Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms

Multivariate Gaussian models are widely adopted in continuous Estimation of Distribution Algorithms (EDAs), and covariance matrix plays the essential role in guiding the evolution. In this paper, we propose a new framework for Multivariate Gaussian based EDAs (MGEDAs), named Eigen Decomposition EDA (ED-EDA). Unlike classical EDAs, ED-EDA focuses on eigen analysis of the covariance matrix, and it explicitly tunes the eigenvalues. All existing MGEDAs can be unified within our ED-EDA framework by applying three different eigenvalue tuning strategies. The effects of eigenvalue on influencing the evolution are investigated through combining maximum likelihood estimates of Gaussian model with each of the eigenvalue tuning strategies in ED-EDA. In our experiments, proper eigenvalue tunings show high efficiency in solving problems with small population sizes, which are difficult for classical MGEDA adopting maximum likelihood estimates alone. Previously developed Covariance Matrix Repairing (...

• Type: Journal
• Year: 2008
• Where: ISCI
• Authors: Weishan Dong, Xin Yao
• Keywords: Covariance Matrix, Eigenvalue Tuning, Eigenvalues, ISCI 2008