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Convergence Theorems of Estimation of Distribution Algorithms

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Markov Networks in Evolutionary Computation

Part of the book series: Adaptation, Learning, and Optimization ((ALO,volume 14))

Abstract

Estimation of Distribution Algorithms (EDAs) have been proposed as an extension of genetic algorithms.We assume that the function to be optimized is additively decomposed (ADF). The interaction graph of the ADF function is used to create exact or approximate factorizations of the Boltzmann distribution. Convergence of the algorithmMN-GIBBS is proven.MN-GIBBS uses a Markov network easily derived from the ADF and Gibbs sampling. We discuss different variants of Gibbs sampling. We show that a good approximation of the true distribution is not necessary, it suffices to use a factorization where the global optima have a large enough probability. This explains the success of EDAs in practical applications using Bayesian networks.

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Author information

Authors and Affiliations

  1. Fraunhofer Institut IAIS, Sankt Augustin, Germany

    Heinz Mühlenbein

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  1. Heinz Mühlenbein
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Editors and Affiliations

  1. Transformation Practice, BT Innovate & Design, Business Modelling and Operational, Cauldwell Hall Road 172, Ipswich, IP4 5DB, United Kingdom

    Siddhartha Shakya

  2. Intelligent Systems Group, Faculty of Informatics, University of the Basque Country, Boadilla del Monte, San Sebastian, Spain

    Roberto Santana

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Mühlenbein, H. (2012). Convergence Theorems of Estimation of Distribution Algorithms. In: Shakya, S., Santana, R. (eds) Markov Networks in Evolutionary Computation. Adaptation, Learning, and Optimization, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28900-2_6

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  • DOI: https://doi.org/10.1007/978-3-642-28900-2_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28899-9

  • Online ISBN: 978-3-642-28900-2

  • eBook Packages: EngineeringEngineering (R0)

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