兼顾公平和效率的地铁列车时刻表与车厢预留协同优化
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作者单位:

1.兰州交通大学 交通运输学院;2.北京交通大学 系统科学学院

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中图分类号:

U292.4+1

基金项目:

国家自然科学基金(72361020);国家铁路局课题(KF2023-047)。


Collaborative Optimization of Subway Train Timetables and Carriage Reservations Balancing Fairness and Efficiency
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Affiliation:

1.School of Traffic and Transportation,Lanzhou Jiaotong University;2.School of Systems Science,Beijing Jiaotong University

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    摘要:

    地铁高峰时段客流的大量聚集对乘客组织和运营调度造成严峻挑战,传统的均匀调度方案严重影响不同时空位置乘客出行的公平性和出行效率。为解决这一难题,本文提出一种客流过饱和状态下考虑车厢预留的列车非均衡调度策略。通过引入两组累积0-1变量,建立了动态客流需求与列车服务之间的匹配关系,并以乘客最大错过列车次数作为不同站点乘车公平性的度量指标。在此基础上,以最小化乘客总等待时间为目标,构建了面向时变客流需求的列车时刻表与车厢预留协同优化模型。为高效求解非线性混合整数规划模型,设计了基于自适应大规模邻域搜索的启发式算法,通过引入多组破坏与修复算子提升算法收敛效率,以快速获取高质量近似最优解。最后,以北京地铁大兴线为数值实验验证了模型与算法的性能及有效性。结果表明,本文提出的方法能够在较短计算时间内高效获取列车时刻表与车厢预留方案,与传统的均衡发车方案相比,乘客总等待时间下降了57.53%,乘客最大错过列车数由10列降低为1列,极大提升了乘客乘车公平性。

    Abstract:

    The bulk accumulation of subway passenger flow at stations during peak hours is considered to pose a significant challenge to passenger organization and train scheduling, while traveling efficiency and boarding fairness across different spatial and temporal dimensions are severely compromised by traditional uniform scheduling strategies. To address this thorny problem, an unbalanced train scheduling strategy with carriage reservation under oversaturated conditions is proposed to improve passenger traveling efficiency and boarding fairness. By introducing two groups of cumulative 0–1 variables, a matching relationship between dynamic passenger demand and scheduled trains is established, and boarding fairness for passengers located at different stations is measured by the maximum number of trains missed by each passenger. A collaborative optimization model for train scheduling and carriage reservation is developed to minimize total passenger waiting time under time-dependent passenger demand. To efficiently solve the nonlinear mixed-integer programming model, a heuristic algorithm based on adaptive large neighborhood search is developed to obtain near-optimal solutions efficiently, in which several effective destroy and repair operators are designed to accelerate algorithm convergence. Finally, numerical experiments are conducted based on the Beijing Subway Daxing Line to verify the performance and effectiveness of the proposed model and algorithm. The experimental results indicate that high-quality train timetables and carriage reservation plans can be effectively obtained within a short computing time using the proposed method. Compared with the traditional even-headway schedule, total passenger waiting time is reduced by 57.53%, and the maximum number of missed trains per passenger is decreased from 10 to 1, thereby significantly improving boarding fairness.

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高如虎,曹书瑞,崔琦平,等. 兼顾公平和效率的地铁列车时刻表与车厢预留协同优化[J]. 科学技术与工程, , ():

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历史
  • 收稿日期:2026-03-25
  • 最后修改日期:2026-06-08
  • 录用日期:2026-07-31
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