Hybridizing GA and Enhanced Jaya Algorithm for Nonlinear Least-Squares Problems

Abstract

The least squares problem (LSP) including general simultaneous linear equations is the most important model such as a linear regression and multivariate linear regression models in machine learning, as well as approximation problems in the material science, estimation of transfer functions in the control system, traffic flow prediction problem and various engineering optimization problems. It is attracting attention that the solution of this LSP model is obtained by iterative calculation and without using any inverse matrix. If the order of the LSP model is m, the conventional method by Yahagi's method required a 2m x 2 m matrix operation, whereas the modified Cholesky decomposition method proposed by Gen, et al has the advantage of the m x m matrix operation is sufficient with the small number of division operations. In this presentation, we propose a hybrid evolutionary algorithm (genetic algorithm and enhanced Jaya algorithm: HGA+EJA) for effectively solving LSP models including nonlinear LSP models including general simultaneous linear equations. In the numerical experiments, several numerical examples of general simultaneous linear equations, the ill-structured simultaneous linear equations, and linear/nonlinear LSP models are demonstrated, and the solution precision and computational time by the conventional method and the proposed method: HGA+EJA are quantitatively compared with each other. Finally, we clarify the effectiveness of the proposed method.