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On the computation of all supported efficient solutions in multi-objective integer network flow problems

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  • Eusébio, Augusto
  • Figueira, José Rui

Abstract

This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets.

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  • Eusébio, Augusto & Figueira, José Rui, 2009. "On the computation of all supported efficient solutions in multi-objective integer network flow problems," European Journal of Operational Research, Elsevier, vol. 199(1), pages 68-76, November.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:68-76
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    References listed on IDEAS

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    7. Hamacher, Horst W. & Pedersen, Christian Roed & Ruzika, Stefan, 2007. "Multiple objective minimum cost flow problems: A review," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1404-1422, February.
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    Cited by:

    1. Hela Masri & Saoussen Krichen, 2018. "Exact and approximate approaches for the Pareto front generation of the single path multicommodity flow problem," Annals of Operations Research, Springer, vol. 267(1), pages 353-377, August.
    2. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.

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