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

Univariate marginal distribution algorithm dynamics for a class of parametric functions with unitation constraints” by Li-vang Lozada-Chang and Roberto Santana. Information Sciences, vol. 181, no. 11, 2011, pp. 2340-2355.

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.

BibTeX entry:

@article{Lozada_and_Santana:2011,
   author = {Li-vang Lozada-Chang and Roberto Santana},
   title = {Univariate marginal distribution algorithm dynamics for a
	class of parametric functions with unitation constraints},
   journal = {Information Sciences},
   volume = {181},
   number = {11},
   pages = {2340-2355},
   year = {2011},
   url = {http://dx.doi.org/10.1016/j.ins.2011.01.024}
}

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