随机时变车辆路径问题的多目标鲁棒优化方法

段征宇; 雷曾翔; 孙硕; 杨东援

doi:10.3969/j.issn.0258-2724.20170617

随机时变车辆路径问题的多目标鲁棒优化方法

doi: 10.3969/j.issn.0258-2724.20170617

基金项目: 国家自然科学基金项目（71001079）

详细信息

作者简介:
段征宇（1978—），男，副教授，研究方向为交通规划与管理，E-mail：d_zy@163.com

中图分类号: U492.22
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- 文章访问数: 512
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- 被引次数: 0
出版历程
- 收稿日期: 2017-08-15
- 修回日期: 2017-10-23
- 网络出版日期: 2019-02-23
- 刊出日期: 2019-06-01

Multi-Objective Robust Optimisation Method for Stochastic Time-Dependent Vehicle Routing Problem

摘要

摘要: 车辆路径问题（vehicle routing problem，VRP）是物流配送的核心问题之一，为了提高物流配送的时效性，在传统VRP模型的基础上，同时考虑了路网交通状态的时变性和随机性，基于最小最大准则，提出了一种带硬时间窗的随机时变车辆路径问题（stochastic time-dependent vehicle routing problem，STDVRP）的多目标鲁棒优化模型. 设计了一种非支配排序蚁群算法（non-dominated sorting ant colony optimisation，NSACO），求解STDVRP多目标优化模型；通过测试算例，对比分析了NSACO算法与改进型非支配排序遗传算法（non-dominated sorting genetic algorithm II，NSGA-II）. 研究结果表明：对于车辆数最小的Pareto边界解，NSACO算法的平均车辆数比NSGA-II算法小3.33%；对于最坏行程时间最小的Pareto边界解，NSACO算法的平均最坏行程时间比NSGA-II算法小17.49%.
- 车辆路径问题 /
- 随机时变路网 /
- 鲁棒优化 /
- 多目标优化 /
- 蚁群算法
Abstract: The vehicle routing problem (VRP) is a core issue of distribution logistics. In order to improve the timeliness of deliveries, a multi-objective robust optimisation model based on the minimax criterion was proposed for the stochastic time-dependent vehicle routing problem (STDVRP) with hard time windows, considering both the stochastic and time-varying nature of link travel times. A non-dominated sorting ant colony optimisation (NSACO) algorithm was designed to solve this multi-objective optimisation model for the STDVRP. The NSACO algorithm was compared with the non-dominated sorting genetic algorithm II (NSGA-II) through computational instances. The results show that for the Pareto boundary of the minimised number of vehicles, the average number of vehicles for NSACO is 3.33% less than that of NSGA-II, and for the Pareto boundary of the minimised worst travel time, the average worst travel time for NSACO is 17.49% less than that of NSGA-II.
- vehicle routing problem /
- stochastic time-dependent network /
- robust optimisation /
- multi-objective optimisation /
- ant colony optimisation algorithm

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图 1 R201算例的Pareto最优解的分布

Figure 1. Distribution of R201’s Pareto optimal solutions

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表 1 各类路段的行程车速

Table 1. Travel speed of various links

路段类型	时段
路段类型	1	2	3	4
1	1.00	3.00	1.20	2.80
2	1.80	2.20	1.60	2.40
3	1.60	2.40	1.80	2.20
4	1.40	2.60	1.00	3.00
5	1.20	2.80	1.40	2.60

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表 2 STDVRP算例的计算结果

Table 2. Computational results of STDVRP instances

算例	算法	边界解	车辆数/辆	最坏行程时间	最坏等待时间	期望行程时间	期望等待时间
C101	NSGA-II	A	18	1 319.93	4 007.66	1 271.38	4 040.33
	NSGA-II	B	12	1 482.58	778.83	1 282.24	912.98
	NSACO	A	12	826.78	1 024.67	703.85	1 083.16
	NSACO	B	12	826.78	1 024.67	703.85	1 083.16
C201	NSGA-II	A	7	970.18	8 344.81	858.08	8 451.99
	NSGA-II	B	5	999.46	5 415.92	864.21	5 542.61
	NSACO	A	5	617.23	5 032.93	534.08	5 097.59
	NSACO	B	4	1 610.53	1 461.69	1 380.19	1 642.52
R101	NSGA-II	A	20	1 342.00	1 113.83	1 238.72	1 239.63
	NSGA-II	B	16	1 375.66	626.21	1 195.39	778.21
	NSACO	A	18	1 267.96	1 060.74	1 096.56	1 192.29
	NSACO	B	16	1 350.62	653.77	1 183.74	801.94
R201	NSGA-II	A	7	1 206.09	1 630.94	1 120.11	1 721.53
	NSGA-II	B	3	1 385.58	145.18	1 199.96	299.86
	NSACO	A	7	1 087.86	2 507.04	956.45	2 597.12
	NSACO	B	3	1 387.48	206.84	1 201.50	355.61
RC101	NSGA-II	A	16	1 334.95	576.61	1 261.48	666.44
	NSGA-II	B	14	1 350.06	357.83	1 210.61	470.25
	NSACO	A	16	1 337.90	638.40	1 140.44	735.28
	NSACO	B	14	1 371.84	306.04	1 218.40	403.19
RC201	NSGA-II	A	8	1 349.75	2 591.40	1 213.29	2 740.82
	NSGA-II	B	4	1 393.53	741.07	1 244.36	864.97
	NSACO	A	8	1 132.08	3 102.31	969.50	3 201.67
	NSACO	B	4	1 539.07	312.02	1 370.44	438.52

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表 3 NSACO算法最优解的相对值

Table 3. Relative values of NSACO algorithm’s optimal solutions

算例	边界解	车辆数相对值/%	最坏行程时间相对值/%	期望行程时间相对值/%
C101	A	66.67	62.64	55.36
C101	B	100.00	55.77	54.89
C201	A	71.43	63.62	62.24
C201	B	80.00	161.14	159.71
R101	A	90.00	94.48	88.52
R101	B	100.00	98.18	99.03
R201	A	100.00	90.20	85.39
R201	B	100.00	100.14	100.13
RC101	A	100.00	100.22	90.40
RC101	B	100.00	101.61	100.64
RC201	A	100.00	83.87	79.91
RC201	B	100.00	110.44	110.13
平均	A	88.02	82.51	76.97
平均	B	96.67	104.55	104.09

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