电动汽车路径规划模型与算法研究进展

doi:10.16182/j.issn1004731x.joss.22-1161

系统仿真学报 ›› 2024, Vol. 36 ›› Issue (2): 320-337.doi: 10.16182/j.issn1004731x.joss.22-1161

电动汽车路径规划模型与算法研究进展

庄鹤林¹^,²(), 夏小云²(), 李康顺³, 陈泽丰⁴, 张先超²

^1.江西理工大学理学院, 江西赣州 341000
^2.嘉兴大学信息科学与工程学院, 浙江嘉兴 314001
^3.东莞城市学院人工智能学院, 广东东莞 523430
^4.中山大学人工智能学院, 广东珠海 519082

收稿日期:2022-09-30 修回日期:2022-12-26 出版日期:2024-02-15 发布日期:2024-02-04
通讯作者: 夏小云 E-mail:zhuanghl1998@163.com;xiaxiaoyun@zjxu.edu.cn
第一作者简介:庄鹤林(1998-)，男，硕士生，研究方向为智能计算、组合优化。E-mail：zhuanghl1998@163.com
基金资助:
国家自然科学基金(62206313);浙江省自然科学基金(LGG19F030010)

Research Advances on Electric Vehicle Routing Problem Models and Algorithms

Zhuang Helin¹^,²(), Xia Xiaoyun²(), Li Kangshun³, Chen Zefeng⁴, Zhang Xianchao²

^1.School of Sciences, Jiangxi University of Science and Technology, Ganzhou 341000, China
^2.School of Information Science and Engineering, Jiaxing University, Jiaxing 314001, China
^3.School of Artificial Intelligence, Dongguan City University, Dongguan 523430, China
^4.School of Artificial Intelligence, Sun Yat-sen University, Zhuhai 519082, China

Received:2022-09-30 Revised:2022-12-26 Online:2024-02-15 Published:2024-02-04
Contact: Xia Xiaoyun E-mail:zhuanghl1998@163.com;xiaxiaoyun@zjxu.edu.cn

摘要/Abstract

摘要：

电动车技术的发展为物流企业提供了一种配送车辆的新方案。电动车具有低污染、低噪音等优点，其续航短、充电站有限等特性也带来了新的挑战。电动车路径问题(electric vehicle routing problems，EVRPs)在交通运输、物流管理等领域得到了广泛应用，受到了众多学者的关注。整理了电动车路径问题及其主流变体的问题描述，分析了其各自的提出背景与适用场景。对EVRPs的求解方法和技术做了归类，分析了各方法的优劣，并介绍了相关实际应用。给出了EVRP基准数据集与带时间窗的电动车辆路径问题的基准数据集的基本信息和部分节点分布图，对比分析了已对EVRP基准数据集应用的算法。展望了EVRPs的发展前景。

关键词: 电动汽车, 路径规划, 低碳, 启发式算法, 物流

Abstract:

The development of electric vehicle provides an alternative to conventional fuel vehicles for logistics companies. Using electric vehicles has the merits of less pollution and low noise, but the characteristics of limited cruising range and limited number of charging stations are new challenges. Electric vehicle routing problems(EVRPs) have been widely used in transportation, logistics and other fields, and have received much attention. A comprehensive survey of EVRP and its many variants are presented and the respective backgrounds and applicable conditions are analyzed. The solving approaches of EVRPs are categorized, the strengths and weaknesses of each algorithm are analyzed, and the related practical applications are reviewed. The basic information and some node distribution maps of EVRP benchmark dataset and EVRP with time windows benchmark dataset are given, and the algorithms that have been applied in EVRP benchmark dataset are compared and analyzed. The future development trends of EVRPs is depicted.

Key words: electric vehicle, vehicle routing problem, low carbon, heuristic algorithms, logistics

中图分类号:

TP18

庄鹤林,夏小云,李康顺等 . 电动汽车路径规划模型与算法研究进展[J]. 系统仿真学报, 2024, 36(2): 320-337.

Zhuang Helin,Xia Xiaoyun,Li Kangshun,et al . Research Advances on Electric Vehicle Routing Problem Models and Algorithms[J]. Journal of System Simulation, 2024, 36(2): 320-337.

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算例	客户数	充电站数	电池容量	车辆容量
E22	21	8	94	6 000
E23	22	9	190	4 500
E30	29	6	178	4 500
E33	32	6	209	8 000
E51	50	9	105	160
E76	75	9	98	220
E101	100	9	103	200

算例	客户数	充电站数	电池容量	车辆容量
X143	142	4	2 243	1 190
X214	213	9	987	944
X351	350	35	649	436
X459	458	20	929	1 106
X573	572	6	1 691	210
X685	684	25	911	408
X749	748	30	790	396
X819	818	25	926	358
X916	915	9	1 591	33
X1001	1 000	9	1 684	131

文献	模型	求解方法	优化目标
[7]	GVRP	混合启发式算法	距离最短
[26]	EVRP	AMPL/CPLEX	距离最短
[38]	EVRPTW	ALNS	耗电最少
[39]	EVRPTW	CPLEX，ALNS	成本最小 (运输、车辆、司机和时间窗惩罚成本)
[40]	多充电技术的电动车路径问题	分支定价法	自定义总充电代价最小
[41]	多车型电动车辆问题	分支定价法	成本最小(运输和车辆成本)
[42]	MEVRP	分支定价法，双向标记算法	成本最小(运输和车辆成本)
[43]	EVRPNL	分支定价法	时间最短
[44]	EVRPTW	分支定价法	距离最短
[15]	EVRP	VNS，SA，GA	距离最短
[45]	EVRPTWNL	改进差分进化混合算法	成本最小(运输和时间窗惩罚成本)
[46]	考虑载重影响耗电率的电动车路径问题	改进自适应大邻域搜索	成本最小(运输、充电和车辆成本)
[47]	EVRPTW	精英遗传算法	耗电最少
[22]	EVRPSTW	结合变邻域搜索算法的粒子群优化算法	成本最小
[48]	EVRP	蚁群优化算法	时间最短
[49]	MEVRP	改进粒子群优化算法	成本最小 (运输、碳排放和时间窗惩罚成本)
[50]	EVRP	增强人工蜂群算法	距离最短
[51]	多车场多车型的电动车路径问题	K-means，改进蚁群算法	成本最小(运输、车辆和电池成本)
[52]	EVRP	禁忌搜索算法	距离最短
[53]	EVRPTWNL	两层遗传算法	时间最短
[8]	EVRP	双层蚁群优化算法	距离最短
[16]	EVRP	基于置信度的双层蚁群算法	距离最短
[54]	EVRP	强化学习	距离最短
[19]	EVRPTW	深度强化学习	距离最短

方法类型	难易程度	灵活性	性能	使用情况
数学软件	容易	低	限小规模算例	较少
精确算法	较容易	中	限小规模算例	较少
启发式算法	较困难	高	可搜索到小规模算例的最优解、大规模算例的优质解	当前主流
机器学习算法	困难	中	训练完成后求解速度快，求解质量一般	有发展前景

算例	统计	VNS	SA	GA	BACO	CBACO
E22	min	384.67	384.67	384.67	384.67	384.67
	max	384.67	384.67	384.67	\	\
	mean	384.67	384.67	384.67	384.67	384.67
	stdev	0	0	0	0	0
E23	min	571.94	571.94	571.94	571.94	571.94
	max	571.94	571.94	571.94	\	\
	mean	571.94	571.94	571.94	571.94	571.94
	stdev	0	0	0	0	0
E30	min	509.47	509.47	509.47	509.47	509.47
	max	509.47	509.47	509.47	\	\
	mean	509.47	509.47	509.47	509.47	509.47
	stdev	0	0	0	0	0
E33	min	840.14	840.57	844.25	840.57	840.57
	max	840.46	873.33	846.21	\	\
	mean	840.43	854.07	845.62	842.30	840.57
	stdev	1.18	12.80	0.92	1.42	0.00
E51	min	529.90	533.66	529.90	529.90	529.90
	max	548.98	533.66	553.23	\	\
	mean	543.26	533.66	542.08	529.90	529.90
	stdev	3.52	0	8.57	0	0
E76	min	692.64	701.03	697.27	692.64	692.64
	max	707.49	716.77	730.92	\	\
	mean	697.89	712.17	717.30	692.85	692.88
	stdev	3.09	5.78	9.58	0.81	0.92
E101	min	839.29	845.84	852.69	840.25	838.84
	max	\	856.74	887.14	\	\
	mean	\	852.48	872.69	845.95	840.56
	stdev	\	3.44	9.58	4.58	0.42

电动汽车路径规划模型与算法研究进展

Research Advances on Electric Vehicle Routing Problem Models and Algorithms

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算例	统计	VNS	SA	GA	BACO	CBACO
X143	min	16 028.05	16 610.37	16 488.60	15 901.23	15 884.58
	max	16 883.38	17 396.06	17 478.86	\	\
	mean	16 459.31	17 188.90	16 911.50	16 031.46	15 930.76
	stdev	242.59	170.44	282.30	262.47	31.15
X214	min	11 323.56	11 404.44	11 762.07	11 133.14	11 091.37
	max	11 660.70	11 881.73	12 309.38	\	\
	mean	11 482.20	11 680.35	12 007.06	11 219.70	11 245.18
	stdev	76.14	116.47	156.69	46.25	66.09
X351	min	27 064.88	27 222.96	28 008.09	26 478.34	26 456.95
	max	27 418.38	27 796.69	28 792.66	\	\
	mean	27 217.77	27 498.03	28 336.07	26 593.18	26 637.80
	stdev	86.20	155.62	205.29	72.86	91.24
X459	min	25 370.80	25 464.84	26 048.21	24 763.93	24 776.44
	max	25 774.62	26 038.65	26 742.11	\	\
	mean	25 582.27	25 809.47	26 345.12	24 916.60	24 911.98
	stdev	106.89	157.97	185.14	94.08	92.95
X573	min	\	51 929.24	54 189.62	53 822.87	52 706.59
	max	\	53 534.01	56 327.62	\	\
	mean	\	52 793.66	55 327.62	54 567.15	52 853.78
	stdev	\	577.24	548.05	231.05	53.12
X685	min	71 345.40	72 549.90	73 925.56	70 834.88	70 943.23
	max	72 187.75	73 693.49	75 535.99	\	\
	mean	71 770.57	73 124.98	74 508.03	71 440.57	71 339.17
	stdev	197.08	320.07	409.43	281.78	297.11
X749	min	81 002.01	81 392.78	84 034.73	80 299.76	80 042.38
	max	81 634.06	82 414.80	85 549.36	\	\
	mean	813 270.39	81 848.13	84 759.79	80 694.54	80 571.38
	stdev	176.19	275.26	376.10	223.91	222.72
X819	min	164 289.95	165 069.77	170 965.68	164 720.80	163 751.23
	max	165 571.48	166 640.37	173 391.76	\	\
	mean	164 926.41	165 895.78	172 410.12	165 565.79	164 826.42
	stdev	318.62	403.70	568.58	401.02	599.22
X916	min	341 649.91	342 796.88	357 391.57	342 993.01	341 369.36
	max	343 338.01	344 521.64	362 422.52	\	\
	mean	342 460.70	343 533.85	360 269.94	344 999.95	343 127.47
	stdev	510.66	556.98	1 192.57	905.72	877.97
X1001	min	77 476.36	78 053.86	78 832.90	76 297.09	75 666.26
	max	78 464.68	79 226.81	79 567.00	\	\
	mean	77 920.52	78 593.50	79 163.34	77 434.33	76 405.53
	stdev	234.73	306.27	229.19	719.86	337.78

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