Chaotic Search-Based Salp Swarm Algorithm for Dealing with System of Nonlinear Equations and Power System Applications

Mohammed A. El-Shorbagy, Islam M. Eldesoky, Mohamady M. Basyouni, Islam Nassar and Adel M. El-Refaey
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Mohammed A. El-Shorbagy: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Islam M. Eldesoky: Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
Mohamady M. Basyouni: Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
Islam Nassar: Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
Adel M. El-Refaey: Basic and Applied Science Department, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, Smart Village Campus, Giza 12577, Egypt

Mathematics, 2022, vol. 10, issue 9, 1-30

Abstract: The system of nonlinear equations (SNLEs) is one of the eminent problems in science and engineering, and it is still open to research. A new hybrid intelligent algorithm is presented in this research to solve SNLEs. It is a composite of the salp swarm algorithm (SSA) and chaotic search technique (CST). The proposed methodology is named chaotic salp swarm algorithm (CSSA). CSSA is designed as an optimization process, whereby feasible and infeasible solutions are updated to move closer to the optimum value. The use of this hybrid intelligent methodology aims to improve performance, increase solution versatility, avoid the local optima trap, speed up convergence and optimize the search process. Firstly, SNLEs are transformed into an optimization problem. Secondly, CSSA is used to solve this optimization problem: SSA is used to update the feasible solutions, whereas the infeasible solutions are updated by CST. One of the most significant advantages of the suggested technique is that it does not ignore infeasible solutions that are updated, because these solutions are often extremely near to the optimal solution, resulting in increased search effectiveness and effective exploration and exploitation. The algorithm’s mathematical model is presented in detail. Finally, the proposed approach is assessed with several benchmark problems and real-world applications. Simulation results show that the proposed CSSA is competitive and better in comparison to others, which illustrates the effectiveness of the proposed algorithm. In addition, a statistical analysis by the Wilcoxon rankings test between CSSA and the other comparison methods shows that all p -values are less than 0.05, and CSSA achieves negative ranks’ sum values (R − ) much better than the positive ranks’ sum values (R + ) in all benchmark problems. In addition, the results have high precision and show good agreement in comparison with similar methods, and they further proved the ability of CSSA to solve real-world applications.

Keywords: system of nonlinear equations; swarm intelligence; salp swarm algorithm; chaotic search technique; hybrid intelligent algorithm; optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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