Metaheuristic Method for Solving Systems of Equations

Abstract

This study investigates the effectiveness of Genetic Algorithms (GAs) in solving both linear and nonlinear systems of equations, comparing their performance to traditional methods such as Gaussian Elimination, Newton's Method, and Levenberg-Marquardt. The GA consistently delivered accurate solutions across various test cases, demonstrating its robustness and flexibility. A key advantage of the GA is its ability to explore the solution space broadly, uncovering multiple sets of solutions -- a feat that traditional methods, which typically converge to a single solution, cannot achieve. This feature proved especially beneficial in complex nonlinear systems, where multiple valid solutions exist, highlighting the GA's superiority in navigating intricate solution landscapes.