High-Speed Rail Train Timetabling Problem: A Time-Space Network Based Method with an Improved Branch-and-Price Algorithm

A time-space network based optimization method is designed for high-speed rail train timetabling problem to improve the service level of the high-speed rail. The general time-space path cost is presented which considers both the train travel time and the high-speed rail operation requirements: (1) service frequency requirement; (2) stopping plan adjustment; and (3) priority of train types. Train timetabling problem based on time-space path aims to minimize the total general time-space path cost of all trains. An improved branch-and-price algorithm is applied to solve the large scale integer programming problem. When dealing with the algorithm, a rapid branching and node selection for branch-and-price tree and a heuristic train time-space path generation for column generation are adopted to speed up the algorithm computation time. The computational results of a set of experiments on China’s high-speed rail system are presented with the discussions about the model validation, the effectiveness of the general time-space path cost, and the improved branch-and-price algorithm.