box enclosure – Optimization Online

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

Published: 2024/08/14

(Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization adaptive refinement, box enclosure, Mixed-integer nonlinear optimization, multi-objective optimization, nonconvex optimization

In this work, we present an algorithm for computing an enclosure for 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 … Read more

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

Published: 2022/07/11

Moritz Link

Stefan Volkwein

(Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Network Optimization adaptive piecewise linear relaxation, box enclosure, energy supply networks, mixed-integer nonlinear programming, multiobjective optimization

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 … Read more

A solver for multiobjective mixed-integer convex and nonconvex optimization

Published: 2022/02/11, Updated: 2023/07/27

Gabriele Eichfelder

Oliver Stein

Leo Warnow

(Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization box enclosure, Branch-and-Bound, branch-and-cut, mixed integer optimization, multiobjective optimization, nonconvex optimization

This paper proposes a general framework for solving multiobjective nonconvex optimization problems, i.e., optimization problems in which multiple objective functions have to be optimized simultaneously. Thereby, the nonconvexity might come from the objective or constraint functions, or from integrality conditions for some of the variables. In particular, multiobjective mixed-integer convex and nonconvex optimization problems are … Read more