Editing Simulated annealing (section)

===The annealing schedule===
{{multiple image
 | align = right
 | total_width = 400
 | image_gap = 1

 | image1 = SimulatedAnnealingFast.jpg
 | alt1 = Fast
 | caption1 = Fast

 | image2 = SimulatedAnnealingSlow.jpg
 | alt2 = Slow
 | caption2 = Slow

| footer= Example illustrating the effect of cooling schedule on the performance of simulated annealing.  The problem is to rearrange the [[pixel]]s of an image so as to minimize a certain [[potential energy]] function, which causes similar [[color]]s to attract at short range and repel at a slightly larger distance.  The elementary moves swap two adjacent pixels.  These images were obtained with a fast cooling schedule (left) and a slow cooling schedule (right), producing results similar to [[amorphous]] and [[crystalline solid]]s, respectively.
}}
The name and inspiration of the algorithm demand an interesting feature related to the temperature variation to be embedded in the operational characteristics of the algorithm. This necessitates a gradual reduction of the temperature as the simulation proceeds. The algorithm starts initially with <math>T</math> set to a high value (or infinity), and then it is decreased at each step following some ''annealing schedule''—which may be specified by the user but must end with <math>T=0</math> towards the end of the allotted time budget.  In this way, the system is expected to wander initially towards a broad region of the search space containing good solutions, ignoring small features of the energy function; then drift towards low-energy regions that become narrower and narrower, and finally move downhill according to the [[steepest descent]] heuristic.

For any given finite problem, the probability that the simulated annealing algorithm terminates with a [[global optimum|global optimal]] solution approaches 1 as the annealing schedule is extended.<ref>{{cite journal |doi=10.1109/34.295910 |title=Simulated annealing: A proof of convergence |year=1994 |last1=Granville |first1=V. |last2=Krivanek |first2=M. |last3=Rasson |first3=J.-P. |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=16 |issue=6 |pages=652–656}}</ref> This theoretical result, however, is not particularly helpful, since the time required to ensure a significant probability of success will usually exceed the time required for a [[Brute-force search|complete search]] of the [[solution space]].<ref>{{Citation |last1=Nolte |first1=Andreas |title=A Note on the Finite Time Behaviour of Simulated Annealing |date=1997 |url=http://link.springer.com/10.1007/978-3-642-60744-8_32 |work=Operations Research Proceedings 1996 |volume=1996 |pages=175–180 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-60744-8_32 |isbn=978-3-540-62630-5 |access-date=2023-02-06 |last2=Schrader |first2=Rainer}}</ref>