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

TL;DR

This paper explores using hierarchical Bayesian optimization and genetic algorithms to find ground states of large, complex SK spin-glass models, surpassing traditional methods in scalability and reliability.

Contribution

It introduces a novel application of hBOA and genetic algorithms for large SK instances, demonstrating improved scalability and reliability over branch and bound methods.

Findings

hBOA reliably finds ground states for larger SK instances

Genetic algorithms with common crossover operators are compared to hBOA

Proposed methods show promise for solving large-scale spin-glass problems

Abstract

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.