Abstract
We show the convergence of 1 + λ-ES with standard step-size update-rules on a large family of fitness functions without any convexity assumption or quasi-convexity assumptions ([3,6]). The result provides a rule for choosing λ and shows the consistency of halting criteria based on thresholds on the step-size.
The family of functions under work is defined through a condition-number that generalizes usual condition-numbers in a manner that only depends on level-sets. We consider that the definition of this condition-number is the relevant one for evolutionary algorithms; in particular, global convergence results without convexity or quasi-convexity assumptions are proved when this condition-number is finite.
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Teytaud, O. (2008). Conditioning, Halting Criteria and Choosing λ . In: Monmarché, N., Talbi, EG., Collet, P., Schoenauer, M., Lutton, E. (eds) Artificial Evolution. EA 2007. Lecture Notes in Computer Science, vol 4926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79305-2_17
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DOI: https://doi.org/10.1007/978-3-540-79305-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79304-5
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