Why Are Genetic Algorithms Markov?
by Khiria E . El-Nady, Usama H. Abou El-Enien, and Amr A. Badr
: 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.
Genetic algorithms, lumped Markov chains, Classification, Central limit theorem, Stationary multivariate normal distribution, Unique chromosomes
Khiria E . El-Nady, firstname.lastname@example.org
Usama H. Abou El-Enien, email@example.com
Amr A. Badr, firstname.lastname@example.org
Ke, Weiming, Weiming.Ke@sdstate.edu
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