交通运输系统工程与信息 ›› 2026, Vol. 26 ›› Issue (3): 315-326.DOI: 10.16097/j.cnki.1009-6744.2026.03.028

• 系统工程理论与方法 • 上一篇    下一篇

双层嵌套决策下的列车编组计划与运行图综合优化

林柏梁* ,李想   

  1. 北京交通大学,交通运输学院,北京100044
  • 收稿日期:2026-01-30 修回日期:2026-04-21 接受日期:2026-04-23 出版日期:2026-06-25 发布日期:2026-06-23
  • 作者简介:林柏梁(1961—),男,浙江龙游人,教授,博士。
  • 基金资助:
    中国国家铁路集团有限公司科技研究开发计划 (N2024X033(JB));国家自然科学基金 (U2268207)。

Integrated Optimization of Train Formation Plan and Timetable Under Bi-level Nested Decisions

LIN Boliang*, LI Xiang   

  1. School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China
  • Received:2026-01-30 Revised:2026-04-21 Accepted:2026-04-23 Online:2026-06-25 Published:2026-06-23
  • Supported by:
    Science and Technology Research and Development Key Program of China Railway (N2024X033(JB)); National Natural Science Foundation of China (U2268207)。

摘要: 列车编组计划确定的列车开行方案是优化运行图的主要依据之一,货物列车运行线接续的优劣又影响到编组计划优化,但传统编组计划研究中普遍未考虑此类相互影响。为实现两者的综合优化,本文构建具有嵌套结构的双层规划模型。上层规划以货物列车的平均旅行时间成本为干扰函数,建立体现运行图质量的编组计划优化模型;依据上层给出的货物列车开行方案,下层运行图优化模型确定货物列车的到发时刻。为适配模型结构,设计基于模拟退火的嵌套求解算法,通过上下层嵌套求解和旅行时间反馈形成迭代。以包含20个车站的铁路线路为对象,设置定线列车数量不同的算例进行方法验证。结果表明,所提方法较先获得最优编组计划,后铺画运行线的独立方法具有更低的总成本,各算例的总成本降幅范围为4.11%~5.59%,并保持相对较高的计算效率。在含36列定线列车的典型算例中,综合方法得到的总成本为89 197.85车小时,较独立方法降低约5.38%,其中编组计划相关成本增加约5.62%,列车旅行时间成本降低约11.41%。

关键词: 铁路运输, 综合优化, 双层嵌套决策, 列车编组计划, 列车运行图, 旅行时间成本

Abstract: The train operation scheme determined by the train formation plan serves as a primary basis for timetable optimization. The quality of freight train path connections also affects the optimization of train formation plan. However, this interaction is usually ignored in traditional studies on formation plan. To achieve the integrated optimization of formation plan and timetable, this study develops a bi-level programming model with a nested structure. The upper-level model optimizes the formation plan and incorporates the average travel time cost of freight trains as a disturbance function to reflect timetable quality. Based on the operation scheme provided by the upper-level, the lower-level model determines the departure and arrival times of freight trains. To adapt to the model structure, a nested optimization algorithm based on simulated annealing is designed, where iterative optimization is achieved through the nested solution of two levels and travel time feedback. Case studies with different numbers of fixed-path trains are conducted on a railway line with 20 stations to validate the proposed method. The results show that, compared with the independent method that first obtains the optimal train formation plan and then arranges the train paths, the proposed method achieves a lower total cost, with the reductions ranging from 4.11% to 5.59% across all cases, while maintaining a relatively high computational efficiency. In a representative case with 36 fixed-path trains, the integrated method yields a total cost of 89 197.85 car-hours, which is about 5.38% lower than that of the independent method, with the costs of train formation plan increasing by about 5.62% and the cost of train travel time decreasing by about 11.41%.

Key words: railway transportation, integrated optimization, bi-level nested decision, train formation plan, train timetable, travel time cost

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