Indicator-based cooperative coevolution for multi-objective optimization

Abstract

Cooperative coevolutionary algorithms (CCAs) are extensions of traditional Evolutionary Algorithms (EAs) that have a lot of potential in addressing some problems on which EAs tend to perform poorly. CCAs have become an important area of research within evolutionary computation and since the cooperative coevolutionary framework was extended to multi-objective optimization, a number of approaches have been proposed incorporating it as a means for improving the performance of multi-objective EAs. The advantage of CCAs is the decomposition of the problem they use, which allows us to learn different parts of the problem instead of the whole problem at once. Cooperative coevolution has a symbiotic approach that evolves species populations (each one managing a part of the problem) which are evaluated based on how well they perform together. In order to form a solution, an individual from each species is selected and combined with the other selected individuals. The solution is then evaluated and the individuals that make up the solution are scored based on the fitness of the combined solution. The way this selection to collaborate is done is a key issue in a cooperative coevolutionary framework. However, the usual approach that has been used in Cooperative Coevolutionary Multi-objective EAs (CCMOEAs) is a method based on Pareto optimality. In this work, we present a novel collaboration formation mechanism for CCMOEAs based on the use of the hypervolume indicator. Our preliminary results confirm the impact that the collaboration mechanism has on the performance of CCMOEAs and indicate that our proposed framework clearly improves the results obtained by a CCMOEA whose selection mechanism for collaboration is based on Pareto optimality.