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The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle

Authors: Heinz Mühlenbein and Robin Höns

Published in: Dagstuhl Seminar Proceedings, Volume 6061, Theory of Evolutionary Algorithms (2006)

Abstract

We assume that the function to be optimized is additively decomposed (ADF). Then the interaction graph $G_{ADF}$ can be used to compute exact or approximate factorizations. For many practical problems only approximate factorizations lead to efficient optimization algorithms. The relation between the approximation used by the FDA algorithm and the minimum relative entropy principle is discussed. A new algorithm is presented, derived from the Bethe-Kikuchi approach in statistical physics. It minimizes the relative entropy to a Boltzmann distribution with fixed $eta$. We shortly compare different factorizations and algorithms within the FDA software. We use 2-d Ising spin glass problems and Kaufman's n-k function as examples.

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Heinz Mühlenbein and Robin Höns. The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle. In Theory of Evolutionary Algorithms. Dagstuhl Seminar Proceedings, Volume 6061, pp. 1-27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{muhlenbein_et_al:DagSemProc.06061.9,
  author =	{M\"{u}hlenbein, Heinz and H\"{o}ns, Robin},
  title =	{{The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle}},
  booktitle =	{Theory of Evolutionary Algorithms},
  pages =	{1--27},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6061},
  editor =	{Dirk V. Arnold and Thomas Jansen and Michael D. Vose and Jonathan E. Rowe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06061.9},
  URN =		{urn:nbn:de:0030-drops-5973},
  doi =		{10.4230/DagSemProc.06061.9},
  annote =	{Keywords: Junction tree, minimum relative entropy, maximum likelihood, Bethe-Kikuchi approximation}
}

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The Factorized Distribution Algorithm and the Minimum Relative Entropy Principle

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