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Estimation of Distribution Algorithms (EDA) have been proposed as an extension of genetic algorithms for optimization. In this paper the major design issues are presented within a general interdisciplinary framework. It is shown that EDA algorithms compute maximum entropy or minimum relative entropy approximations. A special structure learning algorithm LFDA is analyzed in detail. It is based on a finite minimum log-likelihood ratio principle. We investigate important parameters of the presented EDA algorithms by analyzing the performance on synthetic benchmark functions.