A novel framework of the alternating direction method of multipliers with application to traffic assignment problem

This paper proposes a novel algorithmic framework to enhance the convergence efficiency of the alternating direction method of multipliers (ADMM) by incorporating the successive over relaxation (SOR) splitting method. The proposed framework holds applicability across various research fields for improving convergence efficiency. Currently, there exist two main methods for decomposing the separate optimization problems: Gauss-Seidel (GS) and Jacobi methods. The SOR method introduced in this paper offers a more efficient alternative. Following the original ADMM algorithm’s framework, the authors provide a detailed procedure for incorporating the SOR method into the ADMM framework in place of the GS splitting method. This development gives rise to a new method called ADMM-SOR, and then the authors apply this newly proposed algorithm to solve the deterministic user equilibrium (DUE) problem. Subsequently, to ensure the reliability of the proposed algorithm, the authors rigorously prove its convergence by leveraging some properties of variational inequalities. Additionally, the impact of the relaxation factor on the efficiency of the ADMM-SOR method is conducted, and the authors also explore a novel method to self-adjust the relaxation factor during each iteration. The new algorithm is verified based on numerical experiments, revealing that the novel ADMM-SOR framework achieves faster convergence in comparison to the original one, all the while maintaining exceptional parallel performance.

• Record URL:
  • https://doi.org/10.1016/j.trc.2024.104843
• Record URL:
  • http://www.sciencedirect.com/science/article/pii/S0968090X24003644
• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/0968090X
• Supplemental Notes:
  • © 2024 Published by Elsevier Ltd. Abstract reprinted with permission of Elsevier.
• Authors:
  • Zhang, Honggang
  • Dong, Yu
  • 0009-0000-8689-5965
  • Xu, Xiangyang
  • Liu, Zhiyuan
  • 0000-0002-6331-0810
  • Liu, Pan
• Publication Date: 2024-12

Language

• English

Media Info

• Media Type: Web
• Features: Bibliography; References; Tables;
• Pagination: 104843
• Serial:
  • Transportation Research Part C: Emerging Technologies
  • Volume: 169
  • Issue Number: 0
  • Publisher: Elsevier
  • ISSN: 0968-090X
  • Serial URL: http://www.sciencedirect.com/science/journal/0968090X

Subject/Index Terms

• TRT Terms: Advanced traffic management systems; Optimization; Parallel processing; Traffic assignment; Traffic equilibrium; Transportation planning
• Subject Areas: Data and Information Technology; Highways; Operations and Traffic Management;

Filing Info

• Accession Number: 01931896
• Record Type: Publication
• Files: TRIS
• Created Date: Sep 25 2024 5:15PM