  An alternative to Monte Carlo techniques requiring large sampling times is
presented here. Ideas from a genetic algorithm are used to select the best
initial states from many independent, parallel Metropolis-Hastings iterations
that are run on a single graphics processing unit. This algorithm represents
the idealized limit of the parallel tempering method and, if the threads are
selected perfectly, this algorithm converges without any Monte Carlo
iterations--although some are required in practice. Models tested here (Ising,
anti-ferromagnetic Kagome, and random-bond Ising) are sampled on a time scale
of seconds and with a small uncertainty that is free from auto-correlation.
