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Adaptation of a Modified Newton Method for Solving the Asymmetric Traffic Equilibrium Problem

Author

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  • Patrice Marcotte

    (Université de Montréal, Montréal, Quebec, Canada)

  • Jacques Guélat

    (Université de Montréal, Montréal, Quebec, Canada)

Abstract

In this paper a restriction (simplicial decomposition) strategy is employed to efficiently implement a modified Newton method to solve the general asymmetric network equilibrium problem. Implementation details are discussed. Numerical results on one small-scale and one medium-scale problem, with varying asymmetry levels, are presented. Performance of the algorithms with respect to the asymmetry level of the cost mapping is assessed.

Suggested Citation

  • Patrice Marcotte & Jacques Guélat, 1988. "Adaptation of a Modified Newton Method for Solving the Asymmetric Traffic Equilibrium Problem," Transportation Science, INFORMS, vol. 22(2), pages 112-124, May.
    • Handle: RePEc:inm:ortrsc:v:22:y:1988:i:2:p:112-124
    DOI: 10.1287/trsc.22.2.112
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    Cited by:

    1. Meneguzzer, Claudio, 1995. "An equilibrium route choice model with explicit treatment of the effect of intersections," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 329-356, October.
    2. Sullivan, Edward C. & Wong, Sun, 1989. "Development Of A Dynamic Equilibrium Assignment Procedure For Network-level Analysis Of New Technology," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt9ns859v6, Institute of Transportation Studies, UC Berkeley.
    3. García, Ricardo & Marín, Angel, 2005. "Network equilibrium with combined modes: models and solution algorithms," Transportation Research Part B: Methodological, Elsevier, vol. 39(3), pages 223-254, March.
    4. Dulce Rosas & Jordi Castro & Lídia Montero, 2009. "Using ACCPM in a simplicial decomposition algorithm for the traffic assignment problem," Computational Optimization and Applications, Springer, vol. 44(2), pages 289-313, November.
    5. Louis de Grange & Juan Carlos Muñoz, 2007. "An equivalent optimization formulation for the traffic assignment problem with asymmetric linear costs," Transportation Planning and Technology, Taylor & Francis Journals, vol. 32(1), pages 1-25, March.

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