Simulated annealing is a probabilistic technique for approximating the global optimum of a given function. It is often used when the search space is discrete or continuous, and when the optimization problem is known to have multiple local optima. The method works by first selecting a random solution from the search space, then making slight changes to the solution in order to generate a new one. This process is repeated until the criterion for acceptance or rejection of a solution is satisfied.
Simulated annealing is based on the physical phenomenon of annealing, in which a solid material is slowly heated and then rapidly cooled in order to strengthen it. The concept is similar in simulated annealing; the function to be optimized is slowly cooled, like metal alloyed in a furnace.
Simulated annealing works by starting with a random starting point in the search space, and then making small changes to the solution in order to create a new solution. This process is repeated until the desired optimization value is reached. Each time a new solution is generated and compared to the previous solution, a criteria must be used to accept or reject the new solution. Usually, the best solution is to accept the new solution if it is better than the previous one, or if it is worse but the probabilities of such degradation are acceptable. This step is known as the acceptance criterion.
At each step of the optimization process, a scaling factor is applied in order to gradually lower the temperature of the function, thereby increasing the search space and decreasing the acceptance criterion. The scaling factor is usually an iterative function, reducing the temperature each time the same solution is evaluated. The temperature of the function also helps to prevent the algorithm from getting stuck in local optima.
Another important concept to consider in simulated annealing is the cooling schedule. The cooling schedule will determine how quickly the system cools and how much of the search space is explored before acceptance or rejection of a solution. Typically, a logarithmic cooling schedule is used, but there are other schedules available as well.
Overall, simulated annealing is a powerful technique for finding the global optimum. It is an iterative process that gradually reduces the temperature of the problem in order to move towards an optimal solution. The acceptance criterion and cooling schedule are two factors that are used to determine how successful the algorithm is in finding the optimum. It is an effective tool for solving complex optimization problems and can be used in many areas of engineering.
