Journal of Physics A Mathematical and General

Using computer experiments on a simple three-state system and an NP-complete system of permanents we compare different proposed simulated annealing schedules in order to find the cooling strategy which has the least total entropy production during the annealing process for given initial and final states and fixed number of iterations. The schedules considered are constant thermodynamic speed, exponential, logarithmic, and linear cooling schedules. The constant thermodynamic speed schedule is shown to be the best. We are actually considering two different schedules with constant thermodynamic speed, the original one valid for near-equilibrium processes, and a version based on the natural timescale valid also at higher speeds. The latter one delivers better results, especially in case of fast cooling or when the system is far from equilibrium. Also with the lowest energy encountered during the entire optimization (the best-so-far-energy) as the indicator of merit, constant thermodynamic speed is superior. Finally, we have compared two different estimators of the relaxation time. One estimator is using the second largest eigenvalue of the thermalized form of the transition probability matrix and the other is using a simpler approximation for small deviations from equilibrium. These two different expressions only agree at high temperatures.

A comparison of simulated annealing cooling strategies