Adaptive genetic algorithms-modeling and convergence

Abstract

The paper presents a new mathematical analysis of genetic algorithms (GAs); we propose the use of random systems with complete connections (RSCC), a non-trivial extension of the Markovian dependence, accounting for a complete, rather than recent, history of a stochastic evolution. As far as we know, this is the first theoretical modeling of an adaptive GA. First we introduce the RSCC model of an p/sub m/-adaptive GA, then we prove that a "classification of states" is still valid for our model, and finally we derive a convergence condition for the algorithm.