Multi-objective approaches in a single-objective optimization environment

Abstract

This paper presents two new approaches for transforming a single-objective problem into a multi-objective problem. These approaches add new objectives to a problem to make it multi-objective and use a multi-objective optimization approach to solve the newly defined problem. The first approach is based on relaxation of the constraints of the problem and the other is based on the addition of noise to the objective value or decision variable. Intuitively, these approaches provide more freedom to explore and a reduced likelihood of becoming trapped in local optima. We investigated the characteristics and effectiveness of the proposed approaches by comparing the performance on single-objective problems and multi-objective versions of those same problems. Through numerical examples, we showed that the multi-objective versions produced by relaxing constraints can provide good results and that using the addition of noise can obtain better solutions when the function is multimodal and separable.