MATLAB Implementation of Classic Algorithms: Simulated Annealing for Global Optimization

Simulated Annealing is a global optimization algorithm inspired by the metallurgical annealing process, particularly suitable for solving complex nonlinear optimization problems. Its core concept mimics the physical process of high-temperature objects gradually cooling down to search for optimal solutions in the solution space. The algorithm workflow can be summarized into several key steps: First, generate a random initial solution and set the initial temperature. During each iteration, the algorithm produces a new solution by applying random perturbations to the current solution, then decides whether to accept this new solution based on the energy difference (i.e., the change in objective function value) and current temperature. As temperature gradually decreases, the probability of accepting worse solutions reduces, eventually converging near the global optimum. When implementing in MATLAB, three key elements require special attention: the temperature decay function setup, state generation function design, and acceptance criterion implementation. Typical temperature decay methods include exponential decay and linear decay, while state generation commonly uses Gaussian perturbations or uniform perturbations. MATLAB's powerful matrix computation capabilities enable efficient implementation of these calculations, where vectorized operations can significantly accelerate the perturbation and acceptance evaluation processes. This algorithm is particularly suitable for complex optimization scenarios such as Traveling Salesman Problem, function optimization, and parameter estimation. Its main advantage lies in effectively avoiding local optima. In practical applications, tuning parameters like initial temperature, final temperature, and decay coefficient significantly impact algorithm performance, requiring experimental tuning to find optimal parameter combinations for specific problems. MATLAB's parameter sweeping tools can facilitate this tuning process through systematic experimentation. Compared to deterministic algorithms like gradient descent, Simulated Annealing's stochastic nature provides stronger global search capability at the cost of higher computational expense. Algorithm implementation typically requires balancing search breadth and computational efficiency, which is where MATLAB's vectorized programming can make significant contributions - for example, by simultaneously evaluating multiple candidate solutions using matrix operations rather than iterative loops.