Preference-guided evolutionary algorithms for optimization with many objectives

Abstract

Evolutionary Algorithms became very famous in solving multi-objective problems in the last two decades. They were mainly used to approximate the whole extension of the efficient front so a decision maker could choose a preferred solution later. However, this a posteriori way of thinking is not well suited for problems with many objectives, mainly because the number of solutions to approximate the whole front usually increases exponentially, and the decision process can get really hard. Therefore, this work proposes the inclusion of preferences during the optimization process, such that, instead of focusing on the whole Pareto front, a smaller region is considered, so the problem of choosing among many alternatives is alleviated. Two different evolutionary methods - one with the usual non-dominated sorting with Pareto-dominance and another based on indicators - are considered together with their counterparts that take preferences into account. Along with them, a new approach is also proposed here. These algorithms are compared in a benchmark of problems with many objectives, and their outcomes are measured according to convergence and the ability to find the most preferred solutions of the decision maker. The results show that the inclusion of preferences generates significant improvements in the algorithms, indicating that they should deserve more attention in this field.