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A Note on Bar-Gera's Algorithm for the Origin-Based Traffic Assignment Problem

Author

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  • Yu (Marco) Nie

    (Department of Civil and Environmental Engineering, Northwestern University, Evanston, Illinois 60208)

Abstract

Recently, Bar-Gera (Bar-Gera, H. 2002. Origin-based algorithm for the traffic assignment problem. Transportation Sci. 36 (4) 398--417) proposed a quasi-Newton method for the origin-based formulation of the user equilibrium traffic assignment problem. This note shows that Bar-Gera's algorithm may generate negative second-order derivative, leading to a “wrong search direction,” which compromises the overall convergence performance. We prove that this shortcoming can be overcome by approximating the second-order derivative with an upper bound. The revised algorithm not only fixes a theoretical flaw but indeed demonstrates more satisfying computational performance in numerical experiments. This note also offers a rigorous derivation of optimality conditions that synthesizes the results of the literature.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:46:y:2012:i:1:p:27-38
    DOI: 10.1287/trsc.1110.0371
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Jayakrishnan, R. & Tsai, Wei T. & Prashker, Joseph N. & Rajadhyaksha, Subodh, 1994. "A Faster Path-Based Algorithm for Traffic Assignment," University of California Transportation Center, Working Papers qt2hf4541x, University of California Transportation Center.
    5. Hillel Bar-Gera, 2002. "Origin-Based Algorithm for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 36(4), pages 398-417, November.
    6. T. Leventhal & G. Nemhauser & L. Trotter, 1973. "A Column Generation Algorithm for Optimal Traffic Assignment," Transportation Science, INFORMS, vol. 7(2), pages 168-176, May.
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    Cited by:

    1. Hong Zheng, 2015. "Adaptation of Network Simplex for the Traffic Assignment Problem," Transportation Science, INFORMS, vol. 49(3), pages 543-558, August.
    2. Chou, Chang-Chi & Chiang, Wen-Chu & Chen, Albert Y., 2022. "Emergency medical response in mass casualty incidents considering the traffic congestions in proximity on-site and hospital delays," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    3. Wang, Xiaolei & Wang, Jun & Guo, Lei & Liu, Wei & Zhang, Xiaoning, 2021. "A convex programming approach for ridesharing user equilibrium under fixed driver/rider demand," Transportation Research Part B: Methodological, Elsevier, vol. 149(C), pages 33-51.
    4. 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).
    5. 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.
    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, 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).
    8. Amirali Zarrinmehr & Mahmoud Saffarzadeh & Seyedehsan Seyedabrishami & Yu Marco Nie, 2016. "A path-based greedy algorithm for multi-objective transit routes design with elastic demand," Public Transport, Springer, vol. 8(2), pages 261-293, September.

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