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Condensed Matter > Disordered Systems and Neural Networks

arXiv:0801.2997 (cond-mat)
[Submitted on 21 Jan 2008]

Title:Finding Ground States of Sherrington-Kirkpatrick Spin Glasses with Hierarchical BOA and Genetic Algorithms

Authors:Martin Pelikan, Helmut G. Katzgraber, Sigismund Kobe
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Abstract: This study focuses on the problem of finding ground states of random instances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussian couplings. While the ground states of SK spin-glass instances can be obtained with branch and bound, the computational complexity of branch and bound yields instances of not more than about 90 spins. We describe several approaches based on the hierarchical Bayesian optimization algorithm (hBOA) to reliably identifying ground states of SK instances intractable with branch and bound, and present a broad range of empirical results on such problem instances. We argue that the proposed methodology holds a big promise for reliably solving large SK spin-glass instances to optimality with practical time complexity. The proposed approaches to identifying global optima reliably can also be applied to other problems and they can be used with many other evolutionary algorithms. Performance of hBOA is compared to that of the genetic algorithm with two common crossover operators.
Comments: Also available at the MEDAL web site, this http URL
Subjects: Disordered Systems and Neural Networks (cond-mat.dis-nn)
Report number: MEDAL Report No. 2008004
Cite as: arXiv:0801.2997 [cond-mat.dis-nn]
  (or arXiv:0801.2997v1 [cond-mat.dis-nn] for this version)
  https://doi.org/10.48550/arXiv.0801.2997
Journal reference: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2008), ACM Press, 447-454.
Related DOI: https://doi.org/10.1145/1389095.1389176

Submission history

From: Martin Pelikan [view email]
[v1] Mon, 21 Jan 2008 00:19:26 UTC (481 KB)
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