An Enhanced Genetic Algorithm for Root-Finding in Nonlinear Equation

Abstract This paper presents an Enhanced Genetic Algorithm (EGA) designed for the efficient computation of both real and complex roots of nonlinear equations. The proposed approach improves upon the conventional Genetic Algorithm by integrating Sobol quasi-random sampling with a region-filtering mechanism that discards non-promising areas of the search space prior to the evolutionary process. This strategy produces a uniformly distributed initial population while substantially shrinking the effective search domain, leading to improved computational efficiency. Extensive numerical experiments on a variety of nonlinear functions show that the Enhanced GA consistently achieves faster convergence than the standard GA and Quasi-GA, without compromising solution accuracy. These numerical results demonstrate that structured initialization combined with domain reduction significantly enhances evolutionary root-finding performance, establishing the Enhanced GA as a robust and efficient tool for solving nonlinear equations. AMS Subject Classification: 65H04, 65H05 Keywords: Genetic Algorithm, Quasi Genetic Algorithm, Sobol sequence, Region filtering.