Simulated Annealing
Simulated annealing is a commonly used metaheuristic for optimization problems. It is based on the natural process of annealing in metallurgy, where a material is heated to a very high temperature and gradually cooled. Simulated annealing is used in many optimization problems, such as scheduling, routing, design optimization and other combinatorial optimization problems. It is also commonly used in artificial intelligence applications, such as neural networks and game playing.
Simulated annealing is an iterative optimization method that takes inspiration from the process of annealing in metals. In this process, metals are cooled slowly enough so that the resulting structure is in the lowest energy state. By “slowly” cooling the material, the atoms are given time to find the lowest energy state in a relaxed manner. This slow cooling of the material also allows for a number of structures to find their lowest energy state.
In simulated annealing, the objective is to find a solution that minimizes an objective function, such as a cost function or energy function, by simulating a physical system. This is done iteratively by randomly selecting feasible solutions and gradually cooling them. As the selected solution is cooled, its energy tends to decrease towards the global minimum value. Similarly, when the solutions are initially heated up, they tend to explore the search space more extensively.
The temperature of the system is an important parameter which drives the search process and ultimately affects the quality of the solution. The temperature is an upper bound to the magnitude of the solutions that can be explored and should be cooled gradually over time. This ensures that more promising solutions are explored, while irrelevant solutions are discarded.
The search process in simulated annealing involves randomly choosing feasible solutions from a list of available solutions and gradually cooling the system. This process is iterative and the temperature should be gradually reduced over time. The probability of accepting a move depends on the energy difference between the current solution and the proposed solution. An energy difference which is too great is unlikely to be accepted, as it could potentially lead to an incorrect solution.
The cooling schedule is one of the important factors which affects the quality of the solutions. A faster cooling rate will result in poorer solutions, while slower cooling rate is likely to produce higher quality solutions. However, the cooling rate should not be too slow, as the search process could get stuck at a local minimum.
The acceptance criterion is also important and should be adjusted according to the desired solution quality. More stringent acceptance criteria typically result in better solutions and faster convergence, but too stringent acceptance criteria could cause the search to get stuck in a local minimum.
Simulated annealing is a powerful optimization technique which is used for many real-world problems in combinatorial optimization, scheduling, routing and artificial intelligence. It enables us to effectively search the space of feasible solutions and find the best solution for the problem at hand. However, the quality of the solutions is highly dependent on the cooling schedule and acceptance criteria which should be set according to the desired solution quality. If done correctly, simulated annealing can provide near optimal solutions for many types of optimization problems.
