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 (n^3)/(c1*?l) to the number of schemata usefully processed by the genetic algorithm in a population of n=c1*2^l binary strings, with c1 a small integer. We analyze the case of population of n = 2^?l binary strings where ? is a positive parameter (Holland's result is related to the case ?=1). In the main result, for all ?>0 we state a lower bound on the expected number of processed schemata; moreover, we prove that this bound is tight up to a constant for all ?>=1 and, in this case, we strengthen in probability the previous result.

ICSI Technical Report TR-93-001

Technical Report