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Hölder functions and Deception of Genetic Algorithms

Abstract : We present a deception analysis for Hölder functions. Our approach uses a decomposition on the Haar basis, which reflects in a natural way the Hölder structure of the function. It allows to relate the deception, the Hölder exponent, and some parameters of the genetic algorithms (GAs). These results prove that deception is connected to the irregularity of the fitness function, and shed a new light on the schema theory. In addition, this analysis may assist in understanding the influence of some of the parameters on the performance of a GA.
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Jacques Lévy Véhel, Evelyne Lutton. Hölder functions and Deception of Genetic Algorithms. IEEE Transactions on Evolutionary Computation, Institute of Electrical and Electronics Engineers, 1998, 2 (2), pp.56-71. ⟨10.1109/4235.728208⟩. ⟨inria-00592413⟩

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