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Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models

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  • Sabir, Zulqurnain
  • Raja, Muhammad Asif Zahoor
  • Wahab, Hafiz Abdul
  • Altamirano, Gilder Cieza
  • Zhang, Yu-Dong
  • Le, Dac-Nhuong

Abstract

The present research work is to put forth the numerical solutions of the nonlinear second-order Lane–Emden-pantograph (LEP) delay differential equation by using the approximation competency of the artificial neural networks (ANNs) trained with the combined strengths of global/local search exploitation of genetic algorithm (GA) and active-set (AS) method, i.e., ANNGAAS. In the proposed ANNGAAS, the objective function is designed by using the mean square error function with continuous mappings of ANNs for the LEP delay differential equation. The training of these constructed networks is conducted proficiently using the integrated capability of global search with GA and assisted local search along with AS approach. The performance of design computing paradigm ANNGAAS is evaluated effectively on variants of LEP delay differential models, while the statistical investigations based on different operators further validate the accuracy and convergence.

Suggested Citation

  • Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Wahab, Hafiz Abdul & Altamirano, Gilder Cieza & Zhang, Yu-Dong & Le, Dac-Nhuong, 2021. "Integrated intelligence of neuro-evolution with sequential quadratic programming for second-order Lane–Emden pantograph models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 87-101.
    • Handle: RePEc:eee:matcom:v:188:y:2021:i:c:p:87-101
    DOI: 10.1016/j.matcom.2021.03.036
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    References listed on IDEAS

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    1. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Sakar, Mehmet Giyas & Raja, Muhammad Asif Zahoor, 2020. "Novel design of Morlet wavelet neural network for solving second order Lane–Emden equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 172(C), pages 1-14.
    2. Zulqurnain Sabir & Hatıra Günerhan & Juan L. G. Guirao, 2020. "On a New Model Based on Third-Order Nonlinear Multisingular Functional Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-9, February.
    3. Shahid, Farah & Zameer, Aneela & Mehmood, Ammara & Raja, Muhammad Asif Zahoor, 2020. "A novel wavenets long short term memory paradigm for wind power prediction," Applied Energy, Elsevier, vol. 269(C).
    4. Ximing Wang & Panos M. Pardalos, 2017. "A modified active set algorithm for transportation discrete network design bi-level problem," Journal of Global Optimization, Springer, vol. 67(1), pages 325-342, January.
    5. Zulqurnain Sabir & Rizwan Akhtar & Zhu Zhiyu & Muhammad Umar & Ali Imran & Hafiz Abdul Wahab & Muhammad Shoaib & Muhammad Asif Zahoor Raja, 2019. "A Computational Analysis of Two-Phase Casson Nanofluid Passing a Stretching Sheet Using Chemical Reactions and Gyrotactic Microorganisms," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, June.
    6. Sabir, Zulqurnain & Wahab, Hafiz Abdul & Umar, Muhammad & Erdoğan, Fevzi, 2019. "Stochastic numerical approach for solving second order nonlinear singular functional differential equation," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
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    Cited by:

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    2. Sabir, Zulqurnain & Said, Salem Ben & Baleanu, Dumitru, 2022. "Swarming optimization to analyze the fractional derivatives and perturbation factors for the novel singular model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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