MATLAB Implementation of Simulated Annealing Algorithm

Simulated Annealing is a global optimization algorithm inspired by the metallurgical annealing process, commonly used to solve complex nonlinear optimization problems. The core concept simulates physical annealing by accepting inferior solutions with a certain probability to escape local optima. Implementing this algorithm in MATLAB environment effectively addresses various mathematical modeling and engineering optimization challenges. Algorithm Core Logic Parameter Initialization: Set key parameters including initial temperature, termination temperature, cooling coefficient, and generate random initial solution. Iterative Search: Randomly generate new solutions within the neighborhood of current solution and calculate objective function value changes. Metropolis Criterion: Determine acceptance of new solutions based on temperature and objective function difference (even worse solutions may be accepted with probability proportional to temperature). Cooling Process: Gradually reduce temperature according to preset cooling coefficient until termination conditions are met. MATLAB Implementation Features Uses loop structures to implement iterative temperature reduction combined with random number generation for neighborhood solutions. Leverages vectorization operations to enhance computational efficiency, particularly for complex objective functions. Highly extensible design - simply replace the objective function to adapt to different problems (e.g., TSP problems, function extremum solving). Typical Application Scenarios Combinatorial optimization problems (resource scheduling, path planning) Multimodal optimization of continuous functions Hyperparameter tuning in machine learning The MATLAB implementation typically includes modular designs for temperature decay strategies and neighborhood search methods. Users can balance search breadth and precision by adjusting parameters through clear interface functions like defining custom cooling schedules and neighborhood generation functions.