On the use of evolution strategies for optimising certain positive definite quadratic forms

This paper studies the performance of multi-recombinative evolution strategies using isotropically distributed mutations on a class of convex quadratic objective functions that is characterised by the presence of only two different eigenvalues of their Hessian. A simplified model of the strategy's behaviour is developed. Using it, expressions that approximately describe the stationary state that is attained when the mutation strength is adapted are derived. The performance achieved when using cumulative step length adaptation is compared with that obtained when using optimally adapted step lengths.

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