基于双层规划的危险货物配送路径鲁棒优化

马昌喜; 何瑞春; 熊瑞琦

doi:10.19818/j.cnki.1671-1637.2018.05.016

基于双层规划的危险货物配送路径鲁棒优化

doi: 10.19818/j.cnki.1671-1637.2018.05.016

兰州交通大学交通运输学院, 甘肃兰州 730070

基金项目:

国家自然科学基金项目 71861023

详细信息

作者简介:
马昌喜(1979-), 男, 湖北汉川人, 兰州交通大学教授, 工学博士, 从事危险货物运输系统优化与设计研究

通讯作者:
何瑞春(1970-), 女, 甘肃临洮人, 兰州交通大学教授, 工学博士

中图分类号: U492.3
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出版历程
- 收稿日期: 2018-03-26
- 刊出日期: 2018-10-25

Robust optimization on distributing routes of hazardous materials based on bi-level programming

School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China

More Information

Author Bio:
MA Chang-xi(1979-), male, professor, PhD, machangxi@mail.lzjtu.cn

Corresponding author: MA Chang-xi (1979-), male, professor, PhD, E-mail: machangxi@mail.lzjtu.cn

摘要

摘要: 针对不确定环境下带时间窗的多配送中心危险货物配送路径优化问题, 提出一种含鲁棒控制参数的鲁棒优化方法; 综合考虑危险货物运输风险、运输费用和服务时间窗, 构建了危险货物配送路径多目标双层鲁棒优化模型, 上层模型追求运输风险和运输费用最小化, 下层模型采用用户均衡交通分配模型; 根据Bertsimas-Sim鲁棒优化理论, 对含有不确定参数的上层模型进行鲁棒对等转化; 联合增强型Pareto遗传算法和Frank-Wolfe算法构建了求解多目标双层鲁棒优化模型的混合算法, 采用3段式编码和解码方法、等位匹配交叉操作以及翻转变异等遗传操作方法求解上层模型, 采用Frank-Wolfe算法求解下层用户均衡模型; 以经典的Sioux-Falls交通网络为例, 对含有3个配送中心、7个需求点的危险货物配送路径优化问题进行案例分析, 以验证模型及其算法的合理性。研究结果表明: 当鲁棒控制参数分别为0、30和60时, 构建的混合算法能分别快速得到3、2和3组鲁棒最优解, 且所有解均为包含具体运输路段和发车时刻的配送方案, 而非配送顺序; 该混合算法与传统两阶段启发式算法相比, 运算时间能节省54.74%。可见, 该混合算法无论是在求解效率上, 还是在解的表达形式上均优于两阶段启发式算法, 能较好地完成不确定环境下危险货物配送路径多目标双层鲁棒优化任务。
- 交通规划 /
- 危险货物 /
- 配送路径 /
- 双层规划 /
- 鲁棒模型 /
- 多目标优化 /
- 混合算法
Abstract: To solve the optimization problem for the hazardous materials distributing routes (HMDR) with multi-distribution centers and time windows in uncertain environments, a robust optimization method with robust control parameters was proposed.Comprehensively considering the transportation risk, transportation cost and service time window in hazardous materials distributing routes, a multi-objective bi-level optimization model was constructed.The upperlevel model was used to minimize the transportation risk and transportation cost.The lower-level model was constructed as the user equilibrium traffic distribution model.With the Bertsimas-Sim robust optimization theory, the robust peer-to-peer transformation was performed on the upperlevel model with uncertain parameters.The enhanced Pareto genetic algorithm and Frank-Wolfe algorithm were combined to form a hybrid algorithm to solve the multi-objective bi-level robust optimization model.The three-stage coding and decoding method, equipotent matching crossoveroperation and flipping mutation operation were used to solve the upper-level model, and the Frank-Wolfe algorithm was used to solve the lower-level model.Taking the classical Sioux-Falls transportation network as an example, a case study was conducted to verify the rationality of the model and its algorithm for the optimization on the distributing routes of hazardous materials with3 distribution centers and 7 demand points.Research result shows that when the robust control parameters are set as 0, 30 and 60, respectively, the hybrid algorithm can obtain 3, 2 and 3 robust optimal solutions, respectively, and all solutions are delivered with the specific road sections and departure times but not the distribution order.Comparing with the traditional twostage heuristic algorithm, the hybrid algorithm can save 54.74%of the runtime.It can clearly be seen that the hybrid algorithm is superior to the two-stage heuristic algorithm both in the algorithmic efficiency and expression of the solution, and can complete the multi-objective bi-level robust optimization on the hazardous materials distributing routes in uncertain environments.
- traffic planning /
- hazardous material /
- distributing route /
- bi-level programming /
- robust model /
- multi-objective optimization /
- hybrid algorithm

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图 1 增强型Pareto遗传算法流程

Figure 1. Flow of enhanced Pareto genetic algorithm

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图 2 混合算法流程

Figure 2. Flow of hybrid algorithm

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图 3 包含12个节点的交通网络

Figure 3. Traffic network with 12nodes

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图 4 编码与解码

Figure 4. Encoding and decoding

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图 5 交叉操作

Figure 5. Crossover operation

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图 6 变异操作

Figure 6. Mutation operation

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图 7 Sioux-Falls网络

Figure 7. Sioux-Falls network

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图 8 初始种群分布

Figure 8. Initial population distribution

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图 9 进化150代后种群分布

Figure 9. Population distribution after 150evolution generations

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表 1 运输任务信息

Table 1. Information of transport task

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表 2 路段相关参数取值

Table 2. Values of related road parameters

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表 3 λ=0时的Pareto解集

Table 3. Pareto solution sets when λ=0

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表 4 λ=30时的Pareto解集

Table 4. Pareto solution sets when λ=30

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表 5 λ=60时的Pareto解集

Table 5. Pareto solution sets when λ=60

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表 6 λ=0时采用不同算法得到的配送方案对比

Table 6. Comparison of distribution schemes based on different algorithms when λ=0

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