Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses

  • Martin Pelikan
  • Alexander K. Hartmann
  • Kumara Sastry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4193)


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.


Genetic Algorithm Bayesian Network Evolutionary Computation Candidate Solution Spin Glass 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Pelikan
    • 1
  • Alexander K. Hartmann
    • 2
  • Kumara Sastry
    • 3
  1. 1.Missouri Estimation of Distribution Algorithms Laboratory (MEDAL), 320 CCBUniversity of Missouri in St. LouisSt. Louis
  2. 2.Institut für Theoretische PhysikUniversität GöttingenGöttingenGermany
  3. 3.Illinois Genetic Algorithms Laboratory (IlliGAL), 117 TBUniversity of Illinois at Urbana-ChampaignUrbana

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