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Equilibrium in Multi-criteria Transportation Networks

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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.

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Acknowledgments

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.01-2013.10.

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Authors and Affiliations

  1. LMA, Avignon University, Avignon, France

    Dinh The Luc

  2. Center for Information and Computing, VAST, Hanoi, Vietnam

    Dinh The Luc

  3. Quy Nhon University, Quy Nhon, Vietnam

    Truong Thi Thanh Phuong

Authors
  1. Dinh The Luc
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  2. Truong Thi Thanh Phuong
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Correspondence to Dinh The Luc.

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Luc, D.T., Phuong, T.T.T. Equilibrium in Multi-criteria Transportation Networks. J Optim Theory Appl 169, 116–147 (2016). https://doi.org/10.1007/s10957-016-0876-3

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  • DOI: https://doi.org/10.1007/s10957-016-0876-3

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