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时间窗约束下多车型电动车辆路径问题建模与优化

Modeling and Optimization of the Multi-type Electric Vehicle Routing Problem with Time Window Constraints

  • 摘要: 针对带时间窗的多车型电动车辆路径问题(heterogeneous electric vehicle routing problem with time windows,HEVRPTW),综合考虑客户需求差异、车辆异构特性和充电约束等因素,构建以总行驶成本最小化为目标的混合整数规划模型,并提出结合层次聚类机制的混合变邻域搜索算法(hybrid variable neighborhood search,HVNS)进行求解。该算法采用层次聚类机制对客户节点进行空间划分,并结合贪婪算法生成初始解;在局部搜索阶段,整合单点插入、两点交换、两段交换及2-opt等多种邻域操作算子,并引入充电站优化策略优化路径选择。基于标准测试案例通过与Gurobi求解器和遗传算法(genetic algorithm,GA)进行仿真对比实验,并对电池容量、充电时间、时间窗宽度、车辆数量等关键参数进行敏感性分析。结果表明:HVNS能在更短时间内获得与Gurobi相近的优质解,验证了模型正确性及其在不同规模问题求解中的优越性能;与GA相比,HVNS在求解质量上实现了10%~20%的提升,同时在稳定性和收敛性方面更优;通过参数优化确定了最佳配置方案(电池容量为150 kWh、充电时间为45 min、时间窗宽度为90 min、车辆数量为8辆时),实现了总行驶成本最小化与客户满意度最大化的平衡。研究结果验证了HVNS是求解HEVRPTW的有效方法,为物流企业电动车辆路径优化提供了科学的决策支持工具。

     

    Abstract: The heterogeneous electric vehicle routing problem with time windows (HEVRPTW) was studied by comprehensively considering factors such as customer demand differences, vehicle heterogeneity, and charging constraints. A mixed-integer programming model aimed at minimizing total travel costs was constructed. A hybrid variable neighborhood search (HVNS) algorithm incorporating a hierarchical clustering mechanism was proposed for solution. The hierarchical clustering mechanism was utilized to spatially partition customer nodes, and a greedy algorithm was integrated to generate initial solutions. In the local search phase, multiple neighborhood operators, including single-point insertion, two-point exchange, two-segment exchange, and 2-opt, were combined. A charging station optimization strategy was introduced to enhance route selection. Simulation experiments were conducted based on standard test cases, and comparisons were made with the Gurobi solver and genetic algorithm (GA). Sensitivity analyses were performed on key parameters such as battery capacity, charging time, time window width, and vehicle number. The results show that the HVNS is able to obtain high-quality solutions comparable to Gurobi in a shorter time, which verifies the correctness of the model and its superior performance in solving problems of different scales. Compared with GA, the HVNS achieves a 10%–20% improvement in solution quality while demonstrating better stability and convergence. Through parameter optimization, the optimal configuration is determined (with a battery capacity of 150 kWh, charging time of 45 min, time window width of 90 min, and vehicle number of 8), achieving a balance between total travel cost minimization and customer satisfaction maximization. The findings confirm that the HVNS is an effective method for solving the HEVRPTW, providing a scientific decision-support tool for logistics enterprises in optimizing electric vehicle routing.

     

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