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

Author

Listed:
  • 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
    Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt)

  • Islam M. Eldesoky

    (Department of Basic Engineering Science, Faculty of Engineering, Menoufia University, Shebin El-Kom 32511, Egypt
    Basic Sciences Department, Elmenofia Higher Institute of Engineering and Technology, El Bagour 32821, 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)

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.

Suggested Citation

  • Mohammed A. El-Shorbagy & Islam M. Eldesoky & Mohamady M. Basyouni & Islam Nassar & Adel M. El-Refaey, 2022. "Chaotic Search-Based Salp Swarm Algorithm for Dealing with System of Nonlinear Equations and Power System Applications," Mathematics, MDPI, vol. 10(9), pages 1-30, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1368-:d:797398
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    References listed on IDEAS

    as
    1. Michael Bartholomew-Biggs, 2008. "Nonlinear Optimization with Engineering Applications," Springer Optimization and Its Applications, Springer, number 978-0-387-78723-7, September.
    2. El-Shorbagy, M.A. & Mousa, A.A. & Nasr, S.M., 2016. "A chaos-based evolutionary algorithm for general nonlinear programming problems," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 8-21.
    3. Abdelsalam, Ali M. & El-Shorbagy, M.A., 2018. "Optimization of wind turbines siting in a wind farm using genetic algorithm based local search," Renewable Energy, Elsevier, vol. 123(C), pages 748-755.
    4. Yang, Dixiong & Li, Gang & Cheng, Gengdong, 2007. "On the efficiency of chaos optimization algorithms for global optimization," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1366-1375.
    5. M.A El-Shorbagy & A.A Mousa, 2017. "Chaotic Particle Swarm Optimization for Imprecise Combined Economic and Emission Dispatch Problem," Review of Information Engineering and Applications, Conscientia Beam, vol. 4(1), pages 20-35.
    6. repec:pkp:roieaa:2017:p:20-35 is not listed on IDEAS
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    Cited by:

    1. Mohammed A. El-Shorbagy & Fatma M. Al-Drees, 2023. "Studying the Effect of Introducing Chaotic Search on Improving the Performance of the Sine Cosine Algorithm to Solve Optimization Problems and Nonlinear System of Equations," Mathematics, MDPI, vol. 11(5), pages 1-25, March.
    2. Abdulaziz Almalaq & Tawfik Guesmi & Saleh Albadran, 2023. "A Hybrid Chaotic-Based Multiobjective Differential Evolution Technique for Economic Emission Dispatch Problem," Energies, MDPI, vol. 16(12), pages 1-34, June.

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