An adaptive relaxation-refinement scheme for multi-objective mixed-integer nonconvex optimization

Abstract In this work, we present an algorithm for computing an enclosure of the nondominated set of multi-objective mixed-integer nonconvex optimization problems. In contrast to existing solvers for this type of problem, this algorithm is not based on a branch-and-bound scheme but rather relies on a relax-and-refine approach. While this is an established technique in single-objective optimization, several adaptions to the multi-objective setting have to be made in order to exploit the full potential of this idea. To that end, we propose an intensified individualization of the relaxations to the respective parts in the image space resulting in a novel adaptive box-based relaxation technique for nonconvex terms. We provide numerical tests for the new algorithm that show both its strengths and limitations.