城市轨道交通列车车底运用计划优化建模
Optimization Model on the Connection Plan of Rolling Stocks for Urban Rail Transit

车底运用效率是降低地铁运营成本、提升服务质量的关键。本文通过建立多旅行商(MTSP)模型，以接续费用最小为目标函数，综合考虑时空约束、车场约束及禁止空驶约束，构建混合整数规划模型。采用ILOG CPLEX求解器对某城市地铁线路进行求解，优化后总接续费用较人工方案降低12.5%；车辆使用数降低1辆；车底平均有效利用率达81.51%，较人工方案(77.18%)提升4.33%；同时在使用均衡性表现上优于人工方案。研究表明，模型在接续成本、资源利用率和均衡性方面均优于传统方法，验证了MTSP模型的有效性。
The utilization efficiency of the rolling stocks is the key to reduce the operation cost of subway and improve the service quality. In this paper, a mixed integer programming model is constructed by establishing a multi-traveling salesman (MTSP) model, taking the minimum connection cost as the objective function, comprehensively considering the time and space constraints, yard constraints and prohibition of empty driving constraints. The ILOG CPLEX solver is used to solve the subway line of a city. After optimization, the total connection cost is reduced by 12.5 % compared with the manual scheme. The number of vehicles used is reduced by 1; the average effective utilization rate of the rolling stocks is 81.51%, which is 4.33% higher than that of the manual scheme (77.18 %). At the same time, it is superior to the manual scheme in the use of balance performance. The research shows that the model is superior to the traditional method in terms of continuation cost, resource utilization and balance, which verifies the effectiveness of the MTSP model.