Investigação de novas abordagens para otimização multiobjetivo em algoritmos evolutivos

Abstract

Relaxed forms of Pareto dominance have been shown to be the most effective way in which evolutionary algorithms can progress towards the Pareto-optimal set with a widely spread distribution of solutions. A popular concept is the epsilon-dominance technique, which has been employed as an archive update strategy in some multiobjective evolutionary algorithms (MOEA). In spite of the great usefulness of the epsilon-dominance concept, there are still difficulties in computing an appropriate value of epsilon that provides the desirable number of nondominated points. Additionally, several viable solutions may be lost depending on the hypergrid adopted, impacting the diversity of the estimate set. In order to remedy these limitations, we propose a variant of the epsilon-dominance criterion, named cone epsilon-dominance, which maintains the good convergence properties of epsilon-dominance while providing a better control over the resolution of the estimated Pareto front and improving the spread of solutions along the front. This work presents a comprehensive study of the cone epsilon-approach, comparing its performance with the epsilon-dominance and the standard Pareto relation on sixteen well-known benchmark problems. To evaluate the possible differences between these approaches, a designed statistical experiment is performed for four performance metrics, measuring both diversity and convergence to the Pareto front. The results obtained show that a steady-state cone epsilon-MOEA is able to significantly outperform the other techniques tested in terms of finding well spread Pareto-optimal solutions, with an improvement for the diversity metric of about 16% over the epsilon-MOEA and 22% over the NSGA-II, and gains of up to 71% on individual problems. Statistically significant differences are also present for the other metrics tested, but with much smaller effect sizes, strongly suggesting the cone epsilon-criterion as a dominance relation capable of maintaining the good convergence properties of the epsilon-dominance while enhancing the diversity characteristics of the solution sets found.