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.

翻译：本研究探讨了遗传算法（GAs）在求解线性和非线性方程组方面的有效性，并将其性能与高斯消元法、牛顿法和Levenberg-Marquardt算法等传统方法进行了比较。遗传算法在各种测试案例中均能提供精确解，展现了其鲁棒性和灵活性。遗传算法的一个关键优势在于其能够广泛探索解空间，发现多组解——这是通常收敛于单一解的传统方法无法实现的。这一特性在存在多个有效解的复杂非线性系统中尤其有益，凸显了遗传算法在复杂解空间中导航的优越性。