The Covariance Matrix Evolution Strategy Algorithm Based On Cloud Model And Cholesky Factor

Abstract

The covariance matrix adaptive evolution strategy (CMA-ES) is a random search evolution strategy with superior performance and high accuracy. However, when faced with multimodal complex functions, it also has the shortcomings of converging too fast and easily falling into local optimization. Matrix operations in high dimensions also greatly reduce the performance of the algorithm. This paper proposes an improved CMA-ES algorithm based on the cloud model and Cholesky factor update. The cloud model has a good ability to deal with uncertain problems, and the step size is controlled by cloud reasoning, which can better avoid falling into problems such as local optimization and premature convergence. At the same time, the Cholesky factor greatly reduces the computational cost of the algorithm by effectively updating the covariance, especially in high dimensions. Through multiple function tests, multiple experimental verifications and compared with CMA-ES and its Cholesky variant algorithm, the algorithm has the advantages of higher efficiency and more accurate convergence.