IMPLICIT PARALLELISM IN GENETIC ALGORITHMS

This paper is related to Holland's result on implicit parallelism. Roughly speaking, Holland showed a lower bound of the order of n3/c1 square-root l to the number of schemata usefully processed by the genetic algorithm in a population of n = c1 . 2l binary strings, with c1 a small integer. We analyze the case of a population of n = 2betal binary strings where beta is a positive parameter (Holland's result is related to the case beta = 1). In the main result, we state a lower bound on the expected number of processed schemata for all beta > 0; moreover, we prove that this bound is tight up to a constant for all beta greater-than-or-equal-to 1 and, in this case, we strengthen in probability the previous result.