同城地铁物流网络多目标分布鲁棒优化研究

Research on Multi-Objective Distributionally Robust Optimization of Intra-City Metro Logistics Network

基于地铁系统的高效、环保和非高峰时段可以充分利用的空闲运力优势,整合地面车辆和地下地铁两种运输方式,研究了同城快递物流网络设计问题,构建了一种基于分布鲁棒优化(distributionally robust optimization,DRO)方法的多目标优化模型。该模型考虑了不确定快递需求和不确定地铁客流量情形来对地铁物流网络进行最优布局,以降低物流系统总运营成本及最大程度减少快递运输对地铁乘客运输的干扰。由于构建的多目标DRO模型是一个半无限机会约束优化模型,为了有效求解该优化模型,推导了可用CPLEX直接求解的安全逼近形式,并设计了一种NSGA-II算法来求解大规模优化问题。以上海地铁网络为典型案例开展了一系列扩展数值实验,验证了所提出的多目标DRO模型及NSGA-II算法在基于地铁的同城快递物流网络设计中的有效性。通过参数敏感性分析,揭示了折扣系数、允许的最大服务时间和容忍水平对Pareto前沿面的影响。

Based on the advantages of underground system’s high efficiency,environmental protection and spare capacity that can be fully utilized in off-peak hours,this paper integrates two transport modes of ground vehicles and underground metro,studies the design of the logistics network of intra-city express delivery,and constructs a multi-objective optimization model based on distributionally robust optimization(DRO)method.The model takes into account the uncertain express demand and uncertain metro passenger flow to optimize the layout of the metro logistics network,in order to reduce the total operating cost of the logistics system and minimize the interference of express transport on metro passenger transport.Since the constructed multi-objective DRO model is a semi-infinite chance constrained optimization model,in order to solve the optimization model efficiently,this paper derives a safe approximation form that can be solved by CPLEX directly,and designs a NSGA-II algorithm to solve the large-scale optimization problem.Finally,a series of extended numerical experiments are carried out with the Shanghai metro network as a typical case to verify the effectiveness of the proposed multi-objective DRO model and NSGA-II algorithm in the design of metro-based intra-city express logistics network.The effects of discount factor,maximum allowed service time and tolerance level on the Pareto front are revealed through parameter sensitivity analysis.