Covariance matrix repairing in Gaussian based EDAs

Abstract

Gaussian models are widely adopted in continuous Estimation of Distribution Algorithms (EDAs). In this paper, we analyze continuous EDAs and show that they don’t always work because of computation error: covariance matrix of Gaussian model can be ill-posed and Gaussian based EDAs using full covariance matrix will fail under specific conditions. It is a universal problem that all existing Gaussian based EDAs using full covariance matrix suffer from. Through theoretical analysis with examples of simulated data and experiments, we show that the ill-posed covariance matrix strongly affects those EDAs. This paper proposes a Covariance Matrix Repairing (CMR) method to fix ill-posed covariance matrix. CMR significantly improves the robustness of EDAs. Even some EDA’s performance that was previously thought inefficient can be improved surprisingly with the help of CMR. CMR can also guarantee those EDAs to be used with small scale of population (but still should be large enough to find the global optimum) to accelerate the convergence rate while maintaining the quality of solutions.