Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints

In this paper, we introduce a mathematical model for analyzing the dynamics of the univariate marginal distribution algorithm (UMDA) for a class of parametric functions with isolated global optima. We prove a number of results that are used to model the evolution of UMDA probability distributions for this class of functions. We show that a theoretical analysis can assess the effect of the function parameters on the convergence and rate of convergence of UMDA. We also introduce for the first time a long string limit analysis of UMDA. Finally, we relate the results to ongoing research on the application of the estimation of distribution algorithms for problems with unitation constraints. (C) 2011 Elsevier Inc. All rights reserved.