Principles and Implementation Methods of Simulated Annealing Algorithm for Exponential Curve Fitting

In this paper, we provide a comprehensive explanation of the underlying principles and implementation methodology of the simulated annealing algorithm. The algorithm is applied to exponential curve fitting problems, with MATLAB implementation featuring key components such as temperature scheduling functions, energy calculation routines, and acceptance probability mechanisms using Boltzmann distribution criteria. Our implementation compares the algorithm's performance against genetic algorithms (with selection, crossover, and mutation operations) and traditional linear regression methods. Numerical simulation results reveal that the simulated annealing approach achieves superior optimal fitting performance, yielding significant improvements in convergence accuracy. The research findings indicate substantial potential for simulated annealing algorithms in exponential curve fitting applications and provide valuable references for related research domains, particularly in optimization problems involving non-linear parameter estimation.