Cooling Schedules for Optimal Annealing

A Monte Carlo c^timization technique called "simulated annealing" is a descent algorithm modified by random ascent moves in order to escape local minima which are not global minima. Tlie levd of randomization is determined by a control parameter T, called temperature, which tends to zero according to a deterministic "cooling schedule". We give a simple necessary and suffident conditicm on the cooling sdiedule for the algorithm state to converge in probability to the set of globally minimiim cost states. In the spedal case that the cooling schedule has parameuic form r({) » c/log(l + / ) , the condition for convergence is that c be greater than or equal to the depth, suitably defined, of the deepest local minimum which is not a global minimum state.