Metaheuristic Method for Solving Systems of Equations

TL;DR

This paper evaluates the use of Genetic Algorithms for solving linear and nonlinear systems of equations, showing they are robust, flexible, and capable of finding multiple solutions where traditional methods often converge to a single answer.

Contribution

It introduces the application of Genetic Algorithms to systems of equations, demonstrating their ability to explore multiple solutions and outperform traditional methods in complex cases.

Findings

GA consistently finds accurate solutions

GA uncovers multiple solutions in nonlinear systems

Outperforms traditional methods in complex scenarios

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.