The second largest eigenvalue upper bound for the canonical genetic algorithms

Abstract

We provide an analysis of a Markov chain model that explains the convergence properties of canonical genetic algorithms with proportional selection, single point crossover and bit mutation with a mutation rate between 0 and 1. Specifically, we provide a second largest eigenvalue upper bound for canonical genetic algorithms (CGA). We show that, when mutation rate for CGA is 0.5, the second largest eigenvalue for the CGA is zero and the CGA converges to a stationary distribution in the first step after the initial random population initialization.