### Optimal Mutation Rate Using Bayesian Priors for Estimation of Distribution Algorithms

UMDA (the univariate marginal distribution algorithm) was derived by analyzing the mathematical principles behind recombination. Mutation, however, was not considered. The same is true for the FDA (factorized distribution algorithm), an extension of the UMDA which can cover dependencies between variables. In this paper mutation is introduced into these algorithms by a technique called Bayesian prior. We derive theoretically an estimate how to choose the Bayesian prior. The recommended Bayesian prior turns out to be a good choice in a number of experiments. These experiments also indicate that mutation increases in many cases the performance of the algorithms and decreases the dependence on a good choice of the population size.

[1]  Heinz Mühlenbein,et al.  Schemata, Distributions and Graphical Models in Evolutionary Optimization , 1999, J. Heuristics.

[2]  Heinz Mühlenbein,et al.  The Equation for Response to Selection and Its Use for Prediction , 1997, Evolutionary Computation.

[3]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[4]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

[5]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

[6]  S. Wright Evolution in mendelian populations , 1931 .

[7]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[8]  Hans-Paul Schwefel,et al.  Parallel Problem Solving from Nature — PPSN IV , 1996, Lecture Notes in Computer Science.

[9]  T. Mahnig,et al.  Evolutionary algorithms: from recombination to search distributions , 2001 .

[10]  S. Kauffman,et al.  Towards a general theory of adaptive walks on rugged landscapes. , 1987, Journal of theoretical biology.

[11]  D. Falconer,et al.  Introduction to Quantitative Genetics. , 1961 .

[12]  H. Muhlenbein,et al.  Size of neighborhood more important than temperature for stochastic local search , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[13]  Michael I. Jordan Learning in Graphical Models , 1999, NATO ASI Series.