Annealing is a technique in which a metal is heated to a high temperature, then allowed to cool slowly; this relieves internal stresses.

Simulated annealing[S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, ``Optimization by Simulated Annealing'', Science vol. 220, no. 4598 (13 May 1983), pp. 671-680.] is analogous to hill-climbing in which it is possible to make some moves that are locally non-optimal.

By analogy with statistical thermodynamics, it is assumed that the goal is to minimize the ``energy'' E of a system. If a move causes a change &Delta E ,

• If &Delta E &le 0 , the move is accepted.

• If &Delta E > 0 , the move is accepted with probability P(&Delta E) = e^{-&Delta Ek T} where k is the Boltzmann constant and T is temperature. (Compute a random number r in [0, 1] and accept the move if P(&Delta E) > r .)

In simulated annealing, an evaluation function f replaces E . An artificial ``temperature'' is created, initially high enough for many moves to be accepted, and progressively reduced.

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