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

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  • Wen-Xiang Wu
  • Hai-Jun Huang

Abstract

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.

Suggested Citation

  • Wen-Xiang Wu & Hai-Jun Huang, 2014. "A Path‐Based Gradient Projection Algorithm for the Cost‐Based System Optimum Problem in Networks with Continuously Distributed Value of Time," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:271358
    DOI: 10.1155/2014/271358
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