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A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method

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  • Zhang, Honggang
  • Liu, Zhiyuan
  • Wang, Jian
  • Wu, Yunchi

Abstract

This paper presents a novel flow update policy, namely the successive over relaxation (SOR) iteration method, which can be implemented in traffic assignment algorithms. Most existing solution algorithms for the user equilibrium traffic assignment problem (UE-TAP) mainly use two flow update policies: Jacobi and Gauss-Seidel iteration methods. The proposed flow update policy SOR can be a more efficient replacement. Following the path-based gradient projection (GP) algorithm, we developed a new method GP-SOR for the UE-TAP. This study first provides the complete procedure of applying the GP-SOR algorithm to solve the UE-TAP. Subsequently, a few properties of the proposed method are rigorously proven. However, empirical tests of the GP-SOR algorithm demonstrate serious oscillations and poor convergence. To cope with this problem, the Armijo Rule is employed to determine the relaxation factor, which substantially improves the convergence of GP-SOR algorithm. The preliminary numerical examples show that the GP-SOR algorithm has speedier convergence compared with the known alternatives, which is reflected by the evident reduction of the computing time and the number of iterations.

Suggested Citation

  • Zhang, Honggang & Liu, Zhiyuan & Wang, Jian & Wu, Yunchi, 2023. "A novel flow update policy in solving traffic assignment problems: Successive over relaxation iteration method," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:transe:v:174:y:2023:i:c:s1366554523000996
    DOI: 10.1016/j.tre.2023.103111
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    1. Cipriani, Ernesto & Fusco, Gaetano, 2004. "Combined signal setting design and traffic assignment problem," European Journal of Operational Research, Elsevier, vol. 155(3), pages 569-583, June.
    2. Du, Muqing & Tan, Heqing & Chen, Anthony, 2021. "A faster path-based algorithm with Barzilai-Borwein step size for solving stochastic traffic equilibrium models," European Journal of Operational Research, Elsevier, vol. 290(3), pages 982-999.
    3. Wilhelm Niethammer, 2001. "The Successive Over Relaxation Method (SOR) and Markov Chains," Annals of Operations Research, Springer, vol. 103(1), pages 351-358, March.
    4. Cheng, Qixiu & Liu, Zhiyuan & Lin, Yuqian & Zhou, Xuesong (Simon), 2021. "An s-shaped three-parameter (S3) traffic stream model with consistent car following relationship," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 246-271.
    5. Huo, Jinbiao & Liu, Zhiyuan & Chen, Jingxu & Cheng, Qixiu & Meng, Qiang, 2023. "Bayesian optimization for congestion pricing problems: A general framework and its instability," Transportation Research Part B: Methodological, Elsevier, vol. 169(C), pages 1-28.
    6. Xie, Chi, 2016. "New insights and improvements of using paired alternative segments for traffic assignmentAuthor-Name: Xie, Jun," Transportation Research Part B: Methodological, Elsevier, vol. 93(PA), pages 406-424.
    7. Zhang, Fang & Lu, Jian & Hu, Xiaojian, 2022. "Integrated path controlling and subsidy scheme for mobility and environmental management in automated transportation networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 167(C).
    8. Nie, Yu (Marco), 2010. "A class of bush-based algorithms for the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 73-89, January.
    9. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    10. Maria Mitradjieva & Per Olov Lindberg, 2013. "The Stiff Is Moving---Conjugate Direction Frank-Wolfe Methods with Applications to Traffic Assignment ," Transportation Science, INFORMS, vol. 47(2), pages 280-293, May.
    11. Torbjörn Larsson & Michael Patriksson, 1992. "Simplicial Decomposition with Disaggregated Representation for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 26(1), pages 4-17, February.
    12. Bar-Gera, Hillel, 2010. "Traffic assignment by paired alternative segments," Transportation Research Part B: Methodological, Elsevier, vol. 44(8-9), pages 1022-1046, September.
    13. Huang, Ruqing & Han, Lee D. & Huang, Zhongxiang, 2022. "A new network equilibrium flow model: User-equilibrium with quantity adjustment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 163(C).
    14. Dial, Robert B., 2006. "A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration," Transportation Research Part B: Methodological, Elsevier, vol. 40(10), pages 917-936, December.
    15. Xu, Zhandong & Xie, Jun & Liu, Xiaobo & Nie, Yu (Marco), 2020. "Hyperpath-based algorithms for the transit equilibrium assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 143(C).
    16. Yu (Marco) Nie, 2012. "A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem," Transportation Science, INFORMS, vol. 46(1), pages 27-38, February.
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