Simulated Annealing (SA) is a stochastic global optimization procedure that is based on the principles of thermodynamics.SA, also known as annealing process,is designed to find the global optimum of a complex nonlinear system. The global optimum is determined through successive reductions in temperature. In annealing, a given solution is gradually cooled until a solution with minimum energy is attained.
The objective of simulated annealing is to find a solution in a limited search space that minimizes or satisfies a given criterion. This can be done by using a temperature gradient, or cooling rate. In simulated annealing a given solution is cooled until the minimum energy state is attained. However, the cooling rate should not be too rapid, as this could cause the system to remain stuck in a local optimum due to a lack of dynamism.
To achieve a successful optimization using simulated annealing it is desirable to start with a sufficiently high temperature and gradually reduce it by a certain amount. In practice, the cooling of a given solution is done iteratively, that is, over a number of iterations (called the annealing schedule). At each step the system is allowed to make a transition from one solution to another before the next step in the cooling process is initiated.
There are two primary forms of simulated annealing, namely complete annealing and incomplete annealing. Complete annealing involves cooling the given solution until it reaches the minimum energy state. This requires a large number of iterations in order to acheive success, as the process of cooling may cause the optimization to be stuck in a local optimum. This is due to the lack of dynamism that comes with the gradual cooling rate.
Incomplete annealing, on the other hand, involves cooling the solution from an initially high temperature to a lower temperature without completely reaching the minimum energy state. This method is often used when the goal is to find good solutions but not perfect solutions. Incomplete annealing has the advantage of being quicker than complete annealing, as it does not require as many iterations. Additionally, there is less risk of ending up with a local optimum.
The two main methods of performing simulated annealing are generic SA and differential SA (BDSA). Generic SA is a general technique for finding global optima, whereby a given solution is cooled until it is in a state of minimum energy. This requires a large number of iterations and a fixed cooling rate. BDSA, on the other hand, is a more specific approach to simulated annealing, as it involves cooling the solution in small increments. Unlike generic SA, the cooling rate is adjustable, meaning that it can be adjusted depending on the current optimization status.
Simulated annealing is a powerful optimization technique that has been successfully applied to a wide range of problems. Although complete annealing requires more iterations, it has the potential to result in better optima since it is more likely to find the global optimum. On the other hand, incomplete annealing is quicker and less prone to ending up with a local optimum. For this reason, it is often chosen when the goal is to find good solutions rather than perfect solutions.
