基于两阶段分布鲁棒优化的列车停站方案与时刻表协同研究

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 that 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 L_∞-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 the Wuhan-Guangzhou high-speed railway corridor to verify the effectiveness of the developed models, where the Visual C++ software with the 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.