Hybrid Newton–Sperm Swarm Optimization Algorithm for Nonlinear Systems

Obadah Said Solaiman, Rami Sihwail (), Hisham Shehadeh, Ishak Hashim and Kamal Alieyan
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Obadah Said Solaiman: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
Rami Sihwail: Department of Cyber Security, Faculty of Computer Science & Informatics, Amman Arab University, Amman 11953, Jordan
Hisham Shehadeh: Department of Computer Information System, Faculty of Computer Science & Informatics, Amman Arab University, Amman 11953, Jordan
Ishak Hashim: Department of Mathematical Sciences, Faculty of Science & Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor, Malaysia
Kamal Alieyan: Department of Cyber Security, Faculty of Computer Science & Informatics, Amman Arab University, Amman 11953, Jordan

Mathematics, 2023, vol. 11, issue 6, 1-21

Abstract: 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.

Keywords: nonlinear systems; Newton’s method; iterative methods; sperm swarm optimization algorithm; optimization algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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