地铁快慢车运行计划综合优化模型

为了综合优化地铁快慢车运行计划, 建立了综合求解列车开行方案、停站方案和时刻表的优化模型; 分析了地铁列车停站、区间运行、快慢车运行组织与客流出行等特点, 构建了快慢车运行计划的约束条件, 设计了综合协调优化列车运行时间和运输成本的目标函数, 建立了完整的地铁快慢车运行计划优化模型; 分析了模型特点及其复杂度, 设计了两阶段近似算法求解模型, 第1阶段根据乘客能够忍耐的最大候车时间推算出慢车的开行列数, 同时将其均匀分布在编制时段范围内, 并对初始时刻表进行合理调整, 第2阶段采用CPLEX求解器求解地铁快慢车运行计划; 针对上海地铁16号线, 对其早高峰7:00~9:00下行方向的快慢车运行计划进行编制试验。试验结果表明: 快慢车运行计划中共开行列车30列, 其中快车11列, 慢车19列, 完成9次越行, 87次跨站不停车, 快车全程最大节约时间为628 s, 约降低4.1%, 总旅行时间节约4 450 s; 根据客流需求在1:1~1:2之间灵活安排快慢车开行比例; 根据各车站上下车客流需求灵活安排快车停站方案, 快车之间停站方案不固定; 随着列车规模的增大, 模型求解时间大幅增长, 当规模达到一定程度时, 需设计更为高效的求解算法。 

Integrate opitmization model of operation schedule for metro express/local train

In order to optimize express/local train operation schedule of metro, an integrated calculation optimization model of train operation scheme, stop schedule plan and timetable was established.The characteristics of train stop, interstation running, express/local train operation organization and passenger travelling were analysed.The constraint conditions of operation plan of express/local train were built, and an objective function of comprehensive coordination optimization of train operation time and transportation cost was designed.The integrated operation plan optimization model of metro express/local train was established, and a two-stage approximate algorithm was designed to solve the model.At the first stage, according to the maximum waiting time that passengers can endure, the number of local trains can be calculated.The local trains were required to evenly depart in the considered time horizon, then the initialtimetable was reasonably adjusted.At the second stage, the express/local train operation schedule was solved by using CPLEX solver.Aiming at Shanghai Metro Line 16, the express/local train operation schedule experiment was worked out during morning peak 7:00-9:00 in down direction.Experimental result shows that 30 trains operate in the express/local train operation schedule, including 11 express trains and 19 local trains.9 times of overtaking and 87 times of skip-stopping are accomplished, the maximum saving time of express train during whole journey is 628 s, reduces about 4.1%, and the total travel time saves 4 450 s.The ratio of express/local trains are flexibly assigned between 1∶1-1∶2 according to the passenger demands.The stopping scheme of express trains are flexibly assigned according to the inflow and outflow demands of passenger at each station, and their stopping schemes are not constant.The computing time turns to be much longer as the train scale gets larger, so a more effective algorithm need to be designed when the scale increases to a certain extent.