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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, 2022, 48(11): 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, 2022, 48(11): 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, 2022, 48(11): 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, 2022, 48(11): 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(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, 智能优化. 本文通信作者.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

  • 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
    Author Bio:

    HU Rong Associate professor at the School of Information Engineering and Automation, Kunming University of Science and Technology. She received her master degree from Tsinghua University in 2004. Her research interest covers scheduling theory and method, intelligent computation, and decision support system

    LI Yang Master student at the School of Information Engineeing and Automation, KunMing University of Science and Technology. He received his bachelor degree from Kunming University of Science and Technology in 2009. His research interest covers scheduling methods and intelligent optimization algorithms

    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 interest covers scheduling theory and method, and intelligent optimization. Corresponding author of this paper

    JIN Huai-Ping Associate professor at the School of Information Engineering and Automation, Kunming University of Science and Technology. He received his Ph.D. degree from Beijing Institute of Technology in 2016. His research interest covers intelligent computation and soft sensor methods

    XIANG Feng-Huang Professor at the School of Information Engineering and Automation, Kunming University of Science and Technology. He received his Ph.D. degree from Kunming University of Science and Technology in 2002. His research interest covers intelligent optimization and control

  • 摘要: 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.
    1)  1 表7 ~ 表9的完整测试结果可在: https://pan.baidu.com/s/19sqBboZHLCgFqtiZS7Id-Q 提取码3cv6下载.
  • 图  1  EACO_CD (EACO_IBKA_HKMA)结构

    Fig.  1  Framework of EACO_CD (EACO_IBKA_HKMA)

    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  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 $H_{PM}$ 车场P有$H_{PM}$辆$M$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 $V$ 表示客户编号集合$\{1,2,\cdots,\ N\} $ (0表示车场)
    $C_{M1}$ 第$M$种类型车的距离费用系数 $M_t$ 共有$M_t$种类型的车
    $C_{M2}$ 第$M$种类型车的固定发车费用系数 $k$ 车辆编号
    $C_{M3}$ 第$M$种类型车的燃油费用系数 $x_{PMijk}$ 车场$P$车型$M$的第$k$辆车从客户$i$到客户$j$的决策变量
    $C_1$ 配送车辆提前到达的单位惩罚费用 $d_{ij}$ 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
    $i$ 客户点$i$ ${LT}_i$ 客户$i$要求的最晚到达时间
    $j$ 客户点$j$ $S_i$ 客户$i$要求的卸货时间
    $P$ $\{1,2,\cdots,\ P_t\} $ 车场编号$q_i$ 客户i 要求的货物需求量
    $P_s$ 全部车场集合 $t_i$ 车辆到达客户$i$的时间
    $P_t$ 总共有$P_t$个车场$P$ $M$ 第$M$车型编号
    $M_s$ 全部车型集合$\{1,2,\cdots,\ M_t\}$ $Q_M$ 种车型的最大载重量
    $H_{PMS}$ 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
    注: 综合燃油消耗模型中的其他相关参数设定参考文献[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 ${ {T} }({{\rm{s}}} )$
    bestaverageworstSDbestaverageworstSDbestaverageworstSDbestaverageworstSDbestaverageworstSD
    48_211118118001216395107451118111579971155812080125399996501039011026871025511068116639010
    96_217483181551854918318037183791914618716768176751822919015371170091777116916011175591816117419
    144_224628254352698330824880253692720131425435267102770232024366259692741931824475268842835632829
    192_227522285462964941128457294823026141928758295603101942828379298383061843228524308633166544538
    240_231505326993416650832517336773523551832676337233517952932722347693590653433643364753748755048
    288_239217410284332659240412423634416260441179421424469661641283431644432562242606439304513764158
    360_253748562685854484754672574026019986455251578475961988156276586536193889056965594096292991672
    48_3107671103511572831022110827111158410995114921192993917898831048981975410529110958314
    96_316638172781765417417066174911822218215957168211734918014627165821791219115236171861814118429
    144_323443242112568529323659241492589329024211254262637130223194247202610129623297255922699330543
    192_326199271752822539227090280662882639927376281402952940327016284052914740727153293813014542058
    240_329992311303252748430956320613354549431108321053349149931151331013418450432029347263569051972
    288_337337390624125156438476403334204757539205411234255558139305410964220258740565418264297560486
    360_3511765357655744806520565465657320823526085508056768831535845584858976839542405656859920864108
    48_41023910617113138299431041810886841080711144116718689399615988378954510051105398019
    96_416062169431725716616810171461748117515871164251743416016012169071733617916391169911749617738
    144_422700237232548827923650242422518729123765249902594529622747242732560228822841251142650629458
    192_425690266122773737326528272352793838326846276202898839126443278962862840326623288502961441177
    240_429375304473187746130317314013287447330447314113286348330545324843350251131411344013499752196
    288_4365193826640433537376243949341240549383653933841737560384424027841339583396924097442135595115
    360_4504805290455056768513445396056608786519045439256088802520885518458312833535845590459216850144
    平均值281832937730724400288312996831284409291003025031510416286343028931553421292783115632422431
    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}({{{\rm{s}}}})$
    bestaverageworstbestaverageworstbestaverageworstbestaverageworstbestaverageworstbestaverageworst
    48_212801136121390113220146461512812467132931399812607133171392212218137981420213352147921527915
    96_216299167591734217570194612010616238176611859116754177041810116543178381877717746196562030729
    144_222061232652408923361258602671722390236652472122266235332459022838239342521523595261192698444
    192_224847259982693325983269052822826000272012837226039269182823826520277452893926243271742851057
    240_225958271242879726951280022972629253301303075329409300763087830131310343197627221282823002372
    288_232225333563383833783347133629032740352423718932540351563717534050366523867734121350603665387
    360_2483445005051763506955208854440491295287455793488285274353780510945498958025512025260954984108
    48_311896124001311112574139191438611755119991331211995126581323611520122401399912700140581453021
    96_315777159291699716704184941912216011167921768015932168391759416171169601785716871186791931344
    144_320965211712266122207245872539421291223122349021170223662338021717227582396022429248332564865
    192_323624247182559724704255702682324714258502697424748255882683625455266262778324951258262709187
    240_3246802577627367256202661628248278042863429235279482858229351289162977930404258762688228530108
    288_3306213170032158321063298434483311113349335335309293341435335326673516837102324273331434828129
    360_3459334755448245481724950251726466915023753019474015011851004490265274955670486544999752243162
    48_410755109981225711330125331295610700113931198510800114021192710999117661199911443126581308629
    96_414214143491467215047166551722114422151181592714346151711584314566152691608615197168221739357
    144_418878190572050619998220392286519165200852114819057201402104819548204872157120198223602309487
    192_4212732225123043222372301824145222572326824281222822303424158229252396625009224592324824386116
    240_4222152320924642230732396625438250352577826316251612573526431260362680927369233042420625692144
    288_4275632854229950289022968931040280123014931812278423008831815294133165633403291912998631350173
    360_4413504280944034433604455846561420284521847722417764311145711441294747950108437944500447027216
    平均值244072519725970256002694828145252012665927983252302665227636260232760528944258562721728426
    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 ${ {T} }({ {{\rm{s}}} })$
    best average worst SD best average worst SD best average worst SD
    48_2_212145124781285923212880132121350924111632119671222722015
    96_2_216370165261690429517800180711838127215852160111637628531
    144_2_221010213052170432424589248252540633621049216402215434851
    192_2_223664247602565055626040272502821857624863260102694859071
    240_2_224722258322742658826707279032964064127444287202994769296
    288_2_2306903176832227724337723496235457803353113655037076824123
    360_2_239903413034190695143907454484611110594550746098477811197162
    48_3_212999140641442529313656147871537233612742138021433730421
    96_3_216883178691899335818568201152099934316800182831901136348
    144_3_221916237282466845625647277742887453923029249212590649176
    192_3_2242572549226408668266922805929065671266882805229053746109
    240_3_2246722655828026792278843002131675740283823055432236787144
    288_3_230258315723286090734814363193779710173541436956384501092183
    360_3_2393474106142734114143291451874702012634722849291512971389243
    48_3_312284132251375528012830139061444632212123132531379728729
    96_3_315867170821786038817470189111966436816514178741858447862
    144_3_3206202232123193438224882433625294490241282613627154522102
    192_3_3228162397724832631251082638327320708262422758828567743145
    240_3_3242092598227348655266932873130318770278592999531632803192
    288_3_32845829693308928283274234157355309573558237120386221048245
    360_3_3370063861040166107940722424744418611984708149427515231399288
    平均值238142501025945599263952775428775650267372810729175696
    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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出版历程
  • 收稿日期:  2019-12-22
  • 录用日期:  2020-05-03
  • 网络出版日期:  2022-10-24

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