# Simulated Annealing (SA) Algorithm

May 11th, 2015
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Simulated Annealing (SA) is a popular local search meta-heuristic which inspired by the annealing in solids. The idea of SA was generated by a paper published by Metropolis in 1953. The paper related the algorithm to simulate cooling of material in a heat bath. This process is called annealing.

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Simulated Annealing (SA) AlgorithmAbstractSimulated Annealing (SA) is a popular local search meta-heuristic which inspired by the annealing in solids. The idea of SA was generated by a paper published by Metropolis in 1953. The paper related the algorithm to simulate cooling of material in a heat bath. This process is called annealing. The algorithm simulates the cooling process by gradually lowering the temperature of the system until it converges to a steady, frozen state. In 1982, Kirkpatrick et al used the idea of the algorithm and applied to optimisation problems. The idea is to use simulated annealing to search for feasible solutions and converge to an optimal solution. Another main feature to be known in this simulated annealing is that it uses hill-climbing moves to escape local optima in finding global optimum solution. In this paper we will look more on application of Simulated Annealing to discrete and continuous optimization problems, application of convergence theory and also its certain implications on recent advances. Keywords: Meta-heuristics, Discrete and Continuous Optimization, Local Search Algorithms, Simulated Annealing, Convergence Theory.1.0 IntroductionSimulated annealing is a technique for combinational optimization problems, such as minimizing functions of many variables. It is a method created based by an analogy to the statistical mechanics of annealing in solids. For example, lets consider silicon which is in low energy state; the

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