Searching for ground states of Ising spin glasses with hierarchical BOA and cluster exact approximation

Abstract

This chapter applies the hierarchical Bayesian optimization algorithm (hBOA) to the problem of finding ground states of Ising spin glasses with ±J and Gaussian 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 single-bit flips. The results show that hBOA significantly outperforms GA and UMDA on a broad spectrum of spin glass instances. Cluster exact approximation (CEA) is then described and incorporated into hBOA and GA to improve their efficiency. The results show that CEA enables all tested algorithms to solve larger spin glass instances and that hBOA significantly outperforms other compared algorithms even in this case. © Springer-Verlag Berlin Heidelberg 2006.