Choquet optimal set in biobjective combinatorial optimization

Thibaut Lust 1 Antoine Rolland
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We study in this paper the generation of the Choquet optimal solutions of biobjective combinatorial optimization problems. Choquet optimal solutions are solutions that optimize a Choquet integral. The Choquet integral is used as an aggregation function, presenting different parameters, and allowing to take into account the interactions between the objectives. We develop a new property that characterizes the Choquet optimal solutions. From this property, a general method to easily generate these solutions in the case of two objectives is defined. We apply the method to two classical biobjective optimization combinatorial optimization problems: the biobjective knapsack problem and the biobjective minimum spanning tree problem. We show that Choquet optimal solutions that are not weighted sum optimal solutions represent only a small proportion of the Choquet optimal solutions and are located in a specific area of the objective space, but are much harder to compute than weighted sum optimal solutions.
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Thibaut Lust, Antoine Rolland. Choquet optimal set in biobjective combinatorial optimization. Computers and Operations Research, Elsevier, 2013, 40 (10), pp.2260-2269. ⟨10.1016/j.cor.2013.04.003⟩. ⟨hal-01170501⟩



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