Variable screening for reduced dependency modelling in Gaussian-based continuous Estimation of Distribution Algorithms

Estimation of Distribution Algorithms (EDAs) focus on explicitly modelling dependencies between solution variables. A Gaussian distribution over continuous variables is commonly used, with several different covariance matrix structures ranging from diagonal i.e. Univariate Marginal Distribution Algorithm (UMDA_c) to full i.e. Estimation of Multivariate Normal density Algorithm (EMNA). A diagonal covariance model is simple but is unable to directly represent covariances between problem variables. On the other hand, a full covariance model requires estimation of (more) parameters from the selected population. In practice, numerical issues can arise with this estimation problem. In addition, the performance of the model has been shown to be sometimes undesirable. In this paper, a modified Gaussian-based continuous EDA is proposed, called sEDA, that provides a mechanism to control the amount of covariance parameters estimated within the Gaussian model. To achieve this, a simple variable screening technique from experimental design is adapted and combined with an idea inspired by the Pareto-front in multi-objective optimization. Compared to EMNA_global, the algorithm provides improved numerical stability and can use a smaller selected population. Experimental results are presented to evaluate and compare the performance of the algorithm to UMDA_c and EMNA_global.