基于多维网络的增开列车条件下高速铁路列车运行图调整

研究增开列车条件下高速铁路列车运行图的调整问题,并综合考虑列车车站进路的影响。通过构建Time-Station-Track三维时空扩展网络,刻画列车对铁路时空资源的占用。将原多目标优化问题转化为求解列车占用网络弧段最小费用单目标问题,并构建基于Time-Station-Track网络的0-1整数规划模型。针对模型特点,设计拉格朗日松弛算法,将问题进一步分解为求解单列车网络最短路径子问题,由于问题被松弛后求得的解可能不可行。因此,提出基于列车优先序列的启发式策略对对偶解进行可行化。最后以宝兰客运专线为例,验证模型的正确性和算法的可行性。

Train Timetable Rescheduling Based on a Time-Station-Track Multi-dimensional Network under Condition of Running Extra Trains for High-speed Railway

This paper focused on the adjustment of the train timetable under the condition of running extra trains and synthetically considered the effect of train route at stations.A Time-Station-Track multi-dimensional network was constructed to portray the occupancy of railway time-space resources by trains.According to the network characteristics,the original multi-objective programming problem was converted to a single objective optimization problem computing the train minimum cost in the network.A 0-1 integer linear programming model was established based on the multi-dimension network.A Lagrangian relaxation algorithm was designed to relax the complex and difficult constraints in the proposed mathematical model and further decompose the studied problem into a set of sub-problems of the train shortest path in the constructed network.Considering the probable infeasibility of the solution to the relaxed problem,a heuristic strategy based on train priority sequence was proposed to obtain the feasible upper bound of Lagrangian relaxation algorithm.The effectiveness and correctness of proposed model and algorithm were further examined through numerical experiments of real-world high-speed railway train timetable test cases.