Multi-objective Optimization with the Naive $$ \mathbb{M} $$ ID $$ \mathbb{E} $$ A

Abstract

EDAs have been shown to perform well on a wide variety of single-objective optimization problems, for binary and real-valued variables. In this chapter we look into the extension of the EDA paradigm to multi-objective optimization. To this end, we focus the chapter around the introduction of a simple, but effective, EDA for multi-objective optimization: the naive \( \mathbb{M} \) ID\( \mathbb{E} \)AA (mixture-based multi-objective iterated density-estimation evolutionary algorithm). The probabilistic model in this specific algorithm is a mixture distribution. Each component in the mixture is a univariate factorization. As will be shown in this chapter, mixture distributions allow for wide-spread exploration of a multi-objective front, whereas most operators focus on a specific part of the multi-objective front. This wide-spread exploration aids the important preservation of diversity in multi-objective optimization. To further improve and maintain the diversity that is obtained by the mixture distribution, a specialized diversity preserving selection operator is used in the naive \( \mathbb{M} \) ID\( \mathbb{E} \)A. We verify the effectiveness of the naive \( \mathbb{M} \) ID\( \mathbb{E} \)A in two different problem domains and compare it with two other well-known efficient multi-objective evolutionary algorithms (MOEAs).