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. Springer, Proceedings of the 19th International Conference on Multiple Criteria Decision Making, 634, pp.355-365, Lecture Notes in Economics and Mathematical Systems. 〈10.1007/978-3-642-04045-0_30〉. 〈hal-01294546〉

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