Optimal simulated annealing schedules for larger problems

We present a method for optimizing parameters for a search algorithm (we choose simulated annealing as a specific example) on a finite search space. The search is described as a Markov process, giving the average cost on a specific problem as a function of the search parameters. A minimization is then performed over the parameter space to provide an optimal parameter set. We demonstrate this technique on a toy problem; we then use a 'barrier tree' model to reduce 20-variable Max-SAT problems from over a million search points to more manageable 30-40 states. The annealing schedules produced do not perform as well as predicted, but there is some evidence that a single schedule optimized over a problem set may produce better results.