Computing an enclosure for multiobjective mixed-integer nonconvex optimization problems using piecewise linear relaxations

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer problems without any convexity requirements is presented. In fact, our criterion space method makes use of piecewise linear relaxations in order to bypass the nonconvexity of the original problem. The method chooses adaptively which level of relaxation is needed in which parts of the image space. Furthermore, it is guaranteed that after finitely many iterations an enclosure of the nondominated set of prescribed quality is returned. We demonstrate the advantages of this approach by applying it to multiobjective energy supply network problems.

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Universit├Ąt Konstanz, July, 2022

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