高速铁路固定和灵活模式列车开行方案鲁棒优化OA

High speed railway passenger flow demand exhibits significant long-term cyclical fluctuations and uncertainty,and traditional fixed train line planning is prone to cause insufficient peak capacity and wasteful resource allocation during peak periods.To address this issue,a"fixed+flexible"train operation mode was proposed.In this mode,fixed trains maintained consistent train line planning throughout the planning period to guarantee basic passenger demand,while flexible trains were adjusted based on daily passenger flow variations to accommodate demand fluctuations.With the objectives of minimizing train operation costs,passenger travel time,and seat supply-demand deviation,a two-stage distributed robust optimization model was constructed considering basic constraints such as total passenger demand constraints and train capacity constraints,as well as fixed train consistency constraints and robustness constraints.By introducing the L∞ norm ambiguity set,the original model was dually transformed into a mixed integer linear programming model and was solved using GUROBI.The case results of Bijingbei-Hohhotdong section show that the optimal global solution is achieved when 32 fixed train services are operated daily under the"fixed+flexible"mode.Compared with the fully fixed mode and the fully flexible mode,the comprehensive costs are reduced by 4.475%and 1.764%,respectively,and the seat supply-demand deviation of the robust model is decreased by 26.414%compared to the stochastic programming model.It provides theoretical support for the optimization of train line planning under long-term dynamic demand of high speed railways.