How fast should one anneal?
The answer is, of course, dependent upon the optimization problem. However, because Simulated Annealing has its origin from Statistical Mechanics, we know that as one nears a phase transition the specific heat, i.e. CV = dE/dT, shows (possibly sharp) structure as the system cools. When the equivalent of CV in the optimization problem begins to grow, this is a signal (as it is in standard thermodynamic simulations) that we should anneal more slowly so as to access more properly the phase space, for we are approaching a possible change in system trajectory (analogous to a phase transition). There can be critical slowing down and hystersis. Hence, by monitoring the thermodynamically equivalent quantity that is important in the optimization problem (possible something other than CV, such as susceptibility, diffusion, etc.), we may alter the annealing rate to make the search for efficient. This important technique will help in not finding a false “optimal” point. You will note below for the
