面向运营结束时段可达性的地铁末班车时刻表协调优化

Timetable Coordinated Optimization of Last Trains to Maximize the Passenger Accessibility over the End-of-Service Period

以提高运营结束时段所有客流需求的可达性为导向,考虑最大发车间隔、最小发车间隔、最晚收车时刻等约束条件,以运营结束时段内OD可达乘客数量最大化为目标函数,建立地铁末班车时刻表协调优化的混合整数非线性规划模型;提出基于预设车次的求解方法,大幅度减少原始模型中判断乘车车次的变量,并将其重构为混合整数线性规划模型。以武汉地铁为验证,结果表明:求解方法能在更短时间内求得优质解,客流数据的间隔时间越短,其求解速度快的优势越明显;对末班车时刻表优化后,运营结束时段内需乘坐末班车乘客的可达数量可提升10%;与仅考虑乘坐末班车出发乘客的既有研究结果相比,考虑运营结束时段整体客流可使更多的乘客抵达目的地;适当延迟线路收车时刻可提高线网可达乘客的比例,但由于客流需求减小,收车时刻延迟对可达比例的提升存在瓶颈。

To improve the accessibility of passenger demand over the end-of-service period,considering the constraints of maximum and minimum headway and service closure time,a mixed integer nonlinear programming model for timetable coordinated optimization of last trains is established to maximize the number of passengers who can reach their destinations within the end-of-service period.A solution method based on predetermining trains is proposed,which greatly reduces the variables for judging the train number.The original model is then be reformulated into a mixed integer linear programming model.Taking Wuhan metro as an example,the results show that the solution method can obtain high-quality solutions in a shorter time.The smaller the interval of passenger demand data,the more significant the advantage of high-computation speed of the reformulated model and algorithm is.With the optimized timetable of last trains,the number of accessible passengers with demand for last trains can be improved by 10%over the end-of-service period.Compared with the existing study results which only consider the passengers departing on last trains,more passengers can reach their destinations with considering total passengers over the end-of-service period.Properly delaying the line service closure time can increase the proportion of accessible passengers in network.But due to the decrease of passenger demand,there is a bottleneck in the improvement of passenger accessibility with delaying the service closure time.