考虑维修天窗和到发线数量的复线铁路列车运行图优化
Optimization for double-track railway train timetabling considering the maintenance skylight and the number of arrival-departure tracks

摘要 研究了维修天窗与复线铁路列车运行图一体化编制问题，考虑到发线数量、维修限速等约束条件，建立了混合整数规划模型.针对约束的特点对约束进行分类，并运用行生成方法对到发线数量等约束进行分解，运用两阶段法处理较为复杂的维修限速约束，结合商业软件GUROBI求解模型.设计算例进行验证，比较分析了模型约束的不同分解方法.结果显示分解到发线数量约束可以提高求解效率25%~45%，而列车追踪间隔间距约束是否宜采取分解与求解规模有关.
Abstract：This paper investigates the joint optimization on the maintenance skylight and double-track railway train timetabling. A Mixed Integer Linear Progrom(MILP) model is established considering the number of arrival-departure tracks, the speed restriction for maintenance. The constraints are classified according to their characteristics, and some kinds of constraints, e.g. the number of arrival-departure tracks constraints are decomposed using row generation, then the model is solved by commercial software GUROBI. The model and algorithm is tested on a calculation example, in which different decomposition methods are compared, and a two-stage approach is applied to deal with the complex maintenance restriction constraints. The results show that decomposing the number of arrival-departure track constrains can improve the solving efficiency by 25%~45%, and whether it’s beneficial to decompose the headway constrains depen-ding on the solving scale.