Implementation of Simulated Annealing Algorithm with MATLAB Code Examples

Simulated Annealing is a heuristic optimization algorithm inspired by the annealing process in metallurgy. This algorithm mimics the gradual cooling of materials from high temperatures, allowing acceptance of inferior solutions with a certain probability to escape local optima, ultimately finding global or near-optimal solutions in the solution space.

Core Algorithm Concept Simulated Annealing controls the search process through temperature parameters: Initial High-Temperature Phase: The algorithm tends to accept worse solutions to expand search range and avoid local optima. Gradual Cooling Phase: As temperature decreases, the probability of accepting inferior solutions reduces, and the algorithm converges toward optimal solutions. Termination Condition: The algorithm stops when temperature drops below a threshold or solution changes stabilize, outputting the current best solution.

MATLAB Implementation Key Points Implementing Simulated Annealing in MATLAB typically involves: Objective Function Definition: Define the optimization target function where variables are adjusted to minimize/maximize the function value. Example: f = @(x) x(1)^2 + x(2)^2; Initial Solution and Temperature Settings: Generate random initial solutions and set parameters like initial temperature (T_init), final temperature (T_min), and cooling rate (alpha). Neighborhood Search Strategy: Generate new solutions near current solutions through small perturbations or specific rules using functions like randn for Gaussian disturbances. Metropolis Criterion: Calculate acceptance probability for worse solutions using exp(-deltaE/T) where deltaE is energy difference and T is current temperature. Iteration and Cooling: Loop through search and acceptance processes while gradually reducing temperature according to cooling schedule (T = alpha*T) until termination conditions are met.

Advantages and Applications Simulated Annealing is suitable for complex nonlinear optimization problems including combinatorial optimization, path planning, and parameter tuning. Its MATLAB implementation is intuitive and easily adjustable, making it ideal for engineering optimization and research experiments. Proper configuration of temperature decay strategies and neighborhood search ranges can significantly improve convergence speed and solution accuracy.