带时间窗的多中心半开放式VRPSDP问题研究

Multi-depot Half-open Vehicle Routing Problem with Simultaneous Delivery-pickup and Time Windows

针对带时间窗的多中心半开放式同时送取货车辆路径问题,构建了配送中心车辆进出平衡且以车辆配送距离最小化为目标的带时间窗的多中心半开放式同时送取货车辆路径问题的数学模型。设计了混沌变异头脑风暴算法求解该问题,采用顺序交叉策略增加种群多样性,设置2种混沌映射进行混沌变异操作,利用混沌变异的多样性、遍历性和随机性,增强算法全局搜索能力。通过多组算例对比,不仅验证所提算法求解多种车辆路径问题的有效性与稳定性,还验证了带时间窗下的多中心半开放同时送取货配送模式优于多中心闭合式同时送取货配送模式。研究成果不仅拓展了车辆路径类的模型,还为相关物流企业提供一种决策参考。

To solve the multi-depot half-open vehicle routing problem with simultaneous delivery-pickup and time windows,this paper builds a mathematical model of a multi-depot half-open vehicle routing problem with simultaneous delivery-pickup and time windows by balancing the vehicle in and out of the distribution center and minimizing vehicle delivery distance as the goal.According to the characteristics of the problem,a brain storm algorithm based on chaotic mutation is designed to solve this problem,and the sequential crossover strategy is adopted to increase the population diversity.Meanwhile,the algorithm selects two chaotic maps for chaotic mutation operation,which employs the diversity,ergodicity,and randomness of chaotic mutation to enhance the overall search capability of the algorithm.Multiple numerical example comparison not only verifies the effectiveness and stability of the proposed algorithm for solving various vehicle routing problems but also indicates the distribution mode of multi-depot half-open simultaneous delivery-pickup and time windows is superior to that of multi-depot simultaneous delivery-pickup and time windows.The research results expand the vehicle routing problem and provide a decision-making reference for related logistics enterprises.