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On the dual approach to the traffic assignment problem

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  • Fukushima, Masao

Abstract

This paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of its dual problem. It is shown that the dual problem can be formulated as a nonsmooth convex optimization problem of which the objective function values and subgradients are conveniently calculated by solving shortest path problems associated with the transportation network. A subgradient algorithm to solve the dual problem is presented and limited computational experience is reported. The computational results are encouraging enough to demonstrate the effectiveness of the proposed approach.

Suggested Citation

  • Fukushima, Masao, 1984. "On the dual approach to the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 18(3), pages 235-245, June.
  • Handle: RePEc:eee:transb:v:18:y:1984:i:3:p:235-245
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    Cited by:

    1. Frédéric Babonneau & Jean-Philippe Vial, 2008. "An Efficient Method to Compute Traffic Assignment Problems with Elastic Demands," Transportation Science, INFORMS, vol. 42(2), pages 249-260, May.
    2. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Phase transitions of the price-of-anarchy function in multi-commodity routing games," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    3. Kraft, Edwin R., 2002. "Scheduling railway freight delivery appointments using a bid price approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(2), pages 145-165, February.
    4. Leurent, Fabien M., 1997. "Curbing the computational difficulty of the logit equilibrium assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 31(4), pages 315-326, August.
    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. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    7. Xie, Chi & Travis Waller, S., 2012. "Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1023-1042.
    8. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Monotonicity of equilibria in nonatomic congestion games," European Journal of Operational Research, Elsevier, vol. 316(2), pages 754-766.

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