基于候车时间和效益损失的城轨列车运行计划优化

Optimization of Urban Rail Train Operation Plan Based on Waiting Time and Benefits Loss

兼顾乘客和企业的双方利益是编制城轨列车运行计划关注的重点。以两端配有车场的城轨线路为背景,通过考虑列车载客状态及其时间持续对运营效益的影响,提出效益损失概念。针对断面客流不同需求导致效益损失的个体差异,引入体现其差异性的调控因子,以候车时间和效益损失上确界为优化目标,通过考虑列车数量、折返线能力、列车接续及进出场环节等关键约束条件,构建城轨列车运行计划优化模型。因模型求解需要,对模型进行线性化等价重构,并据此设计基于GA(Genetic Algorithm)-Gurobi的混合求解策略。最后,通过算例分析验证了模型及求解策略的合理性,结果分析表明:本文优化得到的列车运行计划节省候车时间约30.1%,减少效益损失约17.9%,节省列车数7.4%,列车运行计划质量得到明显提升。

In an urban rail transit line,the conflicting interests of passengers and enterprise are the major focus of the determination of a train operation plan.Given a line with two depots at the terminals,the concept of benefit loss is proposed by considering the operational effectiveness impacted by the passenger loading state of trains as well as its duration.Considering the individual difference of benefit loss caused by various passenger flow demand at each section,a control factor reflecting this difference is introduced in the optimization objective to optimize the waiting time and the supremum of benefit loss.The optimization model considers operational constraints,such as the number of train cars,the turning-back track's capacity,train connection,as well as the process of train entry and exit depots.To facilitate the model solution,the model is linearized,and a GA(Genetic Algorithm)-Gurobi hybrid solution strategy is designed based on the reconstruction principle.Finally,the effectiveness of the model and solution method is verified by an example analysis.The result analysis shows that:the obtained train operation plan can save passenger waiting time by 30.1%,decrease the benefit loss by 17.9%,and reduce train cars by 7.4%.The performance of the train operation plan can be improved by the model and solution method.