We propose an algorithm for multi-objective optimization using a mixture-based iterated density estimation evolutionary algorithm (MIDEA). The MIDEA algorithm is a probabilistic model building evolutionary algorithm that constructs at each generation a mixture of factorized probability distributions. The use of a mixture distribution gives us a powerful, yet computationally tractable, representation of complicated dependencies. In addition it results in an elegant procedure to preserve the diversity in the population, which is necessary in order to be able to cover the Pareto front. The algorithm searches for the Pareto front by computing the Pareto dominance between all solutions. We test our approach in two problem domains. First we consider discrete multi-objective optimization problems and give two instantiations of MIDEA: one building a mixture of discrete univariate factorizations, the other a mixture of tree factorizations. Secondly, we look at continuous real valued multi-objective optimization problems and again consider two instantiations of MIDEA: a mixture of continuous univariate factorizations, and a mixture of conditional Gaussian factorizations as probabilistic model.
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