Collaborative Optimization for Overnight Train Operation and Maintenance Window Setting of High-Speed Railways
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摘要: 高速铁路夕发朝至列车开行与天窗设置存在动态影响关系,将两者进行协同优化有助于满足旅客夜间出行需求,提升铁路运力资源配置. 以通道型高速铁路为对象,在分析高速铁路夕发朝至列车与天窗设置影响关系的基础上,以高速铁路夕发朝至列车总的旅行时间最少和高速铁路夕发朝至列车的开行对既有列车运行图的影响最小为目标,建立了列车开行模式未定情形下高速铁路夕发朝至列车与天窗协同优化的非线性混合整数规划模型. 结合问题特性,提出了双目标转换和约束线性化处理等模型约简策略,设计了基于自适应大邻域搜索的启发式求解算法. 最后,以京广高速铁路走廊为例,对模型算法的有效性进行了验证. 结果表明:算法经过40次左右迭代便可收敛至最优解,耗时784 s.Abstract: There is a coupling relationship between overnight train operation and maintenance window setting of high-speed railways. Their collaborative optimization contributes to meeting passenger travel demands at night and improves the allocation of railway transportation resources. Taking the corridor-type high-speed railways as the object, the analysis of the dynamic relationship between overnight train operation and maintenance window setting is performed, with the goal of minimizing the total travel time of all overnight trains and the impact of overnight train operation on the existing train timetable. A nonlinear mixed integer programming model is established to realize the collaborative optimization of overnight train operation and maintenance window in the condition of the undetermined train operation mode. Given the complexity of the problem, dimension reduction strategies such as dual-objective transformation and constraint linearization are proposed; then a heuristic algorithm based on the adaptive large neighborhood search is designed to solve the problem. Finally, a case study of Beijing−Guangzhou railway corridors was conducted to verify the method. The results show that the algorithm can converge to the optimal solution after about 40 iterations at a cost of 784 s.
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表 1 最优天窗方案
Table 1. Optimal maintenance window scheme
天窗分段 天窗时间 北京—石家庄 00∶00—04∶00 石家庄—郑州 00∶00—04∶00 郑州—武汉 02∶00—06∶00 武汉—长沙 02∶00—06∶00 长沙—郴州 00∶00—04∶00 郴州—广州 00∶00—04∶00 表 2 京广高铁夕发朝至列车最优解对应的到发时刻表
Table 2. Optimal arrival and departure time table of Beijing−Guangzhou high-speed railways
车次 北京西 石家庄 郑州东 武汉 长沙南 郴州西 广州南 D901 19∶02 20∶12/20∶15 21∶51/21∶51 00∶01/00∶01 01∶30/01∶30 04∶00/04∶00 05∶35 D902 05∶19 04∶07/04∶10 01∶30/01∶30 23∶18/23∶18 21∶51/21∶51 20∶31/20∶31 19∶00 D903 19∶07 20∶17/20∶20 22∶01/22∶06 00∶06/00∶06 01∶35/01∶35 04∶05/04∶05 05∶40 D904 05∶24 04∶12/04∶15 01∶35/01∶35 23∶23/23∶23 21∶56/22∶02 20∶36/20∶36 19∶05 D909 19∶12 20∶22/20∶25 21∶01/21∶06 00∶11/00∶11 01∶40/01∶40 04∶10/04∶10 06∶34 D910 05∶29 04∶17/04∶22 01∶40/01∶40 23∶28/23∶28 22∶01/22∶07 20∶41/20∶41 19∶10 D921 19∶17 20∶27/20∶30 22∶06/22∶11 00∶16/00∶16 01∶45/01∶45 04∶15/04∶15 06∶39 D922 06∶10 04∶32/04∶35 01∶45/01∶45 23∶33/23∶33 22∶12/22∶12 20∶46/20∶46 19∶15 D923 19∶22 20∶32/20∶35 22∶11/22∶16 00∶21/00∶21 01∶50/01∶50 04∶20/04∶20 06∶55 D924 06∶15 04∶37/04∶40 01∶50/01∶50 23∶38/23∶38 22∶17/22∶23 20∶51/20∶51 19∶20 D927 19∶27 20∶37/20∶40 22∶16/22∶21 00∶26/00∶26 01∶55/01∶55 04∶25/04∶25 07∶00 D928 06∶51 04∶42/04∶45 01∶55/01∶55 23∶43/23∶43 22∶28/22∶34 20∶57/20∶57 19∶25 D939 19∶32 20∶42/20∶45 22∶21/22∶26 00∶31/00∶31 02∶00/02∶00 04∶30/04∶30 07∶05 D940 06∶56 04∶50/04∶50 02∶00/02∶00 23∶48/23∶48 22∶33/22∶39 21∶02/21∶02 19∶30 表 3 不同列车开行模式下的目标函数值
Table 3. Objective function values under different overnight train operation modes
列车开行模式 f1/min f2/列 计算时间/s 等线模式 9482 76/0 141 下线模式 9780 38/41 187 下线-上线模式 9360 45/32 432 混合模式 9240 43/38 784 -
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