动态行驶时间取送一体化车辆路径问题

李嫚嫚; 陆建; 张赫

doi:10.3969/j.issn.0258-2724.20170488

动态行驶时间取送一体化车辆路径问题

doi: 10.3969/j.issn.0258-2724.20170488

李嫚嫚^1,2,3,,
陆建^1,2,3, ,,
张赫⁴

基金项目: 国家自然科学基金资助项目（51478110）；江苏省自然科学基金资助项目（BY2016076-05）；江苏省研究生科研与实践创新计划资助项目（KYCX18_0139）

详细信息

作者简介:
李嫚嫚（1991—），女，博士研究生，研究方向为交通运输管理，交通运输规划，优化理论与算法设计，E-mail：230169545@seu.edu.cn

通讯作者:
陆建（1972—），男，教授，博士，研究方向为交通管理、交通安全与智能交通，E-mail：lujian_1972@seu.edu.cn

中图分类号: F253.4
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- 文章访问数: 384
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- 被引次数: 0
出版历程
- 收稿日期: 2017-10-12
- 修回日期: 2018-03-08
- 网络出版日期: 2018-05-30
- 刊出日期: 2019-10-01

Vehicle Routing Problem with Pick-up and Delivery under Dynamic Travel Times

LI Manman^{1,2,3
,},
LU Jian^{1,2,3
, ,},
ZHANG He⁴

摘要

摘要: 为优化真实路网下的车辆配送路径，采用优化 + 调整的两阶段求解方法. 在优化阶段，根据常发拥堵信息，采用遗传算法求解时变取送一体化车辆路径，安排车辆初始配送路径. 在调整阶段，以路段行驶时间为时间间隔，采用滚动更新策略调整车辆配送路线躲避偶发拥堵. 在针对车辆路径调整问题构建了一系列混合整数规划模型的基础上，设计了2-opt + insertion启发式算法求解模型，并结合Dijkstra算法求解到的客户点间最短行驶路线，将车辆配送路径转化成了真实路网中的车辆配送路线. 数值实验测试结果表明：滚动更新策略中，以路段行驶时间为时间间隔比以客户间行驶时间为时间间隔减少车辆行驶时间0.24～11.95 min；以路段行驶时间为时间间隔比以24 min为时间间隔减少车辆行驶时间0.08～8.06 min，比以6 min为时间间隔减少更新次数10.02～34.59次，因此，固定时间滚动更新策略中的最优时间间隔难以确定，其实用性较差. 2-opt + insertion启发式算法求解速度是遗传算法的4倍.
- 货物运输 /
- 交通网络 /
- 车辆路径 /
- 取送一体化 /
- 动态行驶时间 /
- 启发式算法
Abstract: A two-stage method of optimization and adjustment was applied to solving vehicle routing problem with pick-up and delivery under dynamic travel times in an actual urban network. In optimization stage, according to the recurrent congestion information, a genetic algorithm was used to solve time-dependent vehicle routing problem with pick-up and delivery and arrange the initial delivery routes of vehicles. In adjustment stage, the link travel time is set as the time horizon and the rolling update was adopted to adjust delivery routes and avoid non-recurrent congestion. A series of mix-integer linear programming models were formulated for routing adjustment problem and a 2-opt algorithm hybrid with insertion algorithm was designed to solve the model. According to the shortest paths between customers derived from Dijkstra algorithm, the delivery routes are converted into the ones in an actual urban network. The numerical experiments show that in the rolling update, the time horizon of the link travel time can save 0.24–11.95 min in vehicle travel time compared with the time horizon of the travel time between customers; it can also save 0.08–8.06 min compared with the time horizon of the 24 min, and can decrease 10.02–34.59 in the number of updates compared with the time horizon of 6 min. Therefore, it is difficult to determine the optimal time horizon in the rolling update with a fixed horizon and thus it has a poor practicality. And the solving speed of 2-opt algorithm hybrid with insertion algorithm is 4 times the genetic algorithm.
- freight transportation /
- urban network /
- vehicle routing /
- pick-up and delivery /
- dynamic travel times /
- heuristic algorithm

HTML全文

图 1 客户及路网信息

Figure 1. Customers and road network information

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图 2 求解流程

Figure 2. Overview of finding a solution

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图 3 2-opt算法

Figure 3. 2-opt algorithm

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图 4 插入算法

Figure 4. Insertion algorithm

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图 5 测试网络及客户情况

Figure 5. Toy network and customers

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图 6 路段行驶时间

Figure 6. Link travel time

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图 7 测试网络中的初始车辆配送路线

Figure 7. Initial delivery routes in toy network

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图 8 不同干扰频率下的总行驶时间及更新次数

Figure 8. Total travel times and number of updates under different interference frequencies

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图 9 不同行驶时间增加量对应的总行驶时间及更新次数

Figure 9. Total travel times and number of updates under different increments of travel times

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图 10 不同影响路段数对应的总行驶时间及更新次数

Figure 10. Total travel times and number of updates under different numbers of affected links

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表 1 初始车辆配送路线

Table 1. Initial delivery routes in a simple network

车辆编号	行驶路线	行驶时间/min
1	0−n₂−P₁−0	30
2	0−n₁−E₁−0	35

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表 2 算法比较

Table 2. Algorithm comparison

模拟次数	遗传算法		2-opt+insertion
模拟次数	求解时间/s	车辆总驶时间/min	求解时间/s	车辆总驶时间/min
1	0.44	792.00	0.10	792.00
2	0.35	803.00	0.09	803.00
3	0.39	803.00	0.09	803.00
4	0.36	792.00	0.09	792.00
5	0.34	792.00	0.09	792.00
6	0.34	792.00	0.09	792.00
7	0.36	800.00	0.09	800.00
8	0.40	800.00	0.09	800.00
平均值	0.37	796.75	0.09	796.75

下载: 导出CSV

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