Steady state analysis of a multi-recombinative meta-ES on a conically constrained problem with comparison to σSA and CSA

This paper concerns the theoretical analysis of a multi-recombinative meta-ES with repair by projection applied to a conically constrained problem. Using theoretical results for the mean value dynamics and steady state considerations of the inner ES, approximate closed-form expressions for the mean value dynamics and the steady state behavior of the outer ES are derived. The approximation quality is shown by comparison with real meta-ES runs using isolation periods larger than one. The theoretical results are compared to known theoretical results of the multi-recombinative ES with σ-Self-Adaptation and Cumulative Step-Size adaptation. It is shown that the meta-ES achieves the largest steady state progress for the considered problem at the cost of twice the function evaluations compared to the other variants.

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