IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i5p1231-d1086384.html
   My bibliography  Save this article

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

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)

  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/5/1231/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/5/1231/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Luis A. Aguirre & Christophe Letellier, 2009. "Modeling Nonlinear Dynamics and Chaos: A Review," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-35, June.
    4. 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.
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Aguirre, Luis A. & Letellier, Christophe, 2016. "Controllability and synchronizability: Are they related?," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 242-251.
    3. Sun, Yeong-Jeu, 2009. "An exponential observer for the generalized Rossler chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2457-2461.
    4. Sysoeva, Marina V. & Sysoev, Ilya V. & Prokhorov, Mikhail D. & Ponomarenko, Vladimir I. & Bezruchko, Boris P., 2021. "Reconstruction of coupling structure in network of neuron-like oscillators based on a phase-locked loop," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    5. Artur Karimov & Erivelton G. Nepomuceno & Aleksandra Tutueva & Denis Butusov, 2020. "Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding," Mathematics, MDPI, vol. 8(2), pages 1-22, February.
    6. Cui, Yunfei & Geng, Zhiqiang & Zhu, Qunxiong & Han, Yongming, 2017. "Review: Multi-objective optimization methods and application in energy saving," Energy, Elsevier, vol. 125(C), pages 681-704.
    7. Wei-Chiang Hong & Yucheng Dong & Chien-Yuan Lai & Li-Yueh Chen & Shih-Yung Wei, 2011. "SVR with Hybrid Chaotic Immune Algorithm for Seasonal Load Demand Forecasting," Energies, MDPI, vol. 4(6), pages 1-18, June.
    8. Imene Khenissi & Tawfik Guesmi & Ismail Marouani & Badr M. Alshammari & Khalid Alqunun & Saleh Albadran & Salem Rahmani & Rafik Neji, 2023. "Energy Management Strategy for Optimal Sizing and Siting of PVDG-BES Systems under Fixed and Intermittent Load Consumption Profile," Sustainability, MDPI, vol. 15(2), pages 1-28, January.
    9. Coelho, Leandro dos Santos, 2009. "Reliability–redundancy optimization by means of a chaotic differential evolution approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 594-602.
    10. Tuttle, Jacob F. & Blackburn, Landen D. & Andersson, Klas & Powell, Kody M., 2021. "A systematic comparison of machine learning methods for modeling of dynamic processes applied to combustion emission rate modeling," Applied Energy, Elsevier, vol. 292(C).
    11. Salil Bharany & Sandeep Sharma & Surbhi Bhatia & Mohammad Khalid Imam Rahmani & Mohammed Shuaib & Saima Anwar Lashari, 2022. "Energy Efficient Clustering Protocol for FANETS Using Moth Flame Optimization," Sustainability, MDPI, vol. 14(10), pages 1-22, May.
    12. Sultan Almotairi & Elsayed Badr & Mustafa Abdul Salam & Alshimaa Dawood, 2023. "Three Chaotic Strategies for Enhancing the Self-Adaptive Harris Hawk Optimization Algorithm for Global Optimization," Mathematics, MDPI, vol. 11(19), pages 1-27, October.
    13. Cheng, Shen & Zhao, Gaiju & Gao, Ming & Shi, Yuetao & Huang, Mingming & Yousefi, Nasser, 2021. "Optimal hybrid energy system for locomotive utilizing improved Locust Swarm optimizer," Energy, Elsevier, vol. 218(C).
    14. Martin Ćalasan & Dražen Jovanović & Vesna Rubežić & Saša Mujović & Slobodan Đukanović, 2019. "Estimation of Single-Diode and Two-Diode Solar Cell Parameters by Using a Chaotic Optimization Approach," Energies, MDPI, vol. 12(21), pages 1-14, November.
    15. 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.
    16. 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.
    17. M. A. El-Shorbagy & A. Y. Ayoub & A. A. Mousa & I. M. El-Desoky, 2019. "An enhanced genetic algorithm with new mutation for cluster analysis," Computational Statistics, Springer, vol. 34(3), pages 1355-1392, September.
    18. Muhammad Nabeel Hussain & Nadeem Shaukat & Ammar Ahmad & Muhammad Abid & Abrar Hashmi & Zohreh Rajabi & Muhammad Atiq Ur Rehman Tariq, 2022. "Micro-Siting of Wind Turbines in an Optimal Wind Farm Area Using Teaching–Learning-Based Optimization Technique," Sustainability, MDPI, vol. 14(14), pages 1-24, July.
    19. Mohammad H. Nadimi-Shahraki & Ali Fatahi & Hoda Zamani & Seyedali Mirjalili, 2022. "Binary Approaches of Quantum-Based Avian Navigation Optimizer to Select Effective Features from High-Dimensional Medical Data," Mathematics, MDPI, vol. 10(15), pages 1-30, August.
    20. Hossein Lotfi, 2022. "A Multiobjective Evolutionary Approach for Solving the Multi-Area Dynamic Economic Emission Dispatch Problem Considering Reliability Concerns," Sustainability, MDPI, vol. 15(1), pages 1-23, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1231-:d:1086384. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.