Sharp Bounds for Genetic Drift in Estimation of Distribution Algorithms

Estimation of distribution algorithms (EDAs) are a successful branch of evolutionary algorithms (EAs) that evolve a probabilistic model instead of a population. Analogous to genetic drift in EAs, EDAs also encounter the phenomenon that the random sampling in the model update can move the sampling frequencies to boundary values not justified by the fitness. This can result in a considerable performance loss. This article gives the first tight quantification of this effect for three EDAs and one ant colony optimizer, namely, for the univariate marginal distribution algorithm, the compact genetic algorithm, population-based incremental learning, and the max-min ant system with iteration-best update. Our results allow to choose the parameters of these algorithms in such a way that within a desired runtime, no sampling frequency approaches the boundary values without a clear indication from the objective function.