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              面向復雜物流配送場(chǎng)景的車(chē)輛路徑規劃多任務(wù)輔助進(jìn)化算法

              李堅強 蔡俊創(chuàng ) 孫濤 朱慶靈 林秋鎮

              李堅強, 蔡俊創(chuàng ), 孫濤, 朱慶靈, 林秋鎮. 面向復雜物流配送場(chǎng)景的車(chē)輛路徑規劃多任務(wù)輔助進(jìn)化算法. 自動(dòng)化學(xué)報, 2024, 50(3): 544?559 doi: 10.16383/j.aas.c230043
              引用本文: 李堅強, 蔡俊創(chuàng ), 孫濤, 朱慶靈, 林秋鎮. 面向復雜物流配送場(chǎng)景的車(chē)輛路徑規劃多任務(wù)輔助進(jìn)化算法. 自動(dòng)化學(xué)報, 2024, 50(3): 544?559 doi: 10.16383/j.aas.c230043
              Li Jian-Qiang, Cai Jun-Chuang, Sun Tao, Zhu Qing-Ling, Lin Qiu-Zhen. Multitask-based assisted evolutionary algorithm for vehicle routing problems incomplex logistics distribution scenarios. Acta Automatica Sinica, 2024, 50(3): 544?559 doi: 10.16383/j.aas.c230043
              Citation: Li Jian-Qiang, Cai Jun-Chuang, Sun Tao, Zhu Qing-Ling, Lin Qiu-Zhen. Multitask-based assisted evolutionary algorithm for vehicle routing problems incomplex logistics distribution scenarios. Acta Automatica Sinica, 2024, 50(3): 544?559 doi: 10.16383/j.aas.c230043

              面向復雜物流配送場(chǎng)景的車(chē)輛路徑規劃多任務(wù)輔助進(jìn)化算法

              doi: 10.16383/j.aas.c230043
              基金項目: 國家自然科學(xué)基金 (62325307, 62073225, 62203134, 62376163, 62203308),廣東省自然科學(xué)基金 (2023B1515120038, 2019B151502018), 深圳市科技計劃項目(20220809141216003), 深圳大學(xué)科學(xué)儀器開(kāi)發(fā)項目 (2023YQ019) 資助
              詳細信息
                作者簡(jiǎn)介:

                李堅強:深圳大學(xué)計算機與軟件學(xué)院教授. 2008年獲華南理工大學(xué)博士學(xué)位. 主要研究方向為嵌入式系統和物聯(lián)網(wǎng). E-mail: lijq@szu.edu.cn

                蔡俊創(chuàng ):深圳大學(xué)計算機與軟件學(xué)院博士研究生. 主要研究方向為進(jìn)化計算及其在物流領(lǐng)域中的應用. E-mail: caijunchuang2020@email.szu.edu.cn

                孫濤:中興通訊股份有限公司工程師. 2022年獲深圳大學(xué)碩士學(xué)位. 主要研究方向為進(jìn)化計算和路徑規劃. E-mail: 1910272020@email.szu.edu.cn

                朱慶靈:深圳大學(xué)計算機與軟件學(xué)院博士后. 2021年獲香港城市大學(xué)博士學(xué)位. 主要研究方向為進(jìn)化多目標優(yōu)化和機器學(xué)習. E-mail: zhuqingling@szu.edu.cn

                林秋鎮:深圳大學(xué)計算機與軟件學(xué)院副教授. 2014年獲香港城市大學(xué)博士學(xué)位. 主要研究方向為人工免疫系統,多目標優(yōu)化和動(dòng)態(tài)系統. 本文通信作者. E-mail: qiuzhlin@szu.edu.cn

              Multitask-based Assisted Evolutionary Algorithm for Vehicle Routing Problems inComplex Logistics Distribution Scenarios

              Funds: Supported by National Natural Science Foundation of China(62325307, 62073225, 62203134, 62376163, 62203308), Natural ScienceFoundation of Guangdong Province (2023B1515120038, 2019B151502018), Shenzhen Science and Technology Program (20220809141216003), and the Scientific Instrument Developing Project of Shenzhen University (2023YQ019)
              More Information
                Author Bio:

                LI Jian-Qiang Professor at the College of Computer Science and Software Engineering, Shenzhen University. He received his Ph.D. degree from South China University of Technology in 2008. His research interest covers embedded systems and internet of things

                CAI Jun-Chuang Ph.D. candidate at the College of Computer Science and Software Engineering, Shenzhen University. His research interest covers evolutionary computation and its applications in the field of logistics

                SUN Tao Engineer at ZTE Corporation. He received his master degree from Shenzhen University in 2022. His research interest covers evolutionary computation and path planning

                ZHU Qing-Ling Postdoctor at the College of Computer Science and Software Engineering, Shenzhen University. He received his Ph.D. degree from the City University of Hong Kong in 2021. His research interest covers evolutionary multiobjective optimization and machine learning

                LIN Qiu-Zhen Associate professor at the College of Computer Science and Software Engineering, Shenzhen University. He received his Ph.D. degree from the City University of Hong Kong in 2014. His research interest covers artificial immune system, multiobjective optimization, and dynamic system. Corresponding author of this paper

              • 摘要: 在現代社會(huì )中, 復雜物流配送場(chǎng)景的車(chē)輛路徑規劃問(wèn)題(Vehicle routing problem, VRP)一般帶有時(shí)間窗約束且需要提供同時(shí)取送貨的服務(wù). 這種復雜物流配送場(chǎng)景的車(chē)輛路徑規劃問(wèn)題是NP-難問(wèn)題. 當其規模逐漸增大時(shí), 一般的數學(xué)規劃方法難以求解, 通常使用啟發(fā)式方法在限定時(shí)間內求得較優(yōu)解. 然而, 傳統的啟發(fā)式方法從原大規模問(wèn)題直接開(kāi)始搜索, 無(wú)法利用先前相關(guān)的優(yōu)化知識, 導致收斂速度較慢. 因此, 提出面向復雜物流配送場(chǎng)景的車(chē)輛路徑規劃多任務(wù)輔助進(jìn)化算法(Multitask-based assisted evolutionary algorithm, MBEA), 通過(guò)使用遷移優(yōu)化方法加快算法收斂速度, 其主要思想是通過(guò)構造多個(gè)簡(jiǎn)單且相似的子任務(wù)用于輔助優(yōu)化原大規模問(wèn)題. 首先從原大規模問(wèn)題中隨機選擇一部分客戶(hù)訂單用于構建多個(gè)不同的相似優(yōu)化子任務(wù), 然后使用進(jìn)化多任務(wù)(Evolutional multitasking, EMT)方法用于生成原大規模問(wèn)題和優(yōu)化子任務(wù)的候選解. 由于優(yōu)化子任務(wù)相對簡(jiǎn)單且與原大規模問(wèn)題相似, 其搜索得到的路徑特征可以通過(guò)任務(wù)之間的知識遷移輔助優(yōu)化原大規模問(wèn)題, 從而加快其求解速度. 最后, 提出的算法在京東物流公司快遞取送貨數據集上進(jìn)行驗證, 其路徑規劃效果優(yōu)于當前最新提出的路徑規劃算法.
              • 圖  1  VRPPDT模型

                Fig.  1  The model of the VRPPDT

                圖  2  MBEA總體框架圖

                Fig.  2  The overall framework diagram of MBEA

                圖  3  一個(gè)個(gè)體的編碼方法

                Fig.  3  The coding method of an individual

                圖  4  子任務(wù)生成及解碼過(guò)程

                Fig.  4  The generation and decoding process of the subtask

                圖  5  一個(gè)解的切分過(guò)程

                Fig.  5  The splitting process of a solution

                圖  6  基于路徑的交叉過(guò)程

                Fig.  6  The operation process of the route-based crossover

                圖  7  順序交叉操作過(guò)程

                Fig.  7  The operation process of the order crossover

                圖  8  本文提出的方法和對比算法的平均搜索收斂軌跡

                Fig.  8  Averaged search convergence traces of the proposed method and the compared algorithms

                表  1  京東數據集的特性

                Table  1  Properties of Jingdong dataset

                問(wèn)題|V|CJ$ {u_1} $$ {u _2} $
                F201 ~ F2042002.55003000.014
                F401 ~ F4044002.55003000.014
                F601 ~ F6046002.55003000.014
                F801 ~ F8048002.55003000.014
                F1001 ~ F10041 0002.55003000.014
                下載: 導出CSV

                表  2  MBEA算法參數設置

                Table  2  Parameter settings in MBEA

                參數含義
                Evaluation算法總評價(jià)次數18 000
                TE每階段的評價(jià)次數3 600
                N種群大小36
                Nre階段數5
                Nbe保留個(gè)體的數量18
                k子任務(wù)個(gè)數1
                lower子任務(wù)維度最低占比0.7
                下載: 導出CSV

                表  3  MBEA和5種對比算法在京東數據集對比實(shí)驗結果

                Table  3  Comparative experimental results of MBEA and five compared algorithms on Jingdong dataset

                問(wèn)題MBEAEMAMATECCMOGVNSVNSME
                NVTDTC運行
                時(shí)間 (s)
                NVTDTC運行
                時(shí)間 (s)
                NVTDTC運行
                時(shí)間 (s)
                NVTDTC運行
                時(shí)間 (s)
                NVTDTC運行
                時(shí)間 (s)
                NVTDTC運行
                時(shí)間 (s)
                F2014353 85166 7513 2914554 91868 4184 2524253 99766 5978 7125166 09981 3992 9765284 808100 408815060 49475 4943
                F2024453 15566 3553 2704756 28870 3884 3404353 64966 60914 1945263 78279 3822 8395367 75683 6562524959 72874 4282
                F2034354 89967 6793 3564659 00972 8095 4164254 54467 02413 6354967 60882 3082 8815183 07998 3791035165 95181 2512
                F2044353 31166 2112 9834656 45670 2563 9864354 39867 2389 9294862 32976 7292 9705274 57190 1713005160 41575 7152
                F4018199 380123 62011 53893120 041147 9412 56784109 863135 12316 85294124 412152 6128 58098144 757174 1571 22996112 942141 74215
                F40284103 091128 35113 338101122 636152 9362 53587113 871139 97110 742100130 655160 6557 923101160 822191 12226898117 970147 37012
                F4038098 175122 05512 11995122 289150 7892 73184109 212134 41210 15497123 599152 6998 36498160 018189 41842093111 171139 07115
                F4048399 809124 64912 65695116 269144 7692 69486110 555136 29513 709100127 209157 2098 154101136 483166 78365194110 775138 97517
                F601118149 868185 14815 779153202 915248 8162 663126174 424212 34417 795148192 176236 57615 623144240 941284 141702138171 997213 39741
                F602121153 129189 42919 571164204 772253 9722 656129177 851216 55118 839146199 278243 07815 505141227 723270 0231 624143175 068217 96849
                F603120153 681189 74116 090151202 985248 2852 922128176 806215 14617 636151198 996244 29615 032143219 879262 779395142171 057213 65737
                F604122153 477190 13718 569157204 541251 6412 886128176 943215 40318 789154196 028242 22815 201145204 293247 793757141172 956215 25633
                F801159175 009222 70911 565200244 506304 5063 679164196 076245 15620 421200234 549294 54925 467189278 179334 8791 654178189 502242 90282
                F802157173 598220 57713 077210226 736289 7363 657164194 325243 46520 835199236 794296 49425 879184271 798326 9981 153179192 243245 943107
                F803159173 474221 17314 682206240 358302 1583 355165195 539244 91924 212201236 025296 32525 387186231 297287 0971 130180188 245242 24571
                F804156171 956218 75612 743213227 247291 1473 324161191 853240 03321 884198226 353285 75325 707181231 743286 0431 490174186 214238 41481
                F1001212265 385329 0449 698275363 035445 5353 874222293 298359 83825 957279364 136447 83634 957239391 293462 9931 236232278 192347 792154
                F1002211264 034327 2138 655279356 200439 9003 858225291 180358 74027 482284354 899440 09934 582240352 092424 0922 847234278 465348 665126
                F1003212265 409329 0088 910275358 768441 2683 917227295 806363 78626 217283359 276444 17633 748243408 770481 670554231274 553343 853126
                F1004212262 117325 65610 331285362 496447 9963 914223289 035355 81526 180289360 481447 18133 515234348 460418 660890233276 896346 796123
                最佳/
                全部
                18/200/202/200/200/200/20
                下載: 導出CSV

                表  4  RBX和OX的消融實(shí)驗結果

                Table  4  Ablation experiment results of RBX and OX

                問(wèn)題RBXOX RBX + OX
                F20166 51767 96666 751
                F20266 36567 74466 355
                F20368 94871 71867 679
                F20466 97069 37266 211
                F401124 851148 685123 620
                F402128 798146 954128 351
                F403123 550149 781122 055
                F404125 247155 403124 649
                F601187 048246 299185 148
                F602192 623253 252189 429
                F603193 915247 466189 741
                F604193 410245 400190 137
                F801224 758298 889222 709
                F802228 345296 430220 577
                F803226 138302 783221 173
                F804220 988294 788218 756
                F1001342 544442 939329 044
                F1002339 143440 007327 213
                F1003341 946446 173329 008
                F1004336 077445 518325 656
                最佳/全部1/200/2019/20
                下載: 導出CSV

                表  5  MBEA中參數lower的敏感性分析

                Table  5  Sensitivity analysis of lower in MBEA

                問(wèn)題TC (0.7)TC (0.5)TC (0.6)TC (0.8)TC (0.9)
                F20166 75166 66466 92666 89566 971
                F20266 35566 58766 59766 67766 751
                F20367 67968 20667 91968 02767 783
                F20466 21166 21565 92066 20966 150
                F401123 620123 826123 103122 861122 672
                F402128 351127 154127 696127 771127 986
                F403122 055122 428122 703122 343122 270
                F404124 649124 771125 365125 138124 936
                F601185 148185 831186 163185 579186 371
                F602189 429190 317190 661190 363190 731
                F603189 741189 160189 740189 986189 683
                F604190 137189 300189 128189 743188 712
                F801222 709221 057221 905221 221220 910
                F802220 577221 957220 655219 998220 951
                F803221 173222 172222 227221 495221 377
                F804218 756218 002216 628217 680218 297
                F1001329 044330 379330 059330 929329 632
                F1002327 213327 346327 565326 923327 199
                F1003329 008329 596326 035328 369327 482
                F1004325 656325 790325 812326 352327 106
                最佳/全部9/203/203/202/203/20
                下載: 導出CSV

                表  6  MBEA中參數k的敏感性分析

                Table  6  Sensitivity analysis of parameter k in MBEA

                問(wèn)題TC (1)TC (0)TC (2)TC (3)
                F20166 75167 98566 29866 731
                F20266 35567 92067 00267 111
                F20367 67968 18067 91767 680
                F20466 21166 62166 52465 730
                F401123 620124 871124 825123 839
                F402128 351127 377128 292127 603
                F403122 055123 494122 305121 883
                F404124 649126 338124 959125 486
                F601185 148187 055185 004187 381
                F602189 429192 343192 178189 516
                F603189 741190 448190 047190 610
                F604190 137191 208189 940189 096
                F801222 709223 158223 670224 248
                F802220 577222 758223 576225 523
                F803221 173222 456223 684223 939
                F804218 756218 393217 485220 373
                F1001329 044330 374331 387332 643
                F1002327 213329 829329 525326 603
                F1003329 008331 877330 099329 200
                F1004325 656330 725326 082331 858
                最佳/全部12/201/203/204/20
                下載: 導出CSV
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                        • 收稿日期:  2023-02-10
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