轨道列车时刻表问题研究综述

摘要/Abstract

摘要： 广泛的实践应用和复杂的计算挑战，使得轨道列车时刻表优化问题，多年来一直是交通运输及运筹管理学界的热点研究问题。作为轨道交通运营规划的一个子阶段，列车时刻表向上与线路规划(或开行方案)、向下与动车组调度融合，可以得到多个延伸的研究选题。在特定的时空网络中，列车时刻表设计就是为每个列车确定一条无冲突的运行路径，使基于用户的度量指标如乘客候车时间，或企业的度量指标如运营费用达到最优。对于没有列车越行和停站模式给定的情况，通过整数变量可以完整地刻画列车时刻表模型，但如果考虑列车越行或列车停站决策，则需要引入列车在车站出发顺序或停车决策的0-1变量。一般而言，列车时刻表问题的数学模型是一类典型的大规模、多目标、强耦合的NP完全问题。算法设计是列车时刻表问题最为重要和困难的部分。对于问题较简单或规模较小的情况，常用方法是对原有复杂问题进行适当简化和(或) 对难处理表达式进行合理修改，然后使用先进的计算架构和商用优化软件求解更新后模型。当然，分支定界和动态规划这两类直接分解算法，是求解列车时刻表问题的重要方法。对于问题复杂和规模庞大的情况，以拉格朗日和列生成为代表的对偶分解算法，则是求解列车时刻表问题的最佳选择。未来，探讨列车时刻表与各种现实需要(如设施维修)，以及时变票价和客票分配等因素之间的深度融合，是一个有价值的研究方向；其次，研究网络环境下列车时刻表问题，将是一个非常有意义的研究选题；最后，应进一步设计集成了问题特点与现代优化技术的各类求解算法，开发能够完全应用于实际运营的商用软件。

关键词: 铁路运输, 列车时刻表, 选题, 构模, 算法

Abstract: The rail train timetabling problem has always been a hot research topic in the field of transportation and operations research due to its wide practical applications and complex computational challenges. As a sub- stage of the hierarchical planning of rail transit operations, the timetable problem can be extended to multiple related areas by integrating the upper- layer line planning problem and the lower- layer rolling stock scheduling problem. The train timetable design is to determine a conflict- free running path for each train in the elaborated space-time network, in which the objectives are the user- based measurements such as the passenger waiting times or the supply- based measurements such as the operating costs. If the overtaking activities are not allowed and the stop-skip pattern is given, the optimization models for train timetables can be formulated by using integer variables. Otherwise, zero-one variables are required to represent the departure orders or skip- stopping decisions of trains at the stations. Generally, the models are typical large-scale, multi-objective and strong-coupled NP-hard problems. It is important and difficult to design effective solution algorithms for this type of problems. For the cases with simple conditions and small scales, one common approach is to properly simplify the original complex problem and/or reasonably revise the intractable formulations, and then solve the updated model using state- of- the- art solution frameworks and commercialoptimization solvers. Two types of direct decomposition algorithms, i.e., branch and bound and dynamic programming are two effective methods. Furthermore, the dual decomposition algorithm, which is represented by Lagrangian relaxation and column generation, is normally the best choice for the complicated and large scale problems. The future research should explore the timetabling problem with the consideration of many practical requirements (i.e., infrastructure maintenance) and time- dependent fares and ticket distributions. In addition, it is an interesting topic to address the train timetabling problem within network-wide applications. Finally, solution algorithms that combine the characteristics of problems and the advanced optimization technologies, and commercial software that is applicable to the actual operations, should be developed in the future.

Key words: railway transportation, train timetable, topic, modeling, algorithm

中图分类号:

牛惠民. 轨道列车时刻表问题研究综述[J]. 交通运输系统工程与信息, 2021, 21(5): 114-124.

NIU Hui-min. Literature Review on Rail Train Timetabling[J]. Journal of Transportation Systems Engineering and Information Technology, 2021, 21(5): 114-124.

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http://www.tseit.org.cn/CN/Y2021/V21/I5/114

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