Computational Complexity and Simulation of Rare Events of Ising Spin Glasses

We discuss the computational complexity of random 2D Ising spin glasses, which represent an interesting class of constraint satisfaction problems for black box optimization. Two extremal cases are considered: (1) the ±J spin glass, and (2) the Gaussian spin glass. We also study a smooth transition between these two extremal cases. The computational complexity of all studied spin glass systems is found to be dominated by rare events of extremely hard spin glass samples. We show that complexity of all studied spin glass systems is closely related to Fr´echet extremal value distribution. In a hybrid algorithm that combines the hierarchical Bayesian optimization algorithm (hBOA) with a deterministic bit-flip hill climber, the number of steps performed by both the global searcher (hBOA) and the local searcher follow Fr´echet distributions. Nonetheless, unlike in methods based purely on local search, the parameters of these distributions confirm good scalability of hBOA with local searc...

• Type: Conference
• Year: 2004
• Where: GECCO
• Authors: Martin Pelikan, Jiri Ocenasek, Simon Trebst, Matthias Troyer, Fabien Alet
• Keywords: GECCO 2004, Spin Glass, Spin Glass Systems, Spin Glasses