Numerical Analysis Questions
Simulated annealing is a stochastic optimization algorithm used in numerical analysis. It is inspired by the annealing process in metallurgy, where a material is heated and slowly cooled to reduce defects and improve its structure. In the context of numerical analysis, simulated annealing is used to find the global optimum of a given function in a large search space.
The concept of simulated annealing involves starting with an initial solution and iteratively exploring the search space by making small random changes to the current solution. These changes are accepted or rejected based on a probability distribution, which is influenced by the current temperature parameter. Initially, the algorithm allows for more exploratory moves, but as the temperature decreases, it becomes more selective and focuses on exploiting promising regions.
Simulated annealing is particularly useful when dealing with complex optimization problems that may have multiple local optima. By allowing occasional uphill moves, simulated annealing can escape local optima and eventually converge to the global optimum. The cooling schedule, which determines how the temperature decreases over time, plays a crucial role in the algorithm's performance and finding an optimal solution.
Overall, simulated annealing provides a powerful approach for solving optimization problems in numerical analysis by combining random exploration and exploitation strategies, mimicking the annealing process in metallurgy.