Freight train line planning for large-scale high-speed rail network: An integer Benders decomposition-based branch-and-cut algorithm

Shengdong Li , Dajie Zuo , Wenqing Li , Yongxiang Zhang , Li Shi
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Abstract

This paper aims to study and address the problem of completely re-scheduling high-speed freight train line plans under the conditions of a large-scale network, particularly for direct freight trains between central network nodes. First, we constructed a line pool of candidate trains. Then, considering constraints such as flow balance, station capacity, and train transport capacity, we formulated an integer programming model with 0–1 variables. The objective is to minimize train operation costs and freight transfer fees, determining the origin and destination stations and the operating frequency of freight trains. To address the structural characteristics of the model, an integer Benders decomposition-based branch-and-cut algorithm (IBD-BCA) is proposed. This algorithm, within the framework of branch-and-bound, solves the master problem decomposed by Benders and adds two sets of integer Benders cuts to achieve the optimal solution of the model. To demonstrate the effectiveness and performance of the model and algorithm, numerical experiments were conducted based on actual data from the main high-speed railway network in China. The results show that the IBD-BCA in this study can obtain optimal solutions within a reasonable time and requires adding a relatively small number of cuts during the search process. Compared with branch-and-bound algorithms and direct solving using Gurobi, the IBD-BCA proposed maintains sufficient efficiency when dealing with large-scale problems. Additionally, sensitivity analyses of parameters such as capacity and costs validate the robustness and scalability of the presented model and algorithm.

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大规模高速铁路网的货运列车线路规划:基于整数本德斯分解的分支与切割算法
本文旨在研究和解决大规模网络条件下高速货运列车线路计划的完全重排问题,尤其是网络中心节点之间的直达货运列车。首先,我们构建了一个候选列车线路库。然后,考虑到流量平衡、车站容量和列车运输能力等约束条件,我们建立了一个 0-1 变量的整数编程模型。目标是最大限度地降低列车运行成本和货物转运费用,确定货运列车的始发站、终点站和运行频率。针对该模型的结构特点,我们提出了一种基于本德斯分解的整数分支切割算法(IBD-BCA)。该算法在分支与边界的框架内,求解由 Benders 分解的主问题,并添加两组整数 Benders 剪切,以实现模型的最优解。为了证明模型和算法的有效性和性能,基于中国主要高速铁路网的实际数据进行了数值实验。结果表明,本研究中的 IBD-BCA 可以在合理的时间内获得最优解,并且在搜索过程中需要添加的切点数量相对较少。与分支约束算法和使用 Gurobi 直接求解相比,所提出的 IBD-BCA 在处理大规模问题时保持了足够的效率。此外,对容量和成本等参数的敏感性分析验证了所提出模型和算法的稳健性和可扩展性。
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来源期刊
CiteScore
16.20
自引率
16.00%
发文量
285
审稿时长
62 days
期刊介绍: Transportation Research Part E: Logistics and Transportation Review is a reputable journal that publishes high-quality articles covering a wide range of topics in the field of logistics and transportation research. The journal welcomes submissions on various subjects, including transport economics, transport infrastructure and investment appraisal, evaluation of public policies related to transportation, empirical and analytical studies of logistics management practices and performance, logistics and operations models, and logistics and supply chain management. Part E aims to provide informative and well-researched articles that contribute to the understanding and advancement of the field. The content of the journal is complementary to other prestigious journals in transportation research, such as Transportation Research Part A: Policy and Practice, Part B: Methodological, Part C: Emerging Technologies, Part D: Transport and Environment, and Part F: Traffic Psychology and Behaviour. Together, these journals form a comprehensive and cohesive reference for current research in transportation science.
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