中文摘要：

在多路由模式下面的城市的栏杆运输的火车计划能被划分成三部分：在每个时期训练形成，火车操作时期和每路由的相应火车计数。基于旅客的分析一般差旅费和操作员好处，限制和客观功能被定义，为城市的栏杆运输的火车计划的多客观的优化模型被介绍。在多客观的优化模型考虑的因素在 multi-train-routing 模式下面包括运输能力，交通组织的要求，公司好处，旅客要求，和旅客选择行为。根据这个模型和实际计划经验的特征，一个三阶段的答案被设计逐渐地优化火车形成，火车计数以及操作时期。第 2 行长沙地铁的例子验证这条途径的可行性和效率。

英文摘要：

The train plan of urban rail transit under multi-routing mode can be divided into three parts： train formation, train operation periods and corresponding train counts of each routing in each period. Based on the analysis of passen- ger＇s general travel expenses and operator＇s benefits, the constraints and objective functions are defined and the multiobjective optimization model for the train plan of urban rail transit is presented. Factors considered in the multi- objective optimization model include transport capacity, the requirements of traffic organization, corporation benefits, passenger demands, and passenger choice behavior under multi-train-routing mode. According to the characteristics of this model and practical planning experience, a three-phase solution was designed to gradually optimize the train formarion, train counts as well as operation periods. The instance of Changsha Metro Line 2 validates the feasibility and efficiency of this approach.