Multiobjective optimization is a central problem in a wide range of contexts, such as multi-agent optimization and multicriteria decision support or decision under risk and uncertainty. The presence of several objectives leads to multiple non-dominated solutions and requires the use of a sophisticated decision model allowing various attitudes towards preference aggregation. The Choquet Integral is one of the most expressive parameterized models introduced in decision theory to scalarize performance vectors and support decision making. However, its use in optimization contexts raises computational issues. This paper proposes new computational models based on mathematical programming to optimize the Choquet integral on implicit sets. A new linearization of the Choquet integral exploiting the vertices of the core of the convex capacity is proposed, combined with a constraint generation algorithm. Then the computational model is extended to the bipolar Choquet Integral to allow asymmetric aggregation with respect to a specific reference point.
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