Convergence of estimation of distribution algorithms in optimization of additively noisy fitness functions

Noise is a common phenomenon in many real-world optimizations. It has long been argued that evolutionary algorithm (EA) should be relatively robust against it. As a novel computing model in evolutionary computations, estimation of distribution algorithm (EDA) is also encountered with it. This paper initially presents three dynamic models of EDA under the additively noisy environment with three different selection methods (proportional selection method, truncation selection method and tournament selection method). We verify that when the population size is infinite, EDA can converge to the global optimal point. This concept establishes the theoretic foundation for optimization of noisy fitness functions with EDA