An investigation of the selection strategies impact on MOEDAs: CMA-ES and UMDA

Abstract

Researchers have acknowledged the importance of the selection, replacement, and archiving strategies in the behavior of evolutionary algorithms (EAs). However, these important relationships have not been deeply investigated in terms of Estimation of Distribution algorithms (EDAs). In a preliminary research, we focused on UMDA, a simple EDA that uses univariate Gaussian factorizations. Experimental results confirm that the choice of the selection method can provoke probabilistic modeling to be more effective for some classes of functions. Motivated by these results, this study is extended by evaluating several variants of selection strategies and probabilistic modeling approaches. The aim is to detect possible interactions between these two important components of evolutionary algorithms. Specifically, we use the selection strategies as defined for NSGA2, SPEA2, and IBEA algorithms, and the probabilistic models implemented as part of UMDA and CMA-ES, and a simple crossover operator (SBX). The recently introduced COCO framework comprising 55 bi-objective functions is used as the benchmark for the analysis. The results show that probabilistic modeling has an advantage over the classical genetic operator regardless of the selection method applied. Nevertheless, the results also show that some selection methods have a better performance when applied together with EDAs.