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The knapsack problem (KP) and its multidimensional version (MKP) are basic problems in combinatorial optimization. In this paper we consider their multiobjective extension (MOKP and MOMKP), for which the aim is to obtain or to approximate the set of efficient solutions. In a first step, we classify and describe briefly the existing works, that are… (More)

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 dierent parameters, and allowing to take into account the interactions between the objectives.… (More)

We study in this paper the computation of Choquet optimal solutions in decision contexts involving multiple criteria or multiple agents. Choquet optimal solutions are solutions that optimize a Choquet integral, one of the most powerful tools in multicriteria decision making. We develop a new property that characterizes the Choquet optimal solutions. From… (More)

We consider the following problem: to decompose a nonnegative integer matrix into a linear combination of binary matrices that respect the consecutive ones property. This problem occurs in the radiotherapy treatment of cancer. The nonnegative integer matrix corresponds to fields giving the different radiation beams that a linear accelerator has to send… (More)