In minimization problems, a basic obstacle to the determination of the global minimum is the presence of local minima. Iterative methods for seeking a minimum, such as hill climbing, can get trapped in a neighbourhood of a local minimum, because escaping from such a neighbourhood would involve a temporary increase in the value of the function that is to be minimized.
The solution to this problem proposed by simulated annealing is to suspend the minimization process occasionally, in the hope that this will allow the process to escape from a local minimum to some other minimum, and possibly to the global minimum. The process is controlled by a parameter which is varied during the course of the process is such a way as to ensure that escape may occur frequently in the early stages of the process, and less and less frequently as the process continues. This parameter is the analogue of the temperature in physical annealing, where the temperature controls the mobility of atoms and molecues, making them less mobile as the substance cools.
Simulated annealing is an iterative minimization process in which the system moves from state to state, subject to the temperature parameter. At each stage, the system can move either to a state for which the energy is higher than its present state, or to a state of lower energy. The decision as to which state is made randomly, the probabilities of each being determined by the temperature parameter. Early in the process the temperature parameter is high, as is the probability of moving to a state of higher energy. As the process continues, the temperature parameter is reduced, and with it the probability of moving to a state of higher energy. This procedure is applicable to a number of different minimization procedures, and has been found to be effective in finding the global minimum or minima close to the global one.