On the application of linear transformations for genetic algorithms optimization

Article type: Research Article

Authors: Salcedo-Sanz, Sancho^{a; *} | Bousoño-Calzón, Carlos^b

Affiliations: [a] Department of Signal Theory and Communications, Universidad de Alcalá, Alcalá de Henares, Madrid, Spain | [b] Department of Signal Theory and Communications, Universidad Carlos III de Madrid, 28911 Leganés, Madrid, Spain

Correspondence: [*] Corresponding author: Sancho Salcedo-Sanz, Department of Signal Theory and Communications, Universidad de Alcalá. 28805 Alcalá de Henares, Madrid, Spain. Tel.: +34 91 885 6731; Fax: +34 91 885 6699; E-mail: sancho.salcedo@uah.es

Abstract: This paper discusses new results about the effect of linear transformations (LTs) over the representation, the spectrum and the performance of standard genetic algorithms (GAs). Unitary LTs are used to set the basic outcomes and, although they can be used for theoretic GA-hard problems, their applicability is shown to be quite limited. Nevertheless, the redundancy of problems can be exploited by means of non-unitary LTs. We also propose an heuristic for construction of non-unitary LTs. Several experiments are performed in order to discuss the theoretical results of the paper.

Keywords: Genetic algorithms, GA-hard problems, function spectrum, linear transformations, heuristics

DOI: 10.3233/KES-2007-11202

Journal: International Journal of Knowledge-based and Intelligent Engineering Systems, vol. 11, no. 2, pp. 89-104, 2007