A Hybrid Steffensen–Genetic Algorithm for Finding Multi-Roots of Nonlinear Equations and Applications to Biomedical Engineering

A new hybrid of a Steffensen-type method and genetic algorithm is developed for the efficient simultaneous computation of roots of nonlinear equations, particularly in all cases involving non-differentiable functions and multiple roots. Traditional numerical methods often fail to handle these complexities effectively, highlighting the need for a more robust solution. The proposed algorithm combines the global search strength of the genetic algorithm (GA) with the local refinement capabilities of a derivative-free optimal fourth-order Steffensen method. This integration enhances both exploration and exploitation capabilities, leading to improved convergence and computational accuracy. By uniting the GA’s global optimization with the local refinement of iterative solvers, the algorithm forms a higher-order framework capable of locating all roots concurrently. This study validates the performance of this hybrid strategy through diverse applications in biomedical engineering problems.