Why Are Genetic Algorithms Markov?

by Khiria E . El-Nady, Usama H. Abou El-Enien, and Amr A. Badr .

Abstract: : Genetic algorithms are considered. Three algorithms are designed and executed to obtain purely empirical analysis conclusions in order to turn to purely theoretical analysis results about the behavior of genetic algorithms as a finite dimensional Markov and lumped Markov chains, which confirm the conjectures from these experiments and in order to introduce a complete framework toward a new philosophy of machine intelligence. First, we model genetic algorithms using a finite dimensional Markov and lumped Markov chains. Second, we carry on a particle analysis (the basic component) and analyze the convergence properties of these algorithms. Third, we produce two unified Markov and lumped Markov approaches for analysis for a complete framework and propose unique chromosomes for a purely successful optimization of these algorithms. Furthermore, for the Markov approach, we obtain purely theoretical analysis for a classification and Stationary distributions of chains. For the lumped Markov approach, we obtain purely theoretical analysis for all possible conditional multivariate normal distributions of transition probability matrices and stationary multivariate normal distributions of chains.

Key Words: Genetic algorithms, lumped Markov chains, Classification, Central limit theorem, Stationary multivariate normal distribution, Unique chromosomes

Authors:
Khiria E . El-Nady, pr_dr_kh_elnady@yahoo.com
Usama H. Abou El-Enien, ossama.hanafy77@gmail.com
Amr A. Badr, pr.dr.a.badr@gmail.com

Editor: Ke, Weiming, Weiming.Ke@sdstate.edu

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