Obtaining ground states of ising spin glasses via optimizing bonds instead of spins

ABSTRACT

Frustrated Ising spin glasses represent a rich class of challenging optimization problems that share many features with other complex, highly multimodal optimization and combinatorial problems. This paper shows that transforming candidate solutions to an alternative representation that is strongly tied to the energy function simplifies the exploration of the space of potential spin configurations and that it significantly improves performance of evolutionary algorithms with simple variation operators on Ising spin glasses. The proposed techniques are incorporated into the simple genetic algorithm, the univariate marginal distribution algorithm, and the hierarchical Bayesian optimization algorithm.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.6 Learning

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.6 Optimization

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.8 Problem Solving, Control Methods, and Search

General Terms:
Algorithms, Performance

Keywords:
genetic algorithm, hierarchical BOA, problem transformation, spin glass, univariate marginal distribution algorithm