Analysis of the (μ/μI, λ)-σ-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem

Abstract A thorough theoretical analysis of evolution strategies with constraint handling is important for the understanding of the inner workings of evolution strategies applied to constrained problems. Simple problems are of interest for the first analyses. To this end, the behavior of the ( 1 , λ ) -σ-Self-Adaptation Evolution Strategy applied to a conically constrained problem is analyzed. For handling infeasible offspring, a repair approach that projects infeasible offspring onto the boundary of the feasibility region is considered. Closed-form approximations are derived for the expected changes of an individual's parameter vector and mutation strength from one generation to the next. For analyzing the strategy's behavior over multiple generations, deterministic evolution equations are derived. It is shown that those evolution equations together with the approximate one-generation expressions allow to approximately predict the evolution dynamics using closed-form approximations. Those derived approximations are compared to simulations in order to visualize the approximation quality.

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