Abstract: Urban rail transit has become the first choice for cities to solve the urban congestion problem, with its unique advantages of high capacity, high efficiency, low energy consumption and high environmental protection. Among the many factors affecting the optimization of train schedule, passenger flow is obviously the most important factor for therational allocation of transport capacity and transport system, and the formulation of operation schedule. The passenger flow of urban rail transit is obviously unbalanced in time and space, and the passenger flow of inbound and outbound stations along the line is very different, which makes it difficult to optimize the train schedule. The commonly used balanced train mode with equal intervals is widely used to control the operation of state-owned and intercity trains due to its ease of management; However, the time-varying characteristics of passenger flow will inevitably lead to the increase in operating costs or a decrease in service levels, which hinders the improvement of urban rail transit service levels. There are abundant research results on schedule optimization of rail transit at home and abroad. A large number of research results show that the study on schedule optimization should consider not only the time imbalance of passenger flow, but also its spatial imbalance. Therefore, it is very important to use the actual dynamic passenger flow information, scientific modeling method and optimization algorithm to solve the schedule optimization problem of urban rail transit.
Based on a lot of existing research, aimed at the optimization problem of train schedule, the time-varying characteristics of passenger demand in urban rail transit are analyzed, and a method of calculating passenger cost based on passenger transport efficiency is presented. With train departure time as variable, station capacity, train capacity, departure interval, first and last train departure time and the number of spare vehicles as constraint conditions, and minimum total cost of passengers and operating units as optimization objective, an optimization model of train schedule of urban rail transit is constructed. According to the characteristics of model, a two-step genetic algorithm based on simulation is designed. Taking Wuhan Metro Line 1 as an example for empirical analysis, it is found that setting station design ability and train capacity as strong constraints can improve the efficiency of the solution and shorten the search time for feasible initial solution in the process of solving genetic algorithm. Optimization time interval is one of the important factors to determine the optimization result and optimization rate of train progress, so three different time intervals (5s, 10s and 30s) are selected to optimize the model. The optimization results begin to converge after 53 generations, and the optimal solution of the model is obtained at the time interval of 5s. At this time, the optimal solution of the model is 566142 yuan, which is 2736 yuan less than the optimal solution when the time interval is 10s, and 12549 yuan less than the optimal solution when the time interval is 30s. Therefore, the optimal operation plan obtained at a time interval of 5 seconds has a significant cost reduction compared with that of the other two time intervals, which verifies the effectiveness of the model and algorithm.
The results show that the two-step genetic algorithm based on simulation has strong convergence and high solving efficiency. The “small and high-density” train operation plan can balance the interests of passengers and operating units. The smaller platform capacity severely limits the service level of urban rail transit, resulting in the increase of operating costs. The smaller the station capacity is, the higher the operating costs and passenger waiting costs will be. The larger the station capacity, the higher the operating costs and passenger waiting costs. According to the obtained optimal plan, relevant departments can optimize the train operation plan and determine a more reasonable train operation plan (including operation time, routing and train use plan, etc.), which will effectively improve the passenger travel efficiency, reduce the operating cost of each train at the departure station, improve the service level of urban rail transit, and promote the high-quality development of urban rail transit.

Key words: urban transport, genetic algorithm, schedule, passenger flow, time-varying characteristics

摘要： 针对列车时刻表优化问题,考虑客流的时变特性,提出了一个列车运行优化方法。以列车出发时间为变量,以车站容量、列车容量、出发间隔、首末班车出发时间和备用车辆的数量为约束条件,以乘客和运营单位的最小总成本为优化目标,构建了城市轨道交通列车时刻表的优化模型。根据模型的特点,设计了基于仿真的两步遗传算法。以武汉地铁一号线为例,对列车的运行时刻表进行优化,验证了模型和算法的有效性。研究结果表明,设计的算法收敛性强,求解效率高;“小而高密度”列车运行计划可以平衡乘客和运营单位的利益,较小的平台容量严重限制了城市轨道交通的服务水平,导致运营成本增加,车站容量越小,运营成本和乘客等候的成本越高。

关键词: 城市交通, 遗传算法, 时刻表, 客流, 时变特性