The second largest eigenvalue upper bound for the canonical genetic algorithms

Article type: Research Article

Authors: Pendharkar, Parag C.

Affiliations: Information Systems, School of Business Administration, Pennsylvania State University at Harrisburg, 777 West Harrisburg Pike, Middletown, PA 17057, USA. Tel.: +1 717 948 6028; Fax: +1 717 948 6456; E-mail: pxp19@psu.edu

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.

Keywords: Markov chains, Markov processes, approximation methods, heuristics

DOI: 10.3233/KES-2007-11305

Journal: International Journal of Knowledge-based and Intelligent Engineering Systems, vol. 11, no. 3, pp. 193-198, 2007