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Mathematical Problems in Engineering
Volume 2014, Article ID 641562, 15 pages
Research Article

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

School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China

Received 6 December 2013; Revised 12 February 2014; Accepted 24 February 2014; Published 30 April 2014

Academic Editor: Gongnan Xie

Copyright © 2014 Bisheng He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.