On the application of linear transformations for genetic algorithms optimization

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.