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考虑客流需求的高速铁路列车运行图加线模型与算法

赵天胤 张永祥 王蔚 彭其渊 郭经纬

赵天胤, 张永祥, 王蔚, 彭其渊, 郭经纬. 考虑客流需求的高速铁路列车运行图加线模型与算法[J]. 西南交通大学学报, 2025, 60(3): 741-751. doi: 10.3969/j.issn.0258-2724.20240637
引用本文: 赵天胤, 张永祥, 王蔚, 彭其渊, 郭经纬. 考虑客流需求的高速铁路列车运行图加线模型与算法[J]. 西南交通大学学报, 2025, 60(3): 741-751. doi: 10.3969/j.issn.0258-2724.20240637
ZHAO Tianyin, ZHANG Yongxiang, WANG Wei, PENG Qiyuan, GUO Jingwei. Optimization Model and Algorithm of Additional Trains Scheduling in High-Speed Railway Timetables Considering Passenger Demand[J]. Journal of Southwest Jiaotong University, 2025, 60(3): 741-751. doi: 10.3969/j.issn.0258-2724.20240637
Citation: ZHAO Tianyin, ZHANG Yongxiang, WANG Wei, PENG Qiyuan, GUO Jingwei. Optimization Model and Algorithm of Additional Trains Scheduling in High-Speed Railway Timetables Considering Passenger Demand[J]. Journal of Southwest Jiaotong University, 2025, 60(3): 741-751. doi: 10.3969/j.issn.0258-2724.20240637

考虑客流需求的高速铁路列车运行图加线模型与算法

doi: 10.3969/j.issn.0258-2724.20240637
基金项目: 国家重点研发计划(2022YFB4300502);国家自然科学基金项目(72201218); 四川省科技计划(2025YFHZ0125,2023NSFSC0901)
详细信息
    作者简介:

    赵天胤(1997—),男,博士研究生,研究方向为运输组织优化理论与方法,E-mail:zhaotianyin@my.swjtu.edu.cn

    通讯作者:

    王蔚(1982—),男,副研究员,博士,研究方向为轨道交通运输组织仿真及优化,E-mail:ww@swjtu.edu.cn

  • 中图分类号: U292.62

Optimization Model and Algorithm of Additional Trains Scheduling in High-Speed Railway Timetables Considering Passenger Demand

  • 摘要:

    在既有列车运行图中插入新增列车运行线是铁路运输企业编制每季度列车运行图和日计划中列车运行计划所常采用的方法. 然而,传统基于人工的编制手段效率低且难以保证列车运行图编制质量. 对此,本文以降低铁路运营和调度成本以及运输尽可能多的旅客等为优化目标,基于离散时空网络构建综合优化列车开行方案和新增列车运行线的整数线性规划模型;针对模型特点,设计基于拉格朗日松弛的启发式求解算法,将原问题分解为列车开行方案优化子问题和一组为单列列车搜索费用最小的时空路径子问题;最后,以京沪高速铁路为算例,验证模型的正确性和算法可行性. 研究结果表明:所提方法能快速自动生成新增列车运行线后的列车运行图,且求得的上界解质量相比顺序求解方法平均提升了4.58%.

     

  • 图 1  在既有列车运行图中编制新增列车运行线示例

    Figure 1.  Illustration of scheduling additional trains into an original train timetable

    图 2  不同调整策略条件下的新增列车运行线方案

    Figure 2.  Additional train scheduling results based on different adjustment measures

    图 3  京沪高速铁路详细信息及开行的列车运行区间

    Figure 3.  Detailed information and train operation sections of Beijing–Shanghai High-Speed Railway

    图 4  求解场景9时算法迭代过程收敛曲线

    Figure 4.  Convergence curves of algorithm’s iterative process for solving Scenario 9

    图 5  求解场景1生成的列车运行图

    Figure 5.  Train timetable generated for Scenario 1

    表  1  时空弧费用

    Table  1.   Spatio-temporal arc costs

    列车种类 弧类型 弧费用
    既有列车始发弧$ {\beta _1} (\hat t - t + | {t - o_{{\mathrm{dep}},k}} |) $
    运行弧$ {\beta _1} (\hat t - t) $
    终到弧$ {\beta _1} (\hat t - t + | {\hat t - o_{{\mathrm{arr}},k}} |) $
    新增列车所有弧$ {\beta _2} (\hat t - t) $
    下载: 导出CSV

    表  2  各场景求解结果及求解质量指标

    Table  2.   Solution results and solution quality metrics for each scenario

    对照参数 场景编号 参数设置 顺序求解方法 基于拉格朗日松弛的求解算法
    下界解值 上界解值 计算时间/s egap/% 下界解值 上界解值 计算时间/s egap/% Impr/%
    始发时间
    窗长度
    1 7706.15 7976.93 678 3.51 7336.65 7532.89 1174 2.67 5.89
    2 40 min 7705.63 8037.93 678 4.31 7335.56 7664.90 1219 4.49 4.87
    3 50 min 7706.35 7975.68 775 3.49 7336.60 7612.91 1069 3.77 4.77
    客流需求 4 115270 5633.86 5806.79 614 3.07 5262.99 5491.79 1016 4.35 5.74
    5 155958 9952.70 10142.33 603 1.91 9571.84 9902.13 2534 3.45 2.43
    备选停站
    方案数量
    6 短途 7868.33 8054.41 619 1.96 7473.63 7732.41 777 3.46 4.16
    7 均匀 7617.67 7834.25 568 2.84 7256.33 7436.75 1520 2.49 5.35
    运行区间 8 2 个 9076.02 9254.05 591 2.36 8707.45 8857.30 1190 1.72 4.48
    9 4 个 8603.21 8741.14 813 2.76 8232.49 8439.19 869 2.51 3.58
    下载: 导出CSV
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出版历程
  • 收稿日期:  2024-12-02
  • 修回日期:  2025-01-24
  • 网络出版日期:  2025-03-29
  • 刊出日期:  2025-02-26

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