单线铁路区段开行一对摘挂列车运行图优化研究  

Train Working Diagram Optimization of Pick-up and Drop Trains in Single-track Railway Section

作　　者：梁巍 张天伟 李峰 佟璐[3] LIANG Wei;ZHANG Tianwei;LI Feng;TONG Lu(School of Traffic and Transportation,Shijiazhuang Tiedao University,Shijiazhuang 050043,Hebei,China;Department of Investment and Development,HCIG Transportation Investment Co.,Ltd.,Shijiazhuang 050051,Hebei,China;School of Traffic and Transportation,Beijing Jiaotong University,Beijing 100044,China)

机构地区：[1]石家庄铁道大学交通运输学院,河北石家庄050043 [2]河北建投交通投资有限责任公司投资发展部,河北石家庄050051 [3]北京交通大学交通运输学院,北京100044

出　　处：《铁道运输与经济》2024年第9期41-48,共8页Railway Transport and Economy

基　　金：国家自然科学基金青年基金项目(72001021)。

摘　　要：单线铁路摘挂列车运行图优化,有助于加速车辆周转和货物送达。由于顺向车流在车站等待时间确定,故列车开行时只考虑上行和下行的逆向车流。当每日开行一对摘挂列车时可采用上开口、下开口和交叉方案等3种运行图形式,使用0-1变量将其转换成1种。考虑摘挂列车交叉车站选择逻辑约束,列车在车站到达和出发时刻、停站时间、区间运行时间等运行过程约束,逆向车流在中间站停留总时间、所需货物作业时间等约束,建立以逆向车流在中间站停留车分钟之和最小为目标的非线性整数规划模型。引入大M将其非线性约束转换成线性,得到线性整数规划模型。设计6个车站算例,使用数学软件求得最优解,根据求解结果从不同角度对摘挂列车运行图优化提出建议,为运行图编制和调整提供参考。The optimization of the train working diagram of pick-up and drop trains in single-track railway sections is conducive to vehicle turnover and freight delivery.As the dwelling time of forward wagon flows is fixed,only reverse flows in up and down directions are taken into consideration when discussing the train operation.Three train working diagrams of upper opening,lower opening,and crossing can be applied when running a couple of pick-up and drop trains every day,and 0-1 variables were proposed to convert these 3 plans into a single scheme.Considering the selection logic constraints of pick-up and drop train crossing stations,train operation process constraints such as arrival and departure time,dwelling time at the station and running time between the adjacent stations,and other constraints including the total staying time of reverse wagon flow in the stations and the required cargo operation time,a nonlinear integer programming model was established with minimizing the staying minutes at the stations of the reverse wagon flow as the goal.Large M was introduced to convert its nonlinear constraints into linear ones to produce a linear integer programming model.Optimal solutions to certain examples were obtained by using mathematical software,and these solutions can help put forward suggestions for the optimization of train working diagrams of pick-up and drop trains from different perspectives and provide a reference for the determination of adjustment of the diagrams.

关 键 词：铁路运输 摘挂列车 列车运行图 单线铁路 整数规划模型 

分 类 号：U292.4[交通运输工程—交通运输规划与管理]