Simulated Annealing Algorithm

In computer science, simulated annealing is a stochastic optimization algorithm designed to find global optimum solutions within large search spaces. The algorithm derives its name from the physical annealing process in metallurgy, where materials are heated to high temperatures and then gradually cooled to achieve a minimal-energy crystalline state. Similarly, the algorithmic process begins with random exploration of the solution space and progressively reduces randomness through a cooling schedule, allowing the search to concentrate around global optima. Key implementation components include: 1) A temperature parameter controlling acceptance probabilities, 2) A neighbor generation function for creating candidate solutions, and 3) An acceptance criterion that occasionally permits suboptimal moves to escape local minima using the Metropolis-Hastings algorithm. Practically applied in combinatorial optimization and machine learning domains, simulated annealing demonstrates remarkable flexibility and robustness through features like adaptive cooling schedules and restart mechanisms. The algorithm's core function can be implemented with a temperature-decay loop that evaluates energy differences between current and proposed states, making it particularly effective for NP-hard problems like traveling salesman and circuit design.