generalizations of it [Gold88, Gold89b, BrGo89], a result concerning selection of the
optimal population size for the algorithm [Gold85] in terms of the solution space dimen-
sion and the examination of the properties which make a problem difficult for genetic
algorithms (the so called minimal deceptive problem) [Gold87, Gold89b]. Also, both De
Jong [Dejo75] and Goldberg/Segrest [GoSe87] employ Markov chain methodology
accompanied by approximate numerical analysis to examine certain specific problems
concerning finite length chain behavior (e.g. genetic drift in a binary allele genetic algo-
rithm).
No complete theoretical model exists for describing the operation of the simple f
genetic algorithm executing on a specified optimization problem. The central theme of
the work underlying this paper is an attempt to develop such a model based upon the
asymptotic behavior of a Markov chain which represents the algorithm.