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Equilibrium in Multi-criteria Transportation Networks

Author

Listed:
  • Dinh The Luc

    (Avignon University
    VAST)

  • Truong Thi Thanh Phuong

    (Quy Nhon University)

Abstract

We develop a new method to generate the set of equilibrium flows of a multi-criteria transportation network. To this end, we introduce two optimization problems by using a vector version of the Heaviside step function and the distance function to Pareto minimal elements and show that the optimal solutions of these problems are exactly the equilibria of the network. We study the objective functions by establishing their generic differentiability and local calmness at equilibrium solutions. Then we present an algorithm to generate a discrete representation of equilibrium solutions by using a modified Frank–Wolfe reduced gradient method and prove its convergence. We give some numerical examples to illustrate our algorithm and show its advantage over a popular method by using linear scalarization.

Suggested Citation

  • Dinh The Luc & Truong Thi Thanh Phuong, 2016. "Equilibrium in Multi-criteria Transportation Networks," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 116-147, April.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-016-0876-3
    DOI: 10.1007/s10957-016-0876-3
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    References listed on IDEAS

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    1. Goh, C. J. & Yang, X. Q., 1999. "Vector equilibrium problem and vector optimization," European Journal of Operational Research, Elsevier, vol. 116(3), pages 615-628, August.
    2. Nagurney, Anna & Dong, June, 2002. "A multiclass, multicriteria traffic network equilibrium model with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 445-469, June.
    3. I. Konnov, 2013. "Vector network equilibrium problems with elastic demands," Journal of Global Optimization, Springer, vol. 57(2), pages 521-531, October.
    4. Li, S.J. & Teo, K.L. & Yang, X.Q., 2008. "A remark on a standard and linear vector network equilibrium problem with capacity constraints," European Journal of Operational Research, Elsevier, vol. 184(1), pages 13-23, January.
    5. S. Li & X. Yang & G. Chen, 2006. "A note on vector network equilibrium principles," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 327-334, October.
    6. G. Y. Chen & C. J. Goh & X. Q. Yang, 1999. "Vector network equilibrium problems and nonlinear scalarization methods," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 49(2), pages 239-253, April.
    7. Tan, Zhijia & Yang, Hai & Guo, Renyong, 2014. "Pareto efficiency of reliability-based traffic equilibria and risk-taking behavior of travelers," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 16-31.
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