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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 432096, 7 pages
Research Article

A Bilevel Programming Model to Optimize Train Operation Based on Satisfaction for an Intercity Rail Line

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

Received 12 December 2013; Revised 5 January 2014; Accepted 14 January 2014; Published 20 February 2014

Academic Editor: Wuhong Wang

Copyright © 2014 Zhipeng Huang and Huimin Niu. 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 passenger travel demands for intercity rail lines fluctuate obviously during different time periods, which makes the rail departments unable to establish an even train operation scheme. This paper considers an optimization problem for train operations which respond to passenger travel demands of different periods in intercity rail lines. A satisfactory function of passenger travelling is proposed by means of analyzing the passengers’ travel choice behavior and correlative influencing factors. On this basis, the paper formulates a bilevel programming model which maximizes interests of railway enterprises and travelling satisfaction of each passenger. The trains operation in different periods can be optimized through upper layer planning of the model, while considering the passenger flow distribution problem based on the Wardrop user equilibrium principle in the lower layer planning. Then, a genetic algorithm is designed according to model features for solving the upper laying. The Frank-Wolfe algorithm is used for solving the lower layer planning. Finally, a numerical example is provided to demonstrate the application of the method proposed in this paper.