Implicit parallelism in genetic algorithms

摘要

This paper is related to Holland's result on implicit parallelism. Roughly speaking, Holland showed a lower bound of the order of n3c1√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 = 2βl binary strings where β is a positive parameter (Holland's result is related to the case β = 1). In the main result, we state a lower bound on the expected number of processed schemata for all β > 0; moreover, we prove that this bound is tight up to a constant for all β ⩾ 1 and, in this case, we strengthen in probability the previous result.