城市轨道交通列车交路方案优化模型研究

为了对城市轨道交通列车交路方案进行优化，建立非线性规划模型及多目标规划模型。非线性规划模型以最少的运用车底数为优化目标，有效地将列车交路折返点及列车开行数量进行综合优化，但该模型求解难度较大，仅适合对列车交路方案优化做理论分析。多目标规划模型则充分考虑了实际情况，首先确定列车折返点，或者提供几种备选形式，再运用多目标规划求解各交路最优列车开行对数，得出列车交路方案的最优解。最后用算例验证了多目标规划模型的有效性。

Research on the Model about the Optimization of Train Routing in Urban Rail Transit

In order to optimize the urban rail transit train routing scheme ,two models are established, which are nonlinear program- ming model and multi-objective programming model. The nonlinear programming model takes minimum rolling stocks as the optimization goal, and synthetically optimize reentry of trains and quantity of trains effectively, but it is hard to solve this problem, so it is just suitable for optimization study of train routing problem. While the multi-objective programming model takes practical situations into account suffi- ciently, firstly, the reentry points of trains are determined, or some alternative schemes of reentry points of trains are provided ; and then the optimum solution is achieved by calculating the optimum number of running trains of each train routing using multi-objective program- ruing method. At last, an example is given, which verifies the effectiveness of the multi-objective programming model.