Bivariate empirical and n-variate Archimedean copulas in Estimation of Distribution Algorithms

In evolutionary optimization, the class of algorithms that employ probabilistic modeling are usually called estimation of distribution algorithms (EDAs). In EDAs probabilistic models are learnt from the selected individuals and used to generate new solutions. This is a significant difference with respect to other evolutionary algorithms based on crossover and mutation operators. EDAs have been successfully applied to solve problems with discrete and continuous representations. This emerging research line investigates, in collaboration with UPM, the use of empirical and Archimedean copulas as probabilistic models of continuous estimation of distribution algorithms (EDAs). A method for learning and sampling empirical bivariate copulas to be used in the context of n-dimensional EDAs is first introduced. Then, by using Archimedean copulas instead of empirical makes possible to construct n-dimensional copulas with the same purpose. Those Copula-based EDAs could be applied to other optimization problems