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

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).

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