Simulated Annealing (SA) is a popular optimization method widely used for nonlinear and constraint optimization problems. Simulated Annealing (SA) is an iterative optimization technique based on the physical process of annealing in metallurgy, which inspired its name. SA was developed and first described by Kirkpatrick et al.in 1983.
The major idea of simulated annealing is stochastic optimization by gradually changing the temperature of the system, which can improve the solution in an appropriate direction. Generally speaking, simulated annealing (SA) searches for an optimal solution of the problem by gradually decreasing the temperature of the system. When the “temperature” is high enough, the solution of the problem is generated randomly and it is more likely to accept the complex states. As the temperature decreases, the generated solution is more precise, and the optimum solution can be obtained when the temperature reaches the “effective zero”.
Simulated annealing can be viewed as a restricted form of a genetic algorithm, where each person consists of real numbers instead of genes. The advantage of simulated annealing over a naive random search is its use of memory of previously visited solutions. This allows the algorithm to identify the best solution from a set of much more random solutions.
The iterative process of SA is described as follows:
At first, a starting temperature is set. At each iteration, a solution is randomly generated as a candidate solution. If this solution is better than the current one, it is accepted; if worse, it is accepted with a certain probability. This probability is calculated with a Boltzmann factor that is based on the difference of the two solutions at the current temperature.
The temperature is then decreased. Repeat this process until some predefined stopping criterion is met.
The effectiveness of SA lies on four parameters - the initial temperature, the cooling rate, the length of each run, and the definition of better, which is usually defined by some energy (cost) function.
Therefore SA has several advantages:
* Global optima may be found, as the algorithm samples all possible solutions in its search space.
* It is not prone to get stuck in local minima, due to its stochastic nature.
* It is simple and easy to implement.
* It works well for both discrete and continuous optimization problems.
However, simulated annealing does have some drawbacks. Its effectiveness is strongly related to the choice of the four parameters mentioned above. If the parameters are not set reasonably, SA may not find global optima or take too much time to find them. Also, SA is sensitive to the definition of better, which can be difficult to formulate correctly in some cases.
In conclusion, simulated annealing is an effective optimization technique that can be used in a variety of situations. It has its advantages and disadvantages, but it can be very useful in many optimization problems, when the parameters are set right and the problem is defined properly.
