Simulated Annealing

Simulated annealing is a metaheuristic optimization algorithm inspired by the annealing process in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects. In the context of optimization problems, simulated annealing is used to find an approximate global optimum in a large search space. It starts with a random solution and iteratively makes small changes to the solution.

At each iteration, changes that improve the optimization objective are accepted, and changes that worsen the objective may also be accepted with a probability that decreases with time, allowing the algorithm to escape local optima in the early stages and refine towards a global optimum as the "temperature" decreases. This cooling schedule is critical to the effectiveness of simulated annealing, balancing exploration of the search space with convergence to an optimal solution.

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Simulated annealing is applied in various domains requiring optimal solutions in complex search spaces. In AI and ML, it can be used for feature selection where the goal is to find the best subset of features that maximizes model performance; each state represents a different combination of features, and simulated annealing navigates through these states to find the optimal set.

In scheduling problems, such as the traveling salesman problem, simulated annealing helps find the shortest possible route that visits a set of cities and returns to the origin city. In these examples, simulated annealing provides a flexible and powerful approach to finding near-optimal solutions where exhaustive search is computationally infeasible, leveraging its ability to navigate large and complex search spaces efficiently.

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