eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Dagstuhl Seminar Proceedings
1862-4405
2008-05-06
1
0
10.4230/DagSemProc.08051.4
article
Evaluating Stationary Distribution of the Binary GA Markov Chain in Special Cases
Mitavskiy, Boris S.
Cannings, Chris
The evolutionary algorithm stochastic process is well-known to be
Markovian. These have been under investigation in much of the
theoretical evolutionary computing research. When mutation rate is
positive, the Markov chain modeling an evolutionary algorithm is
irreducible and, therefore, has a unique stationary distribution,
yet, rather little is known about the stationary distribution. On the other
hand, knowing the stationary distribution may provide
some information about the expected times to hit optimum, assessment of the biases due to recombination and is of importance in population
genetics to assess what's called a ``genetic load" (see the
introduction for more details). In this talk I will show how the quotient
construction method can be exploited to derive rather explicit bounds on the ratios of the stationary distribution values of various subsets of
the state space. In fact, some of the bounds obtained in the current
work are expressed in terms of the parameters involved in all the
three main stages of an evolutionary algorithm: namely selection,
recombination and mutation. I will also discuss the newest developments which may allow for further improvements of the bounds
https://drops.dagstuhl.de/storage/16dagstuhl-seminar-proceedings/dsp-vol08051/DagSemProc.08051.4/DagSemProc.08051.4.pdf
Genetic algorithms
Markov chains
stationary distribution
lumping quotient