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].
Islam TeCNo on 09 Jun 09Algorithm for finding shortest path is graph
recommended !! :D Mathematics for Algorithmic Sets Functions and Relations Vectors and Matrices Linear Inequalities and Linear Equations Greedy Algorithms Knapsack Problem o O-I Knapsack o Fractional Knapsack * Activity Selection Problem * Huffman's Codes * Minimum Spanning Tree * Kruskal's Algorithm * Prim's Algorithm * Dijkstra's Algorithm Divide & Conquer Algorithms Dynamic Programming Algorithms * Knapsack Problem DP Solution * Activity Selection Problem DP Solution Amortized Analysis * Aggregate Method * Accounting Method * Potential Method * Dynamic Table Hash Table Binary Search Tree Graph Algorithms * Breadth First Search (BFS) * Depth First Search (DFS) * Topological Sort * Strongly Connected Components * Euler Tour * Generic Minimum Spanning Tree * Kruskal's Algorithm * Prim's Algorithm * Single Source Shortest Path o Dijkstra's Algorithm o Bellman-Ford Algorithm String Matching * Naïve String Matching * Knuth-Morris-Pratt Algorithm * Boyer-Moore Algorithm Sorting * Bubble Sort * Insertion Sort * Selection Sort * Shell Sort * Heap Sort * Merge Sort * Quick Sort Linear-Time Sorting * Counting Sort * Radix Sort * Bucket Sort Computational Geometry Computational Complexity * Information-Theoretic Argument * Adversary Argument * NP-Completeness And Reduction Approximate Algorithms * Vertex Cover * The Traveling Salesman Problem Linear Programming Appendix 1. Parabola 2. Tangent Codes References hoping to discuss these algorithms with each other !
