On multivariate genetic systems

We take into account the problem of extending the univariate marginal distribution genetic algorithm (UMDGA) modeling and analysis to the multivariate framework. In particular, we introduce the basic general concepts and mathematical formalism to devise genetic algorithms useful to solve problems involving dependencies among genes. We state the relationships between the natural component attractors of the (numerous or infinite population) multivariate marginal distribution genetic systems and the equilibrium points of associated neural networks so rephrasing the problem of solving an evolutionary task in terms of the analysis of its properties through suitably designed neural networks.