林立 孟学雷 宋仲仲

摘 要：针对城际列车开行方案没有有效匹配城市轨道交通运能的问题，提出一种考虑区域协调性的城际列车开行方案优化方法。首先，以旅客出行费用最小和铁路运输效益最大为优化目标，考虑城际列车载客能力、出发地目的地（Original Destination，OD）客流需求和通过能力等约束;然后，在此基础上增加运能匹配度的限制，构建了考虑区域协调性的城际列车开行方案多目标非线性规划模型，并设计改进的模拟退火算法求解模型;最后，以广深城际铁路为例并进行两组对比分析。实验结果表明：考虑区域协调性的列车开行方案可以使旅客出行总广义费用降低约4.06%，铁路部门的效益提高约9.58%，旅客和铁路的系统总成本降低约23.27%;与遗传算法相比，改进的模拟退火算法在求解质量与收敛速度上均有较大提高。所提模型和算法可充分兼顾旅客和铁路双方利益，能够为城际列车开行方案优化问题提供有效解决方法。

关键词：城际列车;开行方案;多目标优化;非线性模型;模拟退火算法

中图分类号： TP301.6

文献标志码：A

Abstract： Concerning the problem that intercity train operation plans fail to match urban rail transit capacity effectively， an optimization method of intercity train operation plan considering regional coordination was proposed. Firstly， the minimum passenger travel cost and maximal benefit of railway department were considered as the optimization objectives， the transport capacity of intercity train， traffic demand between origins and destinations and carrying capacity were considered as constraints of this model. Secondly， the matching degree limit of transportation capacity was considered， a multi-objective nonlinear programming model of intercity train operation plan considering regional coordination was constructed and an improved simulated annealing algorithm was designed to solve the model. Finally， the Guangzhou-Shenzhen intercity railway was taken as an example to make two pairs of comparative analyses. The experimental results show that the train operation plan considering the regional coordination makes the total travel cost of passengers reduced by 4.06%， the railway department revenue increased by 9.58%， the total cost of passengers and railway system decreased by 23.27%. Compared with genetic algorithm， the improved simulated annealing algorithm is better in solving quality and convergence speed. The proposed model and algorithm can give full consideration to the interests of both passengers and railway department， and provide an effective solution for the optimization of intercity train operation plan.

Key words： intercity train; train operation plan; multi-objective optimization; nonlinear model; simulated annealing algorithm

0 引言

開行方案旨在确定列车的开行数量、运行径路以及停站序列等要素。合理制定列车开行方案能最大化利用铁路既有设备，提高运输效益和旅客服务水平。

对于列车开行方案的优化问题，大部分研究都考虑构建多目标函数进行求解。对于客流弹性需求下开行方案的研究，文献[1]利用铁路与旅客之间的博弈关系，考虑……