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Journal of Applied Mathematics
Volume 2014, Article ID 271358, 9 pages
Research Article

A Path-Based Gradient Projection Algorithm for the Cost-Based System Optimum Problem in Networks with Continuously Distributed Value of Time

1Beijing Key Lab of Urban Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China
2School of Economics and Management, Beihang University, Beijing 100191, China

Received 30 November 2013; Accepted 11 February 2014; Published 20 March 2014

Academic Editor: Ching-Jong Liao

Copyright © 2014 Wen-Xiang Wu and Hai-Jun Huang. 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 cost-based system optimum problem in networks with continuously distributed value of time is formulated as a path-based form, which cannot be solved by the Frank-Wolfe algorithm. In light of magnitude improvement in the availability of computer memory in recent years, path-based algorithms have been regarded as a viable approach for traffic assignment problems with reasonably large network sizes. We develop a path-based gradient projection algorithm for solving the cost-based system optimum model, based on Goldstein-Levitin-Polyak method which has been successfully applied to solve standard user equilibrium and system optimum problems. The Sioux Falls network tested is used to verify the effectiveness of the algorithm.