MATLAB Implementation of Simulated Annealing Algorithm

Simulated annealing is a global optimization algorithm inspired by the metallurgical annealing process, primarily used for solving complex optimization problems. MATLAB provides an excellent numerical computing environment that is well-suited for implementing such computationally intensive iterative algorithms that require extensive calculations and parameter tuning.

Core Algorithm Concept The simulated annealing algorithm mimics the physical annealing process to search for optimal solutions. In MATLAB implementation, the algorithm starts with a high initial temperature parameter that allows acceptance of worse solutions to escape local optima. As the temperature gradually decreases according to a cooling schedule, the probability of accepting inferior solutions reduces, and the algorithm progressively converges toward the global optimum. The key MATLAB implementation involves temperature management and solution acceptance probability calculations using exponential functions.

Key Parameter Design Initial Temperature: Determines the exploration range during initial phases, typically set to a large value (e.g., 100-1000) in code implementation. Cooling Coefficient: Controls the temperature reduction rate, commonly using values between 0.8 and 0.99, implemented as temperature = temperature * cooling_coefficient in each iteration. Termination Conditions: Can be temperature thresholds (e.g., 1e-6) or maximum iteration counts, implemented through while or for loops with break conditions.

Case Study Example Using the Traveling Salesman Problem (TSP) as an example, simulated annealing can find the shortest path route. In MATLAB code implementation, neighborhood solutions can be generated through swap operations (e.g., randomly exchanging two city positions), and new solutions are accepted or rejected based on the Metropolis criterion using probability calculation: exp(-ΔE/T) > rand(). By adjusting temperature parameters and neighborhood structures, the algorithm balances exploration and exploitation capabilities through carefully designed acceptance probability functions.

Improvement Directions Adaptive Cooling Strategy: Dynamically adjust cooling rates based on search progress using conditional statements and performance monitoring in code. Hybrid Algorithms: Combine simulated annealing with local search methods like gradient descent to enhance convergence speed through mixed optimization approaches. Parallelization: Utilize MATLAB's Parallel Computing Toolbox with parfor loops and distributed arrays to accelerate large-scale problem solving through multi-core processing.

The MATLAB implementation of simulated annealing offers strong flexibility, allowing parameter adjustments and neighborhood operations customization according to specific problem requirements, making it suitable for various continuous or discrete optimization scenarios through modular function design and parameterization.