Eigenspace sampling in the mirrored variant of (1, λ)-CMA-ES

We propose a novel variant of the (1, λ)-CMA-ES that uses the mirrored sampling and sequential selection methods. Instead of sampling all the mirrored directions along the principal axes of the covariance matrix, we cluster the eigen-values of the covariance matrix of a CMA-ES and sample search points on a mirrored eigenspace spanned by eigenvectors that have the same repeated or clustered eigenvalues in the Hessian matrices of the objective functions. We apply this sampling method to a (1, λ)-CMA-ES and compare its performance with that of a standard (1, λ^sm)-CMA-ES that uses the traditional mirroring method. In most of the standard test functions, the new variant is not observed to be marginally worse than the mirrored variant, and it is up to 56% faster on the sphere function when it is compared with the standard (1, λ)-CMA-ES.