灵活编组条件下考虑再生制动能量利用的列车时刻表优化

doi:10.16097/j.cnki.1009-6744.2026.02.023

交通运输系统工程与信息 ›› 2026, Vol. 26 ›› Issue (2): 244-255.DOI: 10.16097/j.cnki.1009-6744.2026.02.023

灵活编组条件下考虑再生制动能量利用的列车时刻表优化

左静^*1 ，蒲璇¹，许旻昊¹ ，张能娥¹，帅斌²

1. 兰州交通大学，自动化与电气工程学院，兰州730070；2.西南交通大学，交通运输与物流学院，成都611756

收稿日期:2025-10-17 修回日期:2026-01-19 接受日期:2026-01-26 出版日期:2026-04-25 发布日期:2026-04-20
作者简介:左静（1983—），女，陕西汉中人，教授，博士。
基金资助:
国家自然科学基金(52262045)；甘肃省重点研发计划资助项目 (23YFGA0045)。

Train Timetable Optimization Considering Regenerative Braking Energy Utilization with Flexible Composition Strategies

ZUO Jing^*1, PU Xuan¹, XU Minhao¹, ZHANG Nenge¹, SHUAI Bin²

1. School of Automation and Electrical Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China; 2. School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 611756, China

Received:2025-10-17 Revised:2026-01-19 Accepted:2026-01-26 Online:2026-04-25 Published:2026-04-20
Supported by:
National Natural Science Foundation of China(52262045)；Project Supported by the Key Research and Development Program of Gansu Province (23YFGA0045)。

摘要/Abstract

摘要： 针对城市轨道交通客流波动显著，能耗成本较高的问题，本文提出灵活编组条件下考虑再生制动能量利用的列车运行图优化方法。通过引入多级速度曲线决策机制，决策列车编组配置、到发时刻、速度曲线和再生制动能量回收，实现运营成本、乘客总等待时间和乘客总在车时间的最小化，并基于动态邻域结构改进模拟退火算法求解本文构建的混合整数非线性规划模型。为验证所建模型的有效性，结合城轨实际运营数据设计3组对比实验，结果表明：与考虑再生制动能量回收的固定编组方案对比，本文所提方案能够使得总牵引能耗降低17.8%，总目标下降7.2%；与仅采用灵活编组的方案对比，本文所提方案使得牵引能耗降低13.9%，总目标下降14.1%；与固定编组且不考虑再生制动能量回收的方案对比，本文所提方案节能效果最为突出，牵引能耗降低31.1%，总目标下降20.1%。在灵活编组条件下考虑再生制动能量利用的综合优化，本文实现列车运营成本、服务水平和系统能效的协同优化，达到降本增效的目的。

关键词: 城市交通, 再生制动能量, 混合整数非线性规划, 列车运行图, 灵活编组

Abstract: To address the challenges of the significant fluctuations of passenger flow and the high costs of energy consumption in urban rail transit, this paper proposes a train timetable optimization method considering the utilization of regenerative braking energy under the conditions of flexible train composition. By introducing a multi-level speed profile decision mechanism, the method jointly optimizes the train formation configuration, arrival/departure times, speed profiles, and regenerative braking energy recovery to minimize the operational costs, total passenger waiting time, and total passenger in-vehicle time. A mixed-integer nonlinear programming model is formulated and then solved through an improved simulated annealing algorithm with dynamic neighborhood structures. To validate the effectiveness of the proposed model, three comparative experiments were conducted with the actual operational data in urban rail. The results demonstrate that: compared to the fixed formation scheme with the regenerative braking energy recovery, the proposed method reduces the total traction energy consumption by 17.8% and the overall objective by 7.2%; compared to the scheme by using flexible train composition alone, it reduces the traction energy consumption by 13.9% and the overall objective by 14.1%; compared to the fixed formation scheme without regenerative braking energy recovery, the proposed method exhibits the most pronounced energy-saving effect, reducing the traction energy consumption by 31.1% and lowering the overall objective by 20.1%.The comprehensive optimization considering regenerative braking energy utilization under the conditions of flexible train composition achieves the synergistic optimization of train operational costs, service quality, and system energy efficiency, thereby it fulfills the objectives of cost reduction and efficiency enhancement.

Key words: urban transportation, regenerative braking energy, mixed-integer nonlinear programming, train timetable, flexible train composition

中图分类号:

U292.4

左静, 蒲璇, 许旻昊, 张能娥, 帅斌. 灵活编组条件下考虑再生制动能量利用的列车时刻表优化[J]. 交通运输系统工程与信息, 2026, 26(2): 244-255.

ZUO Jing, PU Xuan, XU Minhao, ZHANG Nenge, SHUAI Bin. Train Timetable Optimization Considering Regenerative Braking Energy Utilization with Flexible Composition Strategies[J]. Journal of Transportation Systems Engineering and Information Technology, 2026, 26(2): 244-255.

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http://www.tseit.org.cn/CN/Y2026/V26/I2/244

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灵活编组条件下考虑再生制动能量利用的列车时刻表优化

Train Timetable Optimization Considering Regenerative Braking Energy Utilization with Flexible Composition Strategies

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