On the model updating operators in univariate estimation of distribution algorithms

The role of the selection operation-that stochastically discriminate between individuals based on their merit-on the updating of the probability model in univariate estimation of distribution algorithms is investigated. Necessary conditions for an operator to model selection in such a way that it can be used directly for updating the probability model are postulated. A family of such operators that generalize current model updating mechanisms is proposed. A thorough theoretical analysis of these operators is presented, including a study on operator equivalence. A comprehensive set of examples is provided aiming at illustrating key concepts, main results, and their relevance