Hybrid Method for Fitting Nonlinear Height–Diameter Functions

Abstract

Regression analysis is widely applied in many fields of science to estimate important variables. In general, nonlinear regression is a complex optimization problem and presents intrinsic difficulties in estimating reliable parameters. Nonlinear optimization algorithms commonly require a precise initial estimate to return reasonable estimates. In this work, we introduce a new hybrid algorithm based on the association of a genetic algorithm with the Levenberg–Marquardt method (GALM) to adjust biological nonlinear models without knowledge of initial parameter estimates. The proposed hybrid algorithm was applied to 12 nonlinear models widely used in forest sciences and 12 databases under varying conditions considering classic hypsometric relationships to evaluate the robustness of this new approach. The hybrid method involves two stages; the curve approximation process begins with a genetic algorithm with a modified local search approach. The second stage involves the application of the Levenberg–Marquardt algorithm. The final performance of the hybrid method was evaluated using total fitting for all tested models and databases, confirming the reliability of the proposed algorithm in providing stable parameter estimates. The GA was able to predict the initial parameters, which assisted the LM in converging efficiently. The developed GALM method is effective, and its application is recommended for biological nonlinear analyses.