Simulated Annealing
Simulated annealing is a randomized search technique used for optimization problems in computer science, operations research, and other fields. It is an extension of the Metropolis-Hastings algorithm, which is a Monte Carlo method used to calculate partition functions in statistical mechanics.
Simulated annealing was named after a metallurgical process where heating and cooling is used to increase the likelihood of obtaining a desirable result. The technique starts with a randomly generated solution and makes random changes, like the random heating and cooling that occurs in metallurgy. The solution is accepted or rejected based on a probabilistic acceptance criterion. If the proposed solution is better than the current solution, it becomes the current solution; otherwise, it is accepted with a certain probability related to the temperature parameter. As the temperature is gradually decreased, it becomes increasingly unlikely that solutions worse than the current solution will be accepted.
Algorithm
A simulated annealing algorithm begins with an initial solution and iteratively improves it. At each step, the algorithm randomly changes the current solution to get a candidate solution. If the candidate solution is better than the current solution, it is accepted as the new current solution; otherwise, it is accepted with a certain probability related to the temperature parameter. The temperature parameter is gradually decreased over time, thereby decreasing the probability that solutions worse than the current solution will be accepted.
The basic algorithm of simulated annealing can be represented using pseudocode as follows:
1. Set the initial solution
2. Set the initial temperature
3. Repeat until the stopping criterion is met:
i. Generate a random change to the current solution
ii. Calculate the cost of the candidate solution
iii. If the cost of the candidate solution is better than the cost of the current solution, accept the candidate solution as the current solution
iv. Otherwise, accept the candidate solution with a probability proportional to the difference in cost
4. Output the best solution
Applications
Simulated annealing has many applications in optimization problems. It has been successfully applied to problems such as the traveling salesman problem, the quadratic assignment problem, and the protein folding problem. Simulated annealing has also been applied to scheduling, placement, and scheduling problems in the production and transportation industries. Additionally, simulation techniques are frequently used to optimize robotic motion planning and path planning in autonomous robotics.
Conclusion
Simulated annealing is a powerful optimization technique for finding the optimal solution to many different types of problems. By randomly changing the current solution and evaluating it based on a probability criterion, simulated annealing allows for an efficient search of the solution space to identify the optimal solution. The technique has been applied to a variety of problems and exhibit its capabilities as an effective optimization algorithm.
