Adaptive piecewise linear relaxations for enclosure computations for nonconvex multiobjective mixed-integer quadratically constrained programs

In this paper, a new method for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs 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.

Automated summary

In this paper, a new method is proposed for computing an enclosure of the nondominated set of multiobjective mixed-integer quadratically constrained programs without any convexity requirements. The method uses piecewise linear relaxations to bypass the nonconvexity of the original problem. It adaptsively chooses the level of relaxation needed in different parts of the image space. After finitely many iterations, an enclosure of the nondominated set of prescribed quality is guaranteed. The advantages of this approach are demonstrated through its application to multiobjective energy supply network problems.