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基于多节拍组合的城际铁路列车运行图优化

周文梁 李鹏 田俊丽 邓连波

周文梁, 李鹏, 田俊丽, 邓连波. 基于多节拍组合的城际铁路列车运行图优化[J]. 西南交通大学学报, 2019, 54(4): 831-839. doi: 10.3969/j.issn.0258-2724.20170153
引用本文: 周文梁, 李鹏, 田俊丽, 邓连波. 基于多节拍组合的城际铁路列车运行图优化[J]. 西南交通大学学报, 2019, 54(4): 831-839. doi: 10.3969/j.issn.0258-2724.20170153
ZHOU Wenliang, LI Peng, TIAN Junli, DENG Lianbo. Optimization of Train Timetable for Intercity Railway Based on Coordinated Operation of Multi-periodic Trains[J]. Journal of Southwest Jiaotong University, 2019, 54(4): 831-839. doi: 10.3969/j.issn.0258-2724.20170153
Citation: ZHOU Wenliang, LI Peng, TIAN Junli, DENG Lianbo. Optimization of Train Timetable for Intercity Railway Based on Coordinated Operation of Multi-periodic Trains[J]. Journal of Southwest Jiaotong University, 2019, 54(4): 831-839. doi: 10.3969/j.issn.0258-2724.20170153

基于多节拍组合的城际铁路列车运行图优化

doi: 10.3969/j.issn.0258-2724.20170153
基金项目: 国家自然科学基金资助项目(71871226,71401182,71471179);湖南省自然科学基金资助项目(2018JJ3698)
详细信息
    作者简介:

    周文梁(1982—),男,副教授,博士,研究方向为轨道交通运营组织优化,E-mail:zwl_0631@csu.edu.cn

  • 中图分类号: U292.4

Optimization of Train Timetable for Intercity Railway Based on Coordinated Operation of Multi-periodic Trains

  • 摘要: 为了使得城际铁路列车车站到发时刻既能具有严格等时间间隔的周期性规律,又能灵活适应城际铁路客流需求的时间分布,首先提出了列车多节拍组合运行组织模式,并将其与单节拍、非节拍运行组织模式进行特征对比分析. 进而基于列车多节拍组合运行模式,以最小化所有节拍单元列车总旅行时间为优化目标,以同节拍单元列车等时间间隔运行、各类作业安全时间间隔要求等为约束,构建了城际铁路列车多节拍协同运行图优化模型. 在通过确定模型中复杂约束、引入拉格朗日乘子将其松弛的基础上,结合次梯度法设计基于拉格朗日松弛的优化算法求解模型. 以京津城际为背景的算例优化获得由4个节拍列车组合的列车运行图,其中各节拍列车分别以17、34、34、35 min等时间间隔周期性运行,该方案目标函数与其最优下界的相对差距仅为2.55%.

     

  • 图 1  4种列车运行组织模式示意

    Figure 1.  Four organization modes for train operation

    图 2  目标函数上界与下界值随着迭代次数增加的变化关系

    Figure 2.  Variations of the lower and upper bounds of the objective function with the increase of iterations

    表  1  各节拍单元列车运行数量与停站信息

    Table  1.   Number and stops of each period-type train

    节拍单元序号运行数量起点站终点站中途停站
    111北京南天津武清
    26北京南天津亦庄、永乐
    36北京南天津永乐、武清
    45北京南天津亦庄、武清
    下载: 导出CSV

    表  2  各节拍单元列车运行时间范围

    Table  2.   Operation time range of each period-type train

    节拍单元
    序号
    首班车的始发
    时间范围
    运行时间间隔
    范围/min
    1 [07:00,07:30] [10,30]
    2 [08:00,08:30] [30,60]
    3 [07:30,08:00] [30,60]
    4 [07:30,08:00] [30,60]
    下载: 导出CSV

    表  3  各节拍单元首班车运行时刻与运行时间间隔

    Table  3.   Arrival and departure times of the first train and operation interval for each period-type

    节拍单元序号北京南站亦庄站永乐站武清站天津站运行时间间隔/min
    到时发时到时发时到时发时到时发时到时发时
    107:1607:2407:2407:3107:3107:4007:4207:5417
    208:1108:1908:2108:2808:3008:3908:3908:5134
    307:4307:5107:5107:5808:0008:0908:1108:2334
    407:5808:0608:0808:1508:1508:2408:2608:3835
    下载: 导出CSV

    表  4  基于5、10 min等的整数倍为节拍单元列车运行时间间隔的计算指标

    Table  4.   Indexes of setting train operation intervals as the multiples of five or ten minutes

    时间间隔的基数/min上界值/min下界值/min相对差距/%计算时间/s
    51 0981 0752.09654
    101 0981 0732.27452
    151 1081 0713.34384
    201 1141 0713.86356
    下载: 导出CSV
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出版历程
  • 收稿日期:  2017-03-06
  • 修回日期:  2018-03-12
  • 网络出版日期:  2019-03-04
  • 刊出日期:  2019-08-01

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