According to the properties of the full-length and short-turn routing mode in urban railway transit,we develop a multi-objective optimization model of train plan for a single transit line,where the objective functions are minimum passenger waiting time,running kilometers of rolling stocks,and operation time of trains,and the decision variables are frequencies,train formation plans (full-length and short-turn train),and positions of turn-back stations.The linear weighted method is applied to reduce the above model into a single objective model,then the controlled random search algorithm (CRS) is designed to solve it.The validity of the model is verified by a case,and the sensitivities of frequency of short-turn train and positions of turn-back stations are also analyzed.The results indicate that the full-length and short-turn routing mode can significantly reduce the spatial inequality of load factor and the total number of rolling stocks;the shorter length of short-turn routing is not conducive to the passengers,and it can not lead to a more saving of operator's cost.%根据城市轨道交通大小交路运营模式的特点,以最小化乘客等待时间、车辆走行公里和列车运行时间为目标,构建大小交路列车开行方案多目标优化模型.其中决策变量为发车频率、列车编组和小交路折返站位置.采用线性加权法将原模型转化为单目标优化模型,并设计受控随机搜索算法求解.通过案例验证了模型的有效性,对小交路发车频率、折返站位置进行了灵敏度分析.结果表明,开行大小交路可以有效降低大交路列车满载率的非均衡性,减少车辆运用数;小交路长度越短对乘客越不利,且不能使企业成本节省越多.
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