A Branch and Bound Algorithm for Choquet Optimization in Multicriteria Problems

Lucie Galand (), Patrice Perny and Olivier Spanjaard
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Lucie Galand: LIP6-UPMC

A chapter in Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, 2010, pp 355-365 from Springer

Abstract: 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.

Keywords: Multicriteria combinatorial optimization; Choquet integral; Branch and bound; Minimal spanning tree problem; Knapsack problem (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-642-04045-0_30

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DOI: 10.1007/978-3-642-04045-0_30

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