Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of applied mathematics, namely locating a good approximation to the global minimum of a given function in a large search space. It is often used when the search space is discrete (e.g., all tours that visit a given set of cities). For certain problems, simulated annealing may be more effective than exhaustive enumeration — provided that the goal is merely to find an acceptably good solution in a fixed amount of time, rather than the best possible solution.
The name and inspiration come from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. The heat causes the atoms to become unstuck from their initial positions (a local minimum of the internal energy) and wander randomly through states of higher energy; the slow cooling gives them more chances of finding configurations with lower internal energy than the initial one.
By analogy with this physical process, each step of the SA algorithm replaces the current solution by a random "nearby" solution, chosen with a probability that depends on the difference between the corresponding function values and on a global parameter T (called the temperature), that is gradually decreased during the process. The dependency is such that the current solution changes almost randomly when T is large, but increasingly "downhill" as T goes to zero. The allowance for "uphill" moves saves the method from becoming stuck at local minima—which are the bane of greedier methods.
The method was independently described by S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi in 1983 [1], and by V. Černý in 1985 [2]. The method is an adaptation of the Metropolis-Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, invented by N. Metropolis et al. in 1953 [3].
Cached
Janos Haits on 08 May 17"Explore simultaneously in space and time with Time Machine Each Time Machine on this page captures a process in extreme detail over space and time, with billions of pixels of explorable resolution. Choose a time machine and zoom into the image while traveling backwards or forwards through time. Select a Time Warp and the time machine's authors will take you on a guided space-time tour with text annotations explaining what you are viewing. You can even learn how to create your own Time Machines and Warps."
