Hybrid Newton–Sperm Swarm Optimization Algorithm for Nonlinear Systems

Several problems have been solved by nonlinear equation systems (NESs), including real-life issues in chemistry and neurophysiology. However, the accuracy of solutions is highly dependent on the efficiency of the algorithm used. In this paper, a Modified Sperm Swarm Optimization Algorithm called MSSO is introduced to solve NESs. MSSO combines Newton’s second-order iterative method with the Sperm Swarm Optimization Algorithm (SSO). Through this combination, MSSO’s search mechanism is improved, its convergence rate is accelerated, local optima are avoided, and more accurate solutions are provided. The method overcomes several drawbacks of Newton’s method, such as the initial points’ selection, falling into the trap of local optima, and divergence. In this study, MSSO was evaluated using eight NES benchmarks that are commonly used in the literature, three of which are from real-life applications. Furthermore, MSSO was compared with several well-known optimization algorithms, including the original SSO, Harris Hawk Optimization (HHO), Butterfly Optimization Algorithm (BOA), Ant Lion Optimizer (ALO), Particle Swarm Optimization (PSO), and Equilibrium Optimization (EO). According to the results, MSSO outperformed the compared algorithms across all selected benchmark systems in four aspects: stability, fitness values, best solutions, and convergence speed.