基于改进的PESP模型编制高速铁路周期性列车运行图的研究

Research on Establishment of Periodic Train Working Diagram for High Speed Railway Based on Improved PESP Model

针对利用周期事件规划问题(PESP)传统模型编制规模较大的高速铁路周期性列车运行图时易出现无解的情况,对PESP传统模型进行改进,将PESP传统模型中的固定列车区间运行时间约束变为可变区间运行时间约束,并将列车运行安全间隔时间约束分解为2个与列车的区间运行时间无关的约束,以扩大模型的解空间,实现对大规模高速铁路周期性列车运行图编制问题的求解。对PESP改进模型进行灵敏度分析发现:PESP改进模型的求解难度随着列车对数的增加而增大;为此在求解过程中引入割平面和适当增加虚拟车站,以提高模型的求解效率。利用改进的PESP模型编制京沪高速铁路的周期性列车运行图,验证了模型的有效性。

The traditional model based on periodic event scheduling problem（PESP）was prone to no solution to large-scale periodic train working diagram for high speed railway.In order to solve this problem,the traditional PESP model was improved through replacing the fixed train section running time constraints by variable train section running time constraints,and decomposing the safety time interval constraints into two constraints which were independent of section running time.In this way,the solution space was increased to ensure optimal solutions to large-scale cases.Sensitivity analysis on the improved PESP model shows that the difficulty of solving the model increases with the increase of the number of train pairs.Cutting plane is introduced and virtual stations are added in the solving process to improve the solution efficiency of the model.The improved PESP model is used to work out the periodic train working diagram for Beijing-Shanghai high speed railway and the effectiveness of the model is validated.