Bayesian Optimization Algorithms for Multi-objective Optimization

In recent years, several researchers have concentrated on using probabilistic models in evolutionary algorithms. These Estimation Distribution Algorithms (EDA) incorporate methods for automated learning of correlations between variables of the encoded solutions. The process of sampling new individuals from a probabilistic model respects these mutual dependencies such that disruption of important building blocks is avoided, in comparison with classical recombination operators. The goal of this paper is to investigate the usefulness of this concept in multi-objective optimization, where the aim is to approximate the set of Pareto-optimal solutions. We integrate the model building and sampling techniques of a special EDA called Bayesian Optimization Algorithm, based on binary decision trees, into an evolutionary multi-objective optimizer using a special selection scheme. The behavior of the resulting Bayesian Multi-objective Optimization Algorithm (BMOA) is empirically investigated on the multi-objective knapsack problem.