MATLAB Implementation of Simulated Annealing Algorithm with Code Optimization Techniques

Simulated Annealing is a classical optimization algorithm inspired by the physical process of annealing in metallurgy. This algorithm mimics the gradual cooling of high-temperature materials to find global optima in complex search spaces. When implementing simulated annealing in MATLAB, key components include: initializing temperature parameters, defining neighborhood search strategies, designing energy functions (objective functions), and establishing cooling schedules. The algorithm begins with an initial solution and a high starting temperature. During each iteration, MATLAB generates a new solution in the neighborhood of the current solution using random perturbation functions like rand or randn. The acceptance probability is calculated using the Metropolis criterion: exp(-ΔE/T), where ΔE represents the objective function difference and T is the current temperature. This allows worse solutions to be accepted with a certain probability, enabling escape from local optima. As temperature decreases according to cooling schedules (e.g., geometric cooling T_new = α*T_old where α=0.95), acceptance probability for inferior solutions gradually reduces, leading to convergence. MATLAB implementation requires customizing two primary functions: the objective function (typically implemented as a separate .m file) and the neighborhood generation mechanism (using vector operations for efficient computation). Key parameters like initial temperature, cooling rate, and iteration count per temperature level can be optimized using MATLAB's parameter tuning capabilities. Compared to other optimization algorithms like Genetic Algorithms (GA) and Ant Colony Optimization (ACO), simulated annealing offers simpler implementation through basic matrix operations and demonstrates strong performance on both continuous and discrete optimization problems. Beyond simulated annealing, MATLAB provides robust environments for implementing other intelligent algorithms: Ant Colony Optimization (ideal for pathfinding problems using pheromone matrix updates), Genetic Algorithms (global search methods mimicking biological evolution with crossover and mutation operations), and Watershed Algorithm (image segmentation technique utilizing gradient magnitude calculations). Each algorithm possesses distinct characteristics, allowing selection based on problem-specific requirements such as solution space topology and constraint types.