An approach to identify solutions of interest from multi and many-objective optimization problems

Abstract

The result of a multiobjective or a many-objective optimization problem is a large set of non-dominated solutions. Once the Pareto Front (or a good approximation of it) has been found, then providing the decision maker with a smaller set of “interesting solutions” is a key step. Here, the focus is on how to select such a set of solutions of interest which, in contrast to previous approaches that relied on geometrical features, is carried out considering the decision maker’s preferences. The proposed a posteriori approach consists in assigning an interval of potential scores to every solution, where such scores depend on the decision maker’s preferences. The solutions are then compared and filtered according to their corresponding intervals, using a recently proposed possibility degree formula. Three examples, with two, three and many objectives are used to show the benefits of the proposal.