CMA-ES with exponential based multiplicative covariance matrix adaptation for global optimization

Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the proven evolutionary algorithms to solve complex optimization problems. However, CMA-ES is plagued with the computational overload that is associated with the unstable matrix decomposition process. In the current work, the computationally expensive covariance matrix decomposition is replaced with a multiplicative update of the mutation matrix which is a result of first-order exponential approximation. In addition, we incorporate the Heaviside function into the mutation matrix update to appropriately control the mutation step size. The proposed mutation matrix update scheme and the incorporation of the Heaviside function result in a modified evolution path. The performance of the proposed framework, referred to as Exponential Simplified CMA-ES (xSCMA-ES) is favorably compared with the state-of-the-art CMA-ES-based algorithms on - (a) IEEE CEC 2014 benchmark suite (b) with different DE variants on CoCo Framework and (c) hybrid active power filter design problem where the objective is to minimize the harmonic distortions.

Automated summary

CMA-ES is an effective evolutionary algorithm for solving complex optimization problems, but it suffers from the computational burden of unstable matrix decomposition. This paper proposes an improved evolution path by using first-order exponential approximation to replace the costly covariance matrix decomposition, and incorporating the Heaviside function for mutation matrix update to control mutation step size. The proposed xSCMA-ES framework outperforms existing CMA-ES algorithms on various benchmark tests and a hybrid active power filter design problem in minimizing harmonic distortions.