Self-Cooling Simulated Annealing (SCSA) Algorithm for Nonlinear Least Square’s Data Analysis

Abstract

A Self-Cooling Simulated Annealing (SCSA) algorithm is introduced for the optimization of nonlinear least-squares problems. In contrast to conventional simulated annealing techniques that require a predefined cooling schedule, the SCSA algorithm autonomously regulates system temperature based on the lowest figure of merit (ie. χ²) achieved at each iteration. The algorithm incorporates two key enhancements to improve efficiency: the separation of linear and nonlinear parameters, which reduces the dimensionality of the stochastic search space, and an adaptive Gaussian sampling mechanism that dynamically updates parameter-specific variances based on recent optimization history. A thermal resistance parameter (K) regulates the cooling rate and can be adjusted according to problem complexity. Performance benchmarking against standard Monte Carlo and gradient-based methods demonstrates that SCSA offers greater robustness in avoiding local minima and provides reliable convergence across varying levels of optimization difficulty. These characteristics make the method broadly applicable to nonlinear data analysis and other complex optimization tasks.