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 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 = 2βl binary strings where β is a positive parameter (Holland's result is related to the case β=1). In the main result, for all β>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 β≥1 and, in this case, we strengthen in probability the previous result. _______________________________ * This paper has appeared in Artificial Intelligence (61) 2, 307–314. + Universitá Statale di Milano, Dip. di Scenze dell'Informazione, via Comelico 39, 20135 Milano, Italy. # International Computer Science Institute, Berkeley, CA 94704, and Progetto di Intelligenza Artificiale e Robotica, Dip. di Elettronica e Informazione, Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milano, Italy (e-mail: [email protected]).