箱量随机扰动下内河集装箱班轮航线配载优化

Loading Optimization of Inland Container Liner Routes under Random Disturbance of Container Volume

摘要: 在内河集装箱班轮运输过程中，集港时随机事件扰动带来港口待装船出口箱箱量变化，导致航线配载决策需纳入箱量随机扰动考虑。基于事件驱动的滚动策略，以最小化班轮堆栈占用数量和相邻阶段间配载计划偏差为目标，构建内河集装箱班轮航线配载决策的多阶段随机规划模型(Stochastic Programming Model, SPM)。同时，基于鲁棒优化的区间预测方法将其转化为等价的混合整数规划模型(Mixed Integer Programming Model, MIPM)，结合问题特征设计深度Q网络(Modified Deep Q-Network, MDQN)算法求解模型。结果表明：模型与算法均可实现问题求解，对于大规模算例，MDQN算法求解最大耗时37.6 s，平均耗时30.9 s，求解效果更好。同时，对需求扰动下箱量占比变化分析计算表明，MDQN算法具有良好的泛化能力，可实现不同场景下问题的有效寻优。

Abstract: In the process of inland river container liner transportation, random event disturbances during port collection lead to changes in the number of export containers to be loaded at the port, which means that the route loading decision needs to take into account the random disturbance of the container volume. Based on the event-driven rolling strategy, a multi-stage stochastic programming model (SPM) for inland river container liner route loading decision is constructed with the goal of minimizing the number of liner stack occupancy and the deviation of loading plans between adjacent stages. At the same time, it is converted into an equivalent mixed integer programming model (MIPM) based on the interval prediction method of robust optimization, and the deep Q-network (MDQN) algorithm is designed to solve the model in combination with the characteristics of the problem. The results show that both the model and the algorithm can solve the problem. For large-scale examples, the MDQN algorithm takes a maximum of 37.6 seconds to solve and an average of 30.9 seconds to solve, and the solution effect is better. At the same time, the analysis and calculation of the change in the proportion of container volume under demand disturbances show that the MDQN algorithm has good generalization ability and can achieve effective optimization of problems in different scenarios.