MATLAB Implementation of the Classic Simulated Annealing (SA) Algorithm

Simulated Annealing (SA) algorithm is a global optimization method inspired by the metallurgical annealing process, commonly used for solving complex function extremum problems. This algorithm mimics the gradual cooling of high-temperature materials, performing random exploration in the search space while gradually converging to the optimal solution, with the capability to escape local optima.

The core logic for implementing the classic SA algorithm in MATLAB can be divided into the following steps: Parameter Initialization: Set control parameters including initial temperature, stopping temperature, and cooling coefficient, while randomly generating an initial solution. Neighborhood Search: Generate new solutions near the current solution, typically achieved through small perturbations (e.g., using random number generation with MATLAB's rand function). Energy Evaluation: Calculate the objective function value (termed "energy") of the new solution and compare it with the current solution (implemented through function handles in MATLAB). Metropolis Criterion: Accept worse solutions with a certain probability to avoid local optima traps, where acceptance probability decreases as temperature reduces (calculated using exp(-ΔE/T) where ΔE is energy difference). Cooling Process: Reduce temperature according to a predefined cooling schedule (e.g., exponential cooling implemented as T = α*T where α is cooling rate). Termination Condition: Output the current optimal solution when temperature drops below the stopping threshold or maximum iterations are reached.

Taking function extremum solving as an example, assuming the objective function is multimodal (such as Rastrigin function), the SA algorithm can effectively avoid local extremum points and approach the global optimum by adjusting temperature parameters and neighborhood search range. Key implementation considerations in MATLAB include: Temperature decay rate must balance convergence efficiency and search scope; Neighborhood perturbation magnitude should dynamically adjust with temperature changes; Multiple independent runs can improve result stability through statistical analysis.

This algorithm is suitable for engineering optimization, machine learning parameter tuning scenarios, and performs particularly well for non-convex, multi-extremum problems.