1.School of Traffic and Transportation, Beijing Jiaotong University;2.State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing;3.School of Management and Economics, Beijing Institute of Technology
Fundamental Research Funds for the Central Universities (2021RC241),National Natural Science Foundation of China Youth Fund (72001019),The National Science Fund for Distinguished Young Scholars(71825004),State Key Laboratory of Rail Traffic Control and Safety (Contract No. RCS2022K001), Beijing Jiaotong University
列车停站方案与列车时刻表协同优化能够克服两者单独优化难以实现系统最优的弊端, 从而可以得到旅客满意和企业期望的运营方案. 首先, 针对多场景不确定旅客需求概率分布信息已知情形, 综合考虑轨道与车站站线占用等约束, 以极小化列车总行程时间、各场景未被满足旅客需求以及列车冗余之和为目标, 构建列车停站方案与时刻表两阶段随机规划模型. 在此基础上, 进一步考虑旅客需求场景概率分布信息部分已知情形, 构建与之相对应的两阶段分布鲁棒优化模型. 其次, 借助∞ 范数非精确集, 将所构建的列车停站方案与时刻表两阶段分布鲁棒协同优化模型转换为等价的混合整数线性规划模型, 并利用Visual C++平台调用GUROBI 进行求解. 最后, 将所构建模型应用到武汉-广州高速铁路走廊上, 验证其有效性. 结果表明, 相比于随机优化模型, 分布鲁棒优化模型只需付出较小的代价, 即可抵御旅客需求概率分布不确定性带来的影响, 且可以改善最坏情形下解的质量, 为得到鲁棒性较强的铁路列车停站方案与时刻表提供一定的理论依据.
The integrated optimization of train stop planning and train timetabling problems can improve the quality of obtained solution, compared with separately optimizing these two issues, which can help to obtain the operation scheme with passenger satisfaction and enterprise expectation. With the probability distribution of passenger demands in multiple scenarios being known, a two-stage stochastic programming model for the integrated optimization of train stop plan and timetable is first developed to minimize the sum of the total travel time of trains, the number of unsatisfied passenger demands and the number of redundant services in all scenarios. On this basis, for the situation the probability distribution information of each scenario of passenger demands is partially known, a two-stage distributionally robust optimization model is developed. And for computational convenience, a ∞-norm-based ambiguity set is adopted to transform the model into a mixed integer linear programming model. Finally, a series of numerical experiments are carried out on Wuhan-Guangzhou high-speed railway corridor to verify the effectiveness of the developed models, where the Visual C++ software with GUROBI solver is applied to obtain the optimized train stop plan and timetable. The results show that compared with the stochastic programming model, the distributionally robust optimization model can resist the uncertainty of probability distribution with only few cost and improve the solution in the worst case, and has certain reference value for generating more robust train stop plan and timetable.