The successful application of the stochastic optimization method known as simulated annealing can depend very much on the appropriate annealing schedule. While determining optimal schedules for arbitrary complex optimization problems is beyond the current scope, we here determine optimal schedules for a special class of systems with known properties. The state spaces of these special systems have the structure of self similar trees. Using methods of optimal control theory, we are able to predict the optimal schedule analytically for two distinct optimization criteria. These predictions are shown to be in good agreement with numerical results. ©1995 American Institute of Physics.