Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 549374, 13 pages
Research Article

An Optimization to Schedule Train Operations with Phase-Regular Framework for Intercity Rail Lines

School of Traffic and Transportation, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 7 September 2012; Accepted 15 October 2012

Academic Editor: Wuhong Wang

Copyright © 2012 Huimin Niu and Minghui Zhang. 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.


The most important operating problem for intercity rail lines, which are characterized with the train operations at rapid speed and high frequency, is to design a service-oriented schedule with the minimum cost. This paper proposes a phase-regular scheduling method which divides a day equally into several time blocks and applies a regular train-departing interval and the same train length for each period under the period-dependent demand conditions. A nonlinear mixed zero-one programming model, which could accurately calculate the passenger waiting time and the in-train crowded cost, is developed in this study. A hybrid genetic algorithm associated with the layered crossover and mutation operation is carefully designed to solve the proposed model. Finally, the effectiveness of the proposed model and algorithm is illustrated through the application to Hefei-Wuhan intercity rail line in China.