拥挤城市轨道交通线路列车时刻表与常态限流协同优化研究

Research on Collaborative Optimization of Train Timetable and Normal Passenger Flow Control in Congested Urban Rail Transit Lines

针对城市轨道交通线路高峰时段客流压力大、站内过度拥挤等问题,文章从系统优化的角度出发,将运输服务供给与客流需求控制作为一个整体进行研究。首先,引入了列车时刻表变量与限流变量,以乘客等待总时间最小化为目标函数,以列车时刻表约束、乘客进站约束及上下车约束为条件,建立了列车时刻表与常态限流协同优化模型。该模型动态刻画了列车运行过程、车站限流过程和乘客与列车的交互过程,并运用0-1变量累计流的思想,详细描述了乘客排队进站及上车的过程,深刻贯彻了“先到先服务”的原则。通过采用CPLEX软件编程求解,算例结果验证了该模型的有效性——与列车时刻表或限流的单目标优化相比,两者协同优化在减少乘客总等待时间方面具有明显作用。其中,两者协同优化相较于仅考虑时刻表优化,使乘客总等待时间减少了19.99%;相较于仅考虑限流优化,使乘客总等待时间减少了16.66%。

In response to the problems of high passenger flow pressure and overcrowding in urban rail transit during peak hours,this paper studies the control of transportation service supply and passenger flow demand as a whole from the perspective of system optimization.Firstly,the train schedule variables and flow limiting variables are introduced,with the objective function of minimizing the total waiting time of passengers.The train schedule constraints,passenger entry constraints,and boarding and alighting constraints are used as conditions to establish a collaborative optimization model for train schedules and normal flow limiting.This model dynamically depicts the train operation process,station flow restriction process,and passenger train interaction process,and adopts the idea of 0-1 variable cumulative flow to describe in detail the process of passengers queuing to enter and board the station,deeply implementing the principle of"first come,first served".By using CPLEX software programming to solve the problem,the effectiveness of the model is verified by the results of numerical examples;compared to single objective optimization of train schedules or flow limiting,the collaborative optimization of the two has a significant effect on reducing the total waiting time of passengers.Among them,compared to only considering timetable optimization,the total waiting time of passengers has been reduced by 19.99%.Compared to only considering flow restriction optimization,the total waiting time of passengers has been reduced by 16.66%.