Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA can find the global optimum. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where a fixed amount of computing resource is available, finding an approximate global optimum may be more relevant than attempting to find a precise local optimum. In such cases, SA may be preferable to exact algorithms such as gradient descent or branch and bound. The problems solved by SA are currently formulated by an objective function of many variables, subject to several mathematical constraints. In practice, a constraint violation can be penalized as part of the objective function.
Similar techniques have been independently introduced on several occasions, including Pincus (1970), Khachaturyan et al. (1979, 1981), Kirkpatrick, Gelatt and Vecchi (1983), and Cerny (1985). In 1983, this approach was used by Kirkpatrick, Gelatt Jr., and Vecchi for a solution of the traveling salesman problem. They also proposed its current name, simulated annealing.
