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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

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

  • Fatma M. Al-Drees

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

The development of many engineering and scientific models depends on the solution of nonlinear systems of equations (NSEs), and the progress of these fields depends on their efficient resolution. Due to the disadvantages in solving them with classical methods, NSEs are amenable to modeling as an optimization issue. The purpose of this work is to propose the chaotic search sine cosine algorithm (CSSCA), a new optimization approach for solving NSEs. CSSCA will be set up so that it employs a chaotic search to get over the limitations of optimization techniques like a lack of diversity in solutions, exploitation’s unfair advantage over exploration, and the gradual convergence of the optimal solution. A chaotic logistic map has been employed by many studies and has demonstrated its effectiveness in raising the quality of solutions and offering the greatest performance. So, it is used as a local search strategy. Three kinds of test functions—unimodal, multimodal, and composite test functions—as well as numerous NSEs—combustion problems, neurophysiology problems, arithmetic application, and nonlinear algebraic equations—were employed to assess CSSCA. To demonstrate the significance of the changes made in CSSCA, the results of the recommended algorithm are contrasted with those of the original SCA, where CSSCA’s average improvement rate was roughly 12.71, demonstrating that it is very successful at resolving NSEs. Finally, outcomes demonstrated that adding a chaotic search to the SCA improves results by modifying the chaotic search’s parameters, enabling better outcomes to be attained.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1231-:d:1086384
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    References listed on IDEAS

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    1. 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.
    2. Zeinab M. H. Hendawy & M. A. El-Shorbagy, 2015. "Combined Trust Region with Particle swarm for Multi-objective Optimisation," Proceedings of International Academic Conferences 2703860, International Institute of Social and Economic Sciences.
    3. 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.
    4. 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.
    5. Luis A. Aguirre & Christophe Letellier, 2009. "Modeling Nonlinear Dynamics and Chaos: A Review," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-35, June.
    6. Mohammed A. El-Shorbagy & Hala A. Omar & Tamer Fetouh, 2022. "Hybridization of Manta-Ray Foraging Optimization Algorithm with Pseudo Parameter-Based Genetic Algorithm for Dealing Optimization Problems and Unit Commitment Problem," Mathematics, MDPI, vol. 10(13), pages 1-33, June.
    7. M. A. El-Shorbagy & Akif Akgul, 2022. "Chaotic Fruit Fly Algorithm for Solving Engineering Design Problems," Complexity, Hindawi, vol. 2022, pages 1-19, April.
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