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Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses

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Parallel Problem Solving from Nature - PPSN IX (PPSN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4193))

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Abstract

This paper analyzes the hierarchical Bayesian optimization algorithm (hBOA) on the problem of finding ground states of Ising spin glasses with ±J couplings in two and three dimensions. The performance of hBOA is compared to that of the simple genetic algorithm (GA) and the univariate marginal distribution algorithm (UMDA). The performance of all tested algorithms is improved by incorporating a deterministic hill climber (DHC) based on single-bit flips and cluster exact approximation (CEA). The results show that hBOA significantly outperforms GA and UMDA with both types of local search and that CEA enables all tested algorithms to solve larger spin-glass instances than DHC. Using advanced hybrid methods created by combining competent genetic and evolutionary algorithms with advanced local searchers thus proves advantageous in this challenging class of problems.

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Author information

Authors and Affiliations

  1. Missouri Estimation of Distribution Algorithms Laboratory (MEDAL), 320 CCB, University of Missouri in St. Louis, One University Blvd., St. Louis, MO, 63121

    Martin Pelikan

  2. Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077, Göttingen, Germany

    Alexander K. Hartmann

  3. Illinois Genetic Algorithms Laboratory (IlliGAL), 117 TB, University of Illinois at Urbana-Champaign, 104 S. Mathews Ave., Urbana, IL, 61801, USA

    Kumara Sastry

Authors
  1. Martin Pelikan
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  2. Alexander K. Hartmann
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  3. Kumara Sastry
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Editor information

Editors and Affiliations

  1. Science Institute, University of Iceland, P.O. Box, Iceland

    Thomas Philip Runarsson

  2. Vorarlberg University of Applied Sciences, Hochschulstr. 1, A-6850, Dornbirn, Austria

    Hans-Georg Beyer

  3. Automated Scheduling, Optimisation and Planning Group, School of Computer Science & IT, University of Nottingham, NG8 1BB, Nottingham, UK

    Edmund Burke

  4. Depto. Arquitectura y Tecnologa de Computadores, ETS Ingeiera Informtica, C/Daniel Saucedo Aranda, s/n, 18071, Granada, Spain

    Juan J. Merelo-Guervós

  5. Colorado State University, 80523, Fort Collins, CO, USA

    L. Darrell Whitley

  6. University of Birmingham, Birmingham, UK

    Xin Yao

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© 2006 Springer-Verlag Berlin Heidelberg

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Pelikan, M., Hartmann, A.K., Sastry, K. (2006). Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_13

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  • DOI: https://doi.org/10.1007/11844297_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38990-3

  • Online ISBN: 978-3-540-38991-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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