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This study focuses on the problem of finding ground states of randominstances of the Sherrington-Kirkpatrick (SK) spin-glass model with Gaussiancouplings. While the ground states of SK spin-glass instances can be obtainedwith branch and bound, the computational complexity of branch and bound yieldsinstances of not more than about 90 spins. We describe several approaches basedon the hierarchical Bayesian optimization algorithm (hBOA) to reliablyidentifying ground states of SK instances intractable with branch and bound,and present a broad range of empirical results on such problem instances. Weargue that the proposed methodology holds a big promise for reliably solvinglarge SK spin-glass instances to optimality with practical time complexity. Theproposed approaches to identifying global optima reliably can also be appliedto other problems and they can be used with many other evolutionary algorithms.Performance of hBOA is compared to that of the genetic algorithm with twocommon crossover operators.

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