Improving CMA-ES by random evaluation on the minor eigenspace

This paper proposes a modification to the covariance matrix adaptation evolution strategies (CMA-ES). The goal of our modification is to reduce the number of function evaluations to adapt the covariance matrix to the optimal one when the standard CMA-ES is used to optimize convex-quadratic objective functions which have repeated or clustered eigenvalues in their Hessian matrices. By randomly evaluating the minor eigenspace, the modified CMA-ES is evaluated on a standard suite of benchmark problems and its performance is compared with that of the standard CMA-ES. The experimental results show that our proposed modification can improve the performance of the CMA-ES when dominant eigenspaces and minor eigenspaces exist in the Hessian matrices of the underlying objective functions.