Analysis of the $(\mu/\mu_I,\lambda)$-$\sigma$-Self-Adaptation Evolution Strategy with Repair by Projection Applied to a Conically Constrained Problem
| Autor: | Spettel, Patrick, Beyer, Hans-Georg |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 the feasibility region. Closed-form approximations are used for the one-generation progress of the evolution strategy. Approximate deterministic evolution equations are formulated for analyzing the strategy's dynamics. By iterating the evolution equations with the approximate one-generation expressions, the evolution strategy's dynamics can be predicted. The derived theoretical results are compared to experiments for assessing the approximation quality. It is shown that in the steady state the $(\mu/\mu_I,\lambda)$-$\sigma$SA-ES exhibits a performance as if the ES were optimizing a sphere model. Unlike the non-recombinative $(1,\lambda)$-ES, the parental steady state behavior does not evolve on the cone boundary but stays away from the boundary to a certain extent. Comment: This is a PREPRINT of an article submitted to IEEE Transactions On Evolutionary Computation. It is currently under review. Due to size limitations, this manuscript comprises figures with reduced resolution. 10 pages + supplementary material. Copyright 2018 IEEE. The work was supported by the Austrian Science Fund FWF under grant P29651-N32 |
| Databáze: | arXiv |
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