考虑多类型时间窗的集装箱多式联运路径双目标优化研究

Study on the Bi-objective Optimization for the Multimodal Routing Problem with Multiple Time Windows

为提高集装箱多式联运的经济性和时效性,在规划中转节点固定作业时间窗及运输时限软时间窗的基础上研究集装箱多式联运路径优化问题。以费用最小化和集装箱到达终点提早或延迟时间最小化为优化目标,构建集装箱多式联运路径优化的双目标混合整数线性规划模型。采用标准化加权求和法并结合数学规划软件求得双目标优化问题的最优解。设计算例验证优化方法的可行性,并揭示了集装箱多式联运路径优化经济性目标和时效性目标的矛盾关系。同时,算例计算结果表明根据问题优化结果,多式联运经营人可以针对客户实际需求,选择合适的帕累托解规划集装箱多式联运路径方案。

For the improvement of economy and timeliness, the routing problem of the container multimodal transportation is explored based on the formulation of the fixed operation time windows of transshipping nodes and the soft time windows of transit time. Specifically, a bi-objective mixed integer linear programming model was built to minimize the cost and period caused by early or delayed arrival of containers at the destination. The optimal solutions to the bi-objective optimization problem were obtained by using the normalized weighted sum method and mathematical programming software. Then, a numerical case was designed to demonstrate the feasibility of the proposed optimization method and reveal the conflicting relationship between the objectives of economy and timeliness of the multimodal transportation routing problem. Meanwhile, the computational results of the numerical case indicate that the multimodal transportation operator can select the most suitable one from the Pareto solutions to the problem to design the multimodal transportation scheme based on customers’ specific demand on transportation economy and timeliness.