MATLAB Implementation of Simulated Annealing Algorithm for Function Minimization

This implementation demonstrates simulated annealing algorithm in MATLAB for finding the minimum value of a function. Simulated annealing is a stochastic optimization algorithm that mimics the metallurgical annealing process, gradually reducing temperature to search for global optimal solutions. The algorithm effectively handles complex optimization problems and finds extensive applications across various domains including engineering design, operations research, and artificial intelligence. Key implementation aspects include defining appropriate parameters: initial temperature (T0), cooling rate (alpha), and acceptance probability criteria. The code structure typically involves: - Initial solution generation using random initialization or heuristic methods - Temperature scheduling through geometric cooling: T(k+1) = alpha * T(k) - Neighborhood solution generation via perturbation functions - Acceptance probability calculation using Boltzmann distribution: P = exp(-ΔE/T) The algorithm iteratively updates solution states through metropolis criteria, where worse solutions may be accepted with certain probability to escape local optima. Critical MATLAB functions employed include: - rand() for random number generation in solution perturbation - exp() for probability calculations - Objective function evaluation at each iteration Parameter tuning is essential based on problem characteristics - larger initial temperatures enable broader exploration while slower cooling rates improve solution quality. The implementation gradually converges to global optimum through controlled randomization, providing approximate minimum values with proven effectiveness in function optimization.