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Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints. (English) Zbl 1216.68219
Summary: 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.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
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