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

We compare the performance of extremal optimization (EO), flathistogram and equal-hit algorithms for finding spin-glass ground states. The first-passage-times to a ground state are computed. At optimal parameter of τ = 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.