1. Global convergence for evolution strategies in spherical problems: some simple proofs and difficulties
- Author
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Olivier François, Alexis Bienvenüe, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525 (TIMC-IMAG), and VetAgro Sup - Institut national d'enseignement supérieur et de recherche en alimentation, santé animale, sciences agronomiques et de l'environnement (VAS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)
- Subjects
Mathematical optimization ,Adaptive strategies ,[SHS.STAT]Humanities and Social Sciences/Methods and statistics ,General Computer Science ,Markov chain ,Markov chains ,Computation ,Chaotic ,0102 computer and information sciences ,02 engineering and technology ,Mathematical proof ,Global convergence ,01 natural sciences ,Theoretical Computer Science ,Evolution strategies ,010201 computation theory & mathematics ,Simple (abstract algebra) ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Mathematics ,Computer Science(all) - Abstract
International audience; This paper presents simple proofs for the global convergence of evolution strategies in spherical problems. We investigate convergence properties for both adaptive and self-adaptive strategies. Regarding adaptive strategies, the convergence rates are computed explicitly and compared with the results obtained in the so-called “rate-of-progress” theory. Regarding self-adaptive strategies, the computation is conditional to the knowledge of a specific induced Markov chain. An explicit example of chaotic behavior illustrates the complexity in dealing with such chains. In addition to these proofs, this work outlines a number of difficulties in dealing with evolution strategies.
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