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An alternating direction method of multipliers for solving user equilibrium problem

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  • Liu, Zhiyuan
  • Chen, Xinyuan
  • Hu, Jintao
  • Wang, Shuaian
  • Zhang, Kai
  • Zhang, Honggang

Abstract

This paper introduces a new parallel computing algorithm to address the user equilibrium (UE) problem. Searching for efficient solution algorithms for UE has been a recurring study subject in transportation research and has attracted much attention in past decades. Existing solution algorithms can be classified into three categories: link-based, path-based, and origin-based. This paper introduces an alternating direction method of multipliers (ADMM) algorithm that is different from these categories. Based on the origin-based formulation of UE problem, an equivalent problem is proposed which eliminates the flow conservation conditions through the augmented Lagrangian function. In order to make use of the ADMM, the network links should be grouped into different blocks, where the links in the same block are disconnected. This link grouping problem falls into the category of edge-coloring problem in graph theory, and it follows the Vizing theorem. A novel approach is developed for the link grouping problem. For links in the same block, we have a separable subproblem, which is solved in parallel by the gradient projection algorithm. Numerical experiments are conducted to validate the proposed algorithm, which shows its computation efficiency.

Suggested Citation

  • Liu, Zhiyuan & Chen, Xinyuan & Hu, Jintao & Wang, Shuaian & Zhang, Kai & Zhang, Honggang, 2023. "An alternating direction method of multipliers for solving user equilibrium problem," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1072-1084.
    • Handle: RePEc:eee:ejores:v:310:y:2023:i:3:p:1072-1084
    DOI: 10.1016/j.ejor.2023.04.008
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    References listed on IDEAS

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    Cited by:

    1. Liu, Zhiyuan & Zhang, Honggang & Zhang, Kai & Zhou, Zihan, 2023. "Integrating alternating direction method of multipliers and bush for solving the traffic assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    2. Cheng, Qixiu & Lin, Yuqian & Zhou, Xuesong (Simon) & Liu, Zhiyuan, 2024. "Analytical formulation for explaining the variations in traffic states: A fundamental diagram modeling perspective with stochastic parameters," European Journal of Operational Research, Elsevier, vol. 312(1), pages 182-197.

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