A comparison of extremal optimization with flat-histogram dynamics for finding spin-glass ground states

TL;DR

This paper compares extremal optimization, flat-histogram, and equal-hit algorithms for finding spin-glass ground states, highlighting their performance differences and potential for equilibrium thermodynamic calculations.

Contribution

It introduces a comparison of these algorithms' efficiency and proposes a method to adapt EO for equilibrium thermodynamic calculations.

Findings

EO outperforms others for small systems at optimal parameters

Equal-hit algorithm is competitive for large systems

Flat-histogram and equal-hit enable thermodynamic calculations

Abstract

We compare the performance of extremal optimization (EO), flat-histogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of tau=1.15, EO outperforms other methods for small system sizes, but equal-hit algorithm is competitive to EO, particularly for large systems. Flat-histogram and equal-hit algorithms offer additional advantage that they can be used for equilibrium thermodynamic calculations. We also propose a method to turn EO into a useful algorithm for equilibrium calculations. Keywords: extremal optimization. flat-histogram algorithm, equal-hit algorithm, spin-glass model, ground state.