多中心联合配送模式下集货需求随机的<b>VRPSDP</b>问题

范厚明; 刘鹏程; 刘浩; 侯登凯

doi:10.16383/j.aas.c190519

多中心联合配送模式下集货需求随机的VRPSDP问题

doi: 10.16383/j.aas.c190519

1.
大连海事大学交通运输工程学院大连 116026

基金项目: 国家自然科学基金(61473053), 辽宁省社会科学规划基金(L19BGL006), 辽宁省重点研发计划指导计划(2018401002)资助

详细信息

作者简介:
范厚明：大连海事大学交通运输工程学院教授. 主要研究方向为交通运输系统规划与设计, 战略管理与系统规划. 本文通信作者. E-mail: fhm468@163.com

刘鹏程：大连海事大学交通运输工程学院硕士研究生. 主要研究方向为交通运输规划与管理. E-mail: lpc0369@163.com

刘浩：大连海事大学交通运输工程学院硕士研究生. 主要研究方向为物流工程与管理. E-mail: lhao66@126.com

侯登凯：大连海事大学交通运输工程学院博士研究生. 主要研究方向为交通运输规划与管理. E-mail: houdk@dlmusp.com

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出版历程
- 收稿日期: 2019-07-08
- 录用日期: 2019-11-16
- 刊出日期: 2021-07-27

The Multi-depot Vehicle Routing Problem With Simultaneous Deterministic Delivery and Stochastic Pickup Based on Joint Distribution

1.
College of Transportation Engineering, Dalian Maritime University, Dalian 116026

Funds: National Natural Science Foundation of China (61473053), Liaoning Social Science Planning Fund (L19BGL006), the Key Research Plan Guidance Plan of Liaoning Province (2018401002)

More Information

Author Bio:
FAN Hou-Ming　Professor at the College of Transportation Engineering, Dalian Maritime University. His research interest covers transportation system planning and design, strategic management and system planning. Corresponding author of this paper

LIU Peng-Cheng　Master student at the College of Transportation Engineering, Dalian Maritime University. His main research interest is transportation planning and management

LIU Hao　Master student at the College of Transportation Engineering, Dalian Maritime University. His main research interest is logistics engineering and management

HOU Deng-Kai　Ph. D. candidate at the College of Transportation Engineering, Dalian Maritime University. His main research interest is transportation planning and management

摘要

摘要:
针对多中心联合配送模式下集货需求随机的同时配集货车辆路径问题(MDVRPSDDSPJD), 构建了两阶段MDVRPSDDSPJD模型. 预优化阶段基于随机机会约束机制以及车载量约束为客户分配车辆, 生成预优化方案; 重优化阶段采用失败点重优化策略对服务失败点重新规划路径. 根据问题特征, 设计了自适应变邻域文化基因算法(Adaptive memetic algorithm and variable neighborhood search, AMAVNS), 针对文化基因算法易早熟、局部搜索能力弱等缺陷, 将变邻域搜索算法的深度搜索能力运用到文化基因算法的局部搜索策略中, 增强算法的局部搜索能力; 提出自适应邻域搜索次数策略和自适应劣解接受机制平衡种群进化所需的广度和深度. 通过多组算例验证了提出模型及算法的有效性. 研究成果不仅深化和拓展了VRP (Vehicle routing problem)相关理论研究, 也为物流企业制定车辆调度计划提供一种科学合理的方法.
- 车辆路径问题 /
- 多中心 /
- 同时配集货 /
- 随机需求 /
- 文化基因算法 /
- 变邻域搜索算法
Abstract:
A two-stage model is constructed to solve the multi-depot vehicle routing problem with simultaneous deterministic delivery and stochastic pickup based on joint distribution (MDVRPSDDSPJD). In pre-optimization stage, the pre-optimization scheme is generated, and the vehicles is assigned to the customers based on the stochastic chance constrained and vehicle capacity constraints. In re-optimization stage, the failure points rescheduling strategy is used to re-plan the path of the service failure points. According to the characteristics of the problem, a metaheuristic combined adaptive memetic algorithm and variable neighborhood search (AMAVNS) is designed to solve the problem. In this metaheuristic, aiming at the shortcomings of memetic algorithm such as fast convergence speed and weak local search capability, the deep search ability of the variable neighborhood search algorithm is applied to the local search strategy of the memetic algorithm to enhance the local search ability of the algorithm. The strategies include self-adaptive number of neighborhood iterations and adaptive mechanism of selective acceptance of inferior solutions are used to balance the diversification and exploitation in the algorithm iteration process. Numerical results show that the model and metaheuristic we proposed are rather effective. The research results not only deepen and expand the vehicle routing problem (VRP) theory research, but also provide a scientific and reasonable method for logistics enterprises to draw up the vehicle scheduling plan.
- Vehicle routing problem /
- multi-depot /
- simultaneous delivery and pickup /
- stochastic demand /
- memetic algorithm /
- variable neighborhood search

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图 1 MDVRPSDDSPJD的衍生进程

Fig. 1 Derivation of MDVRPSDDSPJD

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图 2 不同失败点重优化策略对比图

Fig. 2 Different failure points re-optimized strategies

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图 3 自适应变邻域文化基因算法框架图

Fig. 3 The basic flow of adaptive memetic algorithm and variable neighborhood search

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图 4 编码方式示意图

Fig. 4 Encoding mode diagram

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图 5 解码路径图

Fig. 5 Decoding routing diagram

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图 6 顺序交叉算子示意图

Fig. 6 The diagram of ordered crossover operator

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图 7 邻域结构示意图

Fig. 7 Neighborhood structures

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图 8 最短路径变化趋势图

Fig. 8 The iterative trend of optimal solution

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图 9 实验3部分算例的求解路径图

Fig. 9 The specific path diagrams of some cases of experiment 3

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表 1 算法性能比较

Table 1 Performance comparison of different types of metaheuristics

算法	$BKS$	$Best$	${\text{%}}Dev$(%)	$Worst$	${\text{%}}Dev$(%)	$Avg$	${\text{%}}Dev$(%)	$CPU\,({\rm{s} })$
聚类分层法^[22]	116.01	123.33	6.31
狼群算法^[23]		122.42	5.53
禁忌搜索算法^[24]		116.01	0.00	343.31	195.93	187.34	61.49	243.00
量子遗传算法^[24]		116.01	0.00	326.48	181.42	176.37	52.03	216.00
云量子遗传算法^[24]		116.01	0.00	162.38	39.97	156.32	34.75	168.00
自适应变邻域文化基因算法		113.62	−2.06	115.39	−0.53	114.33	−1.45	4.78

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表 2 本文算法求解路径

Table 2 The algorithm solution path of this paper

算法	车辆行驶路径	总路程
本文	A-22-30-14-10-7-4-A	113.62
	B-11-29-28-13-8-15-1-B
	C-16-25-5-12-26-18-3-6-C
	C-17-21-19-20-23-24-2-9-27-C

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表 3 MDVRP算例结果比较

Table 3 The results comparison of MDVRP instances

算例	客户规模	$BKS$	GRASP/VND^[25]		GA^[26]		ILS^[27]		AMAVNS
算例	客户规模	$BKS$	$Best$	${\text{%}}Dev$(%)	$Best$	${\text{%}}Dev$(%)	$Best$	${\text{%}}Dev$(%)	$Best$	${\text{%} }Dev\ ({\text{%} })$	$CPU\, ({\rm{s} })$
p01	50	576.87	592.21	2.66	598.45	3.74	606.11	5.07	576.87	0.00	32.60
p02	50	473.53	529.64	11.85	478.65	1.08	496.45	4.84	473.53	0.00	39.22
p03	75	641.19	648.68	1.17	699.23	9.05	675.32	5.32	646.33	0.80	84.06
p04	100	1 001.59	1 055.26	5.36	1 011.36	0.98	1 062.60	6.09	1 039.69	3.80	155.23
p05	100	750.03	769.37	2.58	—	—	782.34	4.31	765.98	2.13	143.73
p06	100	876.50	924.68	5.50	882.88	0.72	910.13	3.84	902.27	2.94	164.82
p07	100	885.80	925.80	4.52	—	—	904.44	2.10	909.22	2.64	159.01

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表 4 VRPSDP算例结果比较

Table 4 The results comparison of VRPSDP instances

算例	TS^[29]			EPSA3^[30]			SavAnt^[31]			SS^[32]		AMAVNS
算例	$Best$	${\text{%}}Dev$(%)	$CPU\,({\rm{s} })$	$Best$	${\text{%}}Dev$(%)	$CPU \,({\rm{s} })$	$Best$	${\text{%}}Dev$(%)	$CPU\,({\rm{s} })$	$Best$	${\text{%}}Dev$(%)	$Best$	${\text{%}}Dev$(%)	$CPU\,({\rm{s} })$
SCA8-0	981.47	2.07	4.14	1 015.06	5.57	—	961.6	0.01	—	981.17	2.05	961.50	0.00	35.31
SCA8-1	1 077.44	2.65	4.27	1 098.91	4.69	—	1 063.0	1.27	—	1 077.44	2.65	1 049.65	0.00	42.05
SCA8-2	1 050.98	1.00	4.20	1 064.54	2.30	—	1 040.6	0.00	—	1 050.98	1.00	1 049.22	0.83	36.63
SCA8-3	983.34	0.00	4.17	1 021.61	3.89	—	985.9	0.26	—	983.34	0.00	983.34	0.00	31.59
SCA8-4	1 073.46	0.55	4.13	1 114.50	4.40	—	1 071.0	0.32	—	1 073.46	0.55	1 065.49	0.00	42.87
SCA8-5	1 047.24	1.68	4.02	1 060.43	2.96	—	1 054.3	2.36	—	1 047.24	1.68	1 029.95	0.00	38.19
SCA8-6	995.59	2.37	3.85	1 004.66	3.31	—	972.5	0.00	—	995.59	2.37	973.27	0.08	34.88
SCA8-7	1 068.56	0.84	4.22	1 080.17	1.93	—	1 059.7	0.00	—	1 068.56	0.84	1 063.22	0.33	29.01
SCA8-8	1 080.58	0.88	3.85	1 098.02	2.51	—	1 082.7	1.08	—	1 080.58	0.88	1 071.18	0.00	33.54
SCA8-9	1 084.80	1.32	4.20	1 123.55	4.94	—	1 081.4	1.00	—	1 084.80	1.32	1 070.71	0.00	46.03
CON8-0	860.48	0.39	4.19	857.17	0.00	—	858.9	0.20	—	860.48	0.39	857.40	0.03	37.86
CON8-1	740.85	0.00	3.89	742.41	0.21	—	740.9	0.01	—	740.85	0.00	740.85	0.00	40.75
CON8-2	723.32	1.38	3.76	715.17	0.24	—	714.3	0.12	—	723.32	1.38	713.44	0.00	35.99
CON8-3	811.23	0.00	4.12	815.59	0.54	—	812.3	0.13	—	811.23	0.00	811.23	0.00	39.37
CON8-4	772.25	0.28	3.75	789.13	2.47	—	770.1	0.00	—	772.25	0.28	772.25	0.28	41.22
CON8-5	756.91	0.23	3.99	759.09	0.52	—	766.6	1.51	—	756.91	0.23	755.16	0.00	40.84
CON8-6	678.92	0.00	4.04	707.83	4.26	—	697.2	2.69	—	678.92	0.00	684.11	0.76	53.95
CON8-7	814.50	0.00	4.00	834.64	2.47	—	814.8	0.04	—	814.50	0.00	814.77	0.03	49.99
CON8-8	775.59	1.05	3.74	787.43	2.59		−771.3	0.49	—	775.59	1.05	767.53	0.00	33.40
CON8-9	809.00	0.00	4.13	813.84	0.60	—	815.1	0.75	—	809.00	0.00	809.00	0.00	34.21
平均值	909.33	0.83	4.03	925.19	2.52	2.98	906.71	0.61	441	909.31	0.83	902.27	0.12	39.38

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表 5 MDVRPSDDSPJD算例结果比较

Table 5 The results comparison of MDVRPSDDSPJD

$\alpha$	规则1			规则2
$\alpha$	$Best$	$Avg$	$CPU\,({\rm{s} })$	$Best$	${\text{%}}Dev$(%)	$Avg$	${\text{%}}Dev$(%)	$CPU\;({\rm{s} })$
0.1	558.98	732.61	98.85	548.86	−1.81	674.40	−7.95	101.57
0.2	565.26	726.67	92.75	549.51	−2.79	673.54	−7.31	110.48
0.3	545.30	713.16	97.43	542.30	−0.55	676.67	−5.12	108.43
0.4	568.42	713.75	108.26	550.14	−3.22	678.61	−4.92	102.49
0.5	549.96	709.65	105.43	543.59	−1.16	650.79	−8.29	109.47
0.6	548.04	651.97	105.67	537.83	−1.86	640.07	−1.83	114.64
0.7	533.85	624.97	102.20	499.96	−6.35	610.54	−2.31	101.35
0.8	545.30	668.99	110.46	537.83	−1.37	641.70	−4.08	148.57
0.9	546.83	657.50	90.26	537.44	−1.72	653.35	−0.63	96.84
1.0	564.64	655.98	95.33	563.24	−0.25	650.85	−0.78	110.28
平均值	552.66	685.53	100.66	541.07	−2.10	655.05	−4.45	110.41

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表 6 MDVRPSDDSPJD算例求解最优解

Table 6 The best solutions of MDVRPSDDSPJD

	车辆行驶路径	车辆数	总路程
规则 1	51-4-18-13-41-40-19-42-51	8	533.85
	53-38-5-37-17-44-15-45-33-39-10-49-53
	53-30-34-21-16-50-9-53
	54-20-3-36-35-54
	52-11-32-27-48-23-7-43-24-52
	54-29-2-1-8-26-31-28-22-54
	52-47-12-46-52
	52-6-14-25-52
规则 2	54-20-2-16-21-29-54	7	499.96
	54-35-36-3-28-31-26-8-22-54
	53-38-5-37-17-44-15-45-33-39-10-49-53
	52-46-11-32-1-27-48-23-7-43-24-6-52
	51-42-19-40-41-13-25-14-52
	52-12-47-18-4-51
	53-30-34-50-9-53

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