  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.
