Model complex control CMA-ES

Abstract

Abstract Covariance Matrix Adaptation Evolution Strategy (CMA-ES) has shown great performance on nonseparable optimization problems largely due to its rotation-invariant feature. However, as the computational cost of the self-adaption operation is sensitive to the scale of problems, the performance of CMA-ES heavily suffers from the well-known curse of dimensionality, which makes it impractical to many Large Scale Global Optimization (LSGO) problems. In this paper, a correlation coefficient based grouping (CCG) strategy is proposed to detect the correlations between variables in a simple yet efficient way. Then coupled with a model complexity control (MCC) framework, a new variant of CMA-ES, named MCC-CCG-CMAES, is presented for LSGO problems, which suffers less from curse of dimensionality and significantly reduces the computational cost compared with the standard CMA-ES. To the best of our knowledge, this work is the first attempt at enhancing CMA-ES with the MCC framework rather than the cooperative coevolution (CC) framework. Experimental results on the CEC′2010 large-scale global optimization (LSGO) benchmark functions show that the performance of MCC-CCG-CMAES outperforms the state-of-the-art counterparts.