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A branch and bound algorithm for Choquet optimization in multicriteria problems

Lucie Galand 1 Patrice Perny 1 Olivier Spanjaard 1
1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
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.
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Lucie Galand, Patrice Perny, Olivier Spanjaard. A branch and bound algorithm for Choquet optimization in multicriteria problems. The 19th International Conference on Multiple Criteria Decision Making, Jan 2008, Auckland, New Zealand. pp.355-365, ⟨10.1007/978-3-642-04045-0_30⟩. ⟨hal-01294546⟩

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