基于交替方向乘子法的高铁快运网络服务方案优化

doi:10.16097/j.cnki.1009-6744.2026.01.016

交通运输系统工程与信息 ›› 2026, Vol. 26 ›› Issue (1): 172-183.DOI: 10.16097/j.cnki.1009-6744.2026.01.016

基于交替方向乘子法的高铁快运网络服务方案优化

高如虎^*1，何佳睿¹，张晓倩²，张莹³

1. 兰州交通大学，交通运输学院，兰州730070；2.中国铁路兰州局集团有限公司，计划统计部，兰州730015；3. 北京交通大学，交通运输学院，北京100044

收稿日期:2025-10-17 修回日期:2025-12-29 接受日期:2026-01-05 出版日期:2026-02-25 发布日期:2026-02-15
作者简介:高如虎（1989—），男，甘肃庆阳人，副教授，博士。
基金资助:
国家自然科学基金(72361020)；国家铁路局课题(KF2023-047)。

Optimization of Express Service Plan in High-speed Railway Networks Based on Alternating Direction Method of Multipliers

GAO Ruhu^*1, HE Jiarui¹, ZHANG Xiaoqian², ZHANG Ying³

1. School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China; 2. Planning and Statistics Department, China Railway Lanzhou Group Co Ltd, Lanzhou 730015, China; 3. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

Received:2025-10-17 Revised:2025-12-29 Accepted:2026-01-05 Online:2026-02-25 Published:2026-02-15
Supported by:
National Natural Science Foundation of China (72361020)；National Railway Administration Project (KF2023-047)。

摘要/Abstract

摘要： 为提升高铁快运服务通达范围和服务效能，在载客动车组捎带模式下，从高铁网络的视角全局优化高铁快运服务方案。通过构建时空扩展网络，准确刻画快件在高铁网络中的服务作业要求和流程。将实际的快件运达期限约束、装载时间约束及列车服务能力约束等转化为时空扩展网络的弧段以及节点的制约关系，并构建以快件运输时间最短为优化目标的快件服务方案多商品流模型。为打破传统分解算法对偶解的对称性问题，设计基于交替方向乘子法的对偶分解算法框架，将快件在高铁网络中的服务方案优化问题分解为关于单个快件在时空扩展网络中的最短路径问题。以银西高铁、西成高铁和郑西高铁等7条高铁线路及动车组列车组成的运营网络为背景，验证高铁快运服务方案优化模型的正确性及算法的高效性。案例结果表明：网络模式相对于单线模式减少了约45.7%的快件滞留量，跨线快件的运输效率提升尤为显著，滞留量降低了92.5%，大幅度提升了快件的运达效率和服务范围。研究成果为高铁快运的网络化运营实践提供了重要理论支撑。

关键词: 铁路运输, 服务方案, 交替方向乘子法, 高铁快运, 时空扩展网络

Abstract: To expand the coverage and improve the efficiency of high-speed railway express, this paper proposes the express service optimization plan for the high-speed rail network under pickup-delivery mode. An extended space-time network with explicit physical meanings is constructed to precisely capture the service operation requirements and processes of express shipments within the high-speed rail network. Some practical constraints including express delivery deadlines, loading time windows, and train service capacities are converted into restrictions on arcs and nodes in the extended space-time network. A multi- commodity flow model for express services is subsequently developed, aiming to minimize the total transportation time of express shipments. To overcome the symmetry issue of dual solutions in traditional decomposition algorithms, a dual decomposition framework based on the Alternating Direction Method of Multipliers (ADMM) is designed. This approach decomposes the express service optimization problem into individual shortest path problems for each shipment within the extended space-time network. The proposed model and algorithm are validated within an operational network comprising seven high-speed rail lines along with their train services. The results validate the correctness of the proposed model and the effectiveness of the algorithm. Case study demonstrates that the network-based mode reduces the accumulation of express parcels by approximately 45.7% compared to the single-line mode. The transportation efficiency of cross-line express shipments improve notably, with a 92.5% reduction in stranded shipments, significantly enhancing both delivery timeliness and service coverage. The findings provide crucial theoretical support for the networked operational practices of high-speed rail express services.

Key words: railway transportation, service plan, alternating direction method of multipliers (ADMM), high-speed railway express, extended time-space network

中图分类号:

U294.1+2

高如虎, 何佳睿, 张晓倩, 张莹. 基于交替方向乘子法的高铁快运网络服务方案优化[J]. 交通运输系统工程与信息, 2026, 26(1): 172-183.

GAO Ruhu, HE Jiarui, ZHANG Xiaoqian, ZHANG Ying. Optimization of Express Service Plan in High-speed Railway Networks Based on Alternating Direction Method of Multipliers[J]. Journal of Transportation Systems Engineering and Information Technology, 2026, 26(1): 172-183.

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基于交替方向乘子法的高铁快运网络服务方案优化

Optimization of Express Service Plan in High-speed Railway Networks Based on Alternating Direction Method of Multipliers

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