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

Authors:
Li-Vang Lozada-Chang;Roberto Santana
Affiliations:
Faculty of Mathematics and Computation, University of Havana, San Lázaro y L, CP-10400 La Habana, Cuba;Intelligent Systems Group, Department of Computer Science and Artificial Intelligence, University of the Basque Country, Paseo Manuel de Lardizábal 1, CP-20080 San Sebastián -Donostia, S ...
Venue:
Information Sciences: an International Journal
Year:
2011

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Abstract

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.