An information theory analysis of the convergence and learning properties of a certain class of genetic algorithms in continuous space and infinite population assumption

An approach based on concepts of classical information theory to analyze the behaviour of genetic algorithms in continuous space is developed. As genetic algorithms are robust and efficient paradigms for modeling evolutionary systems, a major research topic is represented by the theoretical analysis of the corresponding convergence properties. The present issue reports a series of results concerning the characterization of the search process involved by the genetic algorithms in the framework of infinite population assumptions when the combined effects of selection and mutation are taken into consideration. The main mathematical tools used here come from classical information theory based on Shannon entropy. The Kullback-Leibler measure was selected to express the information gain corresponding to such a dynamical process. The main result concerning this topic establishes that the search process is essentially a learning process of the asymptotically distribution whose mean is the optimal global solution of the considered optimization problem.