Hierarchical BOA, Cluster Exact Approximation, and Ising Spin Glasses

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 based on singlebit flips and cluster exact approximation (CEA). The results show that hBOA significantly outperforms GA and UMDA on a broad spectrum of spin-glass instances and that CEA enables all tested algorithms to solve larger spin-glass instances. 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.