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A theoretical performance analysis of the$(\mu/\mu_I,\lambda)$-$\sigma$-Self-Adaptation Evolution Strategy($\sigma$SA-ES) is presented considering a conically constrained problem.Infeasible offspring are repaired using projection onto the boundary of thefeasibility region. Closed-form approximations are used for the one-generationprogress of the evolution strategy. Approximate deterministic evolutionequations are formulated for analyzing the strategy's dynamics. By iteratingthe evolution equations with the approximate one-generation expressions, theevolution strategy's dynamics can be predicted. The derived theoretical resultsare compared to experiments for assessing the approximation quality. It isshown that in the steady state the $(\mu/\mu_I,\lambda)$-$\sigma$SA-ES exhibitsa performance as if the ES were optimizing a sphere model. Unlike thenon-recombinative $(1,\lambda)$-ES, the parental steady state behavior does notevolve on the cone boundary but stays away from the boundary to a certainextent.

Analysis of the $(\mu/\mu_I,\lambda)$-$\sigma$-Self-Adaptation Evolution  Strategy with Repair by Projection Applied to a Conically Constrained Problem