KEW EACO2 TSA_RDA $ {{T}}({{s}})$
    best average best average best average best average best average best average
    96_2 16299 16759 17570 19461 16238 17661 16754 17704 16543 17838 17746 19656 29
    192_2 24847 25998 25983 26905 26000 27201 26039 26918 26520 27745 26243 27174 57
    288_2 32225 33356 33783 34713 32740 35242 32540 35156 34050 36652 34121 35060 87
    360_2 48344 50050 50695 52088 49129 52874 48828 52743 51094 54989 51202 52609 108
    96_3 15777 15929 16704 18494 16011 16792 15932 16839 16171 16960 16871 18679 44
    192_3 23624 24718 24704 25570 24714 25850 24748 25588 25455 26626 24951 25826 87
    288_3 30621 31700 32106 32984 31111 33493 30929 33414 32667 35168 32427 33314 129
    360_3 45933 47554 48172 49502 46691 50237 47401 50118 49026 52749 48654 49997 162
    96_4 14214 14349 15047 16655 14422 15118 14346 15171 14566 15269 15197 16822 57
    192_4 21273 22251 22237 23018 22257 23268 22282 23034 22925 23966 22459 23248 116
    288_4 27563 28542 28902 29689 28012 30149 27842 30088 29413 31656 29191 29986 173
    360_4 41350 42809 43360 44558 42028 45218 41776 43111 44129 47479 43794 45004 216
    平均值 28506 29501 29939 31136 29113 31092 29118 30824 30213 32258 30238 31448 /
    下载: 导出CSV

    表  9  EACO_CD性能验证

    Table  9  EACO_ CD’s performance verification

    $ {{N}}$ _ ${{ P}}_{{t}}$ _ $ {{M}}_{{t}}$ EACO_CD (EACO_IBKA_HKMA) IACO_CD (IACO_NNA_SWA) IHGA ${{T}}({{s}})$
    best average worst SD best average worst SD best average worst SD
    96_2_2 16370 16526 16904 295 17800 18071 18381 272 15852 16011 16376 285 31
    192_2_2 23664 24760 25650 556 26040 27250 28218 576 24863 26010 26948 590 71
    288_2_2 30690 31768 32227 724 33772 34962 35457 803 35311 36550 37076 824 123
    360_2_2 39903 41303 41906 951 43907 45448 46111 1059 45507 46098 47781 1197 162
    96_3_2 16883 17869 18993 358 18568 20115 20999 343 16800 18283 19011 363 48
    192_3_2 24257 25492 26408 668 26692 28059 29065 671 26688 28052 29053 746 109
    288_3_2 30258 31572 32860 907 34814 36319 37797 1017 35414 36956 38450 1092 183
    360_3_2 39347 41061 42734 1141 43291 45187 47020 1263 47228 49291 51297 1389 243
    96_3_3 15867 17082 17860 388 17470 18911 19664 368 16514 17874 18584 478 62
    192_3_3 22816 23977 24832 631 25108 26383 27320 708 26242 27588 28567 743 145
    288_3_3 28458 29693 30892 828 32742 34157 35530 957 35582 37120 38622 1048 245
    360_3_3 37006 38610 40166 1079 40722 42474 44186 1198 47081 49427 51523 1399 288
    平均值 27127 28309 29286 711 30077 31445 32479 770 31090 32438 33607 846 /
    下载: 导出CSV

    表  6  4种不同车型相关参数设置

    Table  6  Related parameter settings for four different vehicle types

    车型列表 车型参数
    载重量(kg) 空车重量(kg) 平均速度(km/h) 固定费用(元) 最大承货物载数(件)
    Type 1 200 1600 60-80 300-400 20
    Type 2 500 2700 50-70 400-500 30
    Type 3 600 3500 40-60 500-600 40
    Type 4 800 5000 30-50 600-800 50
    下载: 导出CSV
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  • 收稿日期:  2019-12-22
  • 录用日期:  2020-05-03

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