Practical Modeling of Simple Genetic Algorithm, via deterministic paths, by Absorbing Markov Chains

Abstract

A practical dynamical model of an efficient Simple Genetic Algorithm is presented, introducing in the matrix of the Nix and Vose Markov model a practical postulate related to the schema theorem, that induces deterministic correction factors in the matrix, through Heavisides unitary step function. This alteration permits SGA to evolve by efficient deterministic channels. The model simulates the real behaviour of an efficient SGA. The Markov chain is transformed into an absorbing Markov chain. Using the absorbing theory, the expected waiting time, EWT, is computed easily in any situation. For the case of maximum uncertainty, it is obtained an expression for EWT that improves from the standard Nix and Vose model, in relation to the experimental data. Through the deterministic paths, the steady state is obtained when the absorbing state, global optimum, is reached. To emphasize that, with this practical improvement, the theoretical unification of the model of Nix and Vose for the SGA with the general model of the evolutionary algorithms with elitism is procured.