Genetic Algorithm for Newton-Raphson and Other Numerical Models

In this paper, we present a novel genetic algorithm-based approach for the Newton-Raphson method and other numerical models. This hybrid technique leverages the strengths of genetic algorithms—such as global optimum search capabilities and adaptive optimization—combined with the advantages of Newton-Raphson method, including rapid convergence and numerical stability. We provide detailed implementation specifics, featuring population initialization routines, fitness evaluation functions, and crossover/mutation operators that interface with Jacobian matrix calculations. The algorithm employs floating-point encoding for continuous variable representation and incorporates elitism selection to preserve superior solutions across generations. We examine its performance across various application scenarios, demonstrating enhanced convergence properties through comparative benchmarks. Additionally, we conduct comprehensive performance comparisons with traditional Newton-Raphson implementations and standalone genetic algorithms, validating the method's superior robustness and practical utility in solving complex nonlinear equations and optimization problems. Code snippets illustrating key components like chromosome evaluation and gradient-based local search integration are discussed throughout the analysis.