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Exact Methods for Computing All Lorenz Optimal Solutions to Biobjective Problems

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Algorithmic Decision Theory (ADT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9346))

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Abstract

This paper deals with biobjective combinatorial optimization problems where both objectives are required to be well-balanced. Lorenz dominance is a refinement of the Pareto dominance that has been proposed in economics to measure the inequalities in income distributions. We consider in this work the problem of computing the Lorenz optimal solutions to combinatorial optimization problems where solutions are evaluated by a two-component vector. This setting can encompass fair optimization or robust optimization. The computation of Lorenz optimal solutions in biobjective combinatorial optimization is however challenging (it has been shown intractable and NP-hard on certain problems). Nevertheless, to our knowledge, very few works address this problem. We propose thus in this work new methods to generate Lorenz optimal solutions. More precisely, we consider the adaptation of the well-known two-phase method proposed in biobjective optimization for computing Pareto optimal solutions to the direct computing of Lorenz optimal solutions. We show that some properties of the Lorenz dominance can provide a more efficient variant of the two-phase method. The results of the new method are compared to state-of-the-art methods on various biobjective combinatorial optimization problems and we show that the new method is more efficient in a majority of cases.

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Authors and Affiliations

  1. PSL, Université Paris-Dauphine LAMSADE, CNRS UMR 7243, 75775, Paris Cedex 16, France

    Lucie Galand

  2. Sorbonne Universités, UPMC Université Paris 06, CNRS, LIP6, UMR 7606, 75005, Paris, France

    Thibaut Lust

Authors
  1. Lucie Galand
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  2. Thibaut Lust
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Correspondence to Thibaut Lust .

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Editors and Affiliations

  1. University of New South Wales, Kensington, Australia

    Toby Walsh

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Galand, L., Lust, T. (2015). Exact Methods for Computing All Lorenz Optimal Solutions to Biobjective Problems. In: Walsh, T. (eds) Algorithmic Decision Theory. ADT 2015. Lecture Notes in Computer Science(), vol 9346. Springer, Cham. https://doi.org/10.1007/978-3-319-23114-3_19

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  • DOI: https://doi.org/10.1007/978-3-319-23114-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23113-6

  • Online ISBN: 978-3-319-23114-3

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