Finding Function Extremes Using Artificial Intelligence Algorithm - Simulated Annealing Algorithm

In the MATLAB environment, the simulated annealing algorithm - one of the artificial intelligence algorithms - can be used to solve function extremes. Simulated annealing is a probability-based global optimization algorithm that finds optimal solutions by simulating the annealing process. Below is a MATLAB program example using simulated annealing to solve function extremes: The program begins with parameter initialization where T0 represents the initial temperature (100), Tf the final temperature (1), alpha the cooling coefficient (0.95), and iter the maximum iteration count (1000). The algorithm starts with random initial solutions for both current (x) and best (best_x) solutions. The core implementation features a temperature-controlled iteration loop that: - Generates new solutions using Gaussian-distributed random steps proportional to current temperature - Calculates solution differences (delta) between current and new solutions - Employs Metropolis criterion for acceptance probability: p = exp(-delta/T0) - Updates current solution based on probability comparison with random threshold - Continuously updates the best solution when better values are found - Implements exponential cooling schedule: T0 = T0 * alpha - Includes termination condition when temperature drops below Tf The function definition section demonstrates a sample quadratic function f(x) = x^2, which can be modified according to specific optimization requirements. Key implementation aspects include the balance between exploration (high temperature phase) and exploitation (low temperature phase), and the probabilistic acceptance mechanism that helps escape local optima. By running this program, you can utilize the simulated annealing algorithm in MATLAB to solve function extreme value problems, with the algorithm particularly effective for non-convex optimization problems where traditional gradient-based methods might fail. Note: The actual function f(x) should be defined according to the specific optimization problem, and parameters may need tuning for different applications to achieve optimal performance.