Simulated Annealing
Simulated annealing is a method of exploring complex search spaces to find optimal solutions. It is typically used for optimization problems, which involve adjusting parameters of a system to arrive at a result which maximizes or minimizes some objective function. It is a probabilistic method, which means that the series of steps taken by the algorithm, called a trajectory, is random, but directed towards the global optimum of the system.
The name “simulated annealing” comes from the physical process of annealing, in which a material is heated to a high temperature and then slowly cooled to some equilibrium state. This slow cooling allows crystallization defects to move off of boundaries and into the bulk of the material, which allows the material to arrive at a position of lower energy than it would have in a rapid cooling. In the same way, simulated annealing explores solutions by randomly jumping around the search space, but with a bias toward the regions of the space with lower energy- the least-costly solutions.
At each step of the algorithm, a new solution is constructed by making a small random change in the current solution. If the new solution has an objective score which is better than the current solution, then it is accepted as the current solution. If the new solution has an objective score which is worse than the current solution, then it is accepted as the current solution with a certain probability- the probability decreases as the difference between the scores increases. This probability also decreases with each step in the trajectory.
Simulated annealing is well-suited to problems in which the optimization space is large and complex, has multiple local optima, and does not have well-defined gradient field that can be used for gradient-descent techniques. It is also well-suited to problems where there is some uncertainty or noise which can be accounted for by accepting solutions with worse scores with some probability.
One of the advantages of simulated annealing is that it tends to find better solutions than other methods, even when the solutions are not optimal. It is particularly powerful when the underlying problem is a complex nonlinear system.
Simulated annealing can also be used to solve a variety of optimization problems, including the traveling salesman problem, bin packing, and scheduling problems. It has been used in the design of integrated circuits, robotics, engineering, computers and discrete optimization.
Simulated annealing is not without its drawbacks. It can be slow, in that it involves many random steps in its search which can take a long time. It can also be difficult to tune the algorithm to the specific problem, since the optimal parameters can vary depending on the problem. Finally, if the optimization space is too large, finding the global optimum can be impossible due to the random nature of the search.
Despite its drawbacks, simulated annealing is a powerful optimization technique, and can be used to solve a variety of problems where gradient-based methods are not applicable or not very effective. Its ability to identify near-optimal solutions, even in highly complex search spaces, makes it an attractive tool for a wide range of applications.
