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A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems

In: Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems

Author

Listed:
  • Lucie Galand

    (LIP6-UPMC)

  • Patrice Perny
  • Olivier Spanjaard

Abstract

This paper is devoted to the search for Choquet-optimal solutions in multicriteria combinatorial optimization with application to spanning tree problems and knapsack problems. After recalling basic notions concerning the use of Choquet integrals for preference aggregation, we present a condition (named preference for interior points) that characterizes preferences favoring well-balanced solutions, a natural attitude in multicriteria optimization. When using a Choquet integral as preference model, this condition amounts to choosing a submodular (resp. supermodular) capacity when criteria have to be minimized (resp. maximized). Under this assumption, we investigate the determination of Choquet-optimal solutions in the multicriteria spanning tree problem and the multicriteria 0-1 knapsack problem. For both problems, we introduce a linear bound for the Choquet integral, computable in polynomial time, and propose a branch and bound procedure using this bound. We provide numerical experiments that show the actual efficiency of the algorithms on various instances of different sizes.

Suggested Citation

  • Lucie Galand & Patrice Perny & Olivier Spanjaard, 2010. "A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems," Lecture Notes in Economics and Mathematical Systems, in: Matthias Ehrgott & Boris Naujoks & Theodor J. Stewart & Jyrki Wallenius (ed.), Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, pages 355-365, Springer.
    • Handle: RePEc:spr:lnechp:978-3-642-04045-0_30
    DOI: 10.1007/978-3-642-04045-0_30
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    Citations

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    Cited by:

    1. Melih Ozlen & Meral Azizoğlu & Benjamin Burton, 2013. "Optimising a nonlinear utility function in multi-objective integer programming," Journal of Global Optimization, Springer, vol. 56(1), pages 93-102, May.
    2. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.

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