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Integrated neuro-evolution-based computing solver for dynamics of nonlinear corneal shape model numerically

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Abstract

In this study, bio-inspired computational techniques have been exploited to get the numerical solution of a nonlinear two-point boundary value problem arising in the modelling of the corneal shape. The computational process of modelling and optimization makes enormously straightforward to obtain accurate approximate solutions of the corneal shape models through artificial neural networks, pattern search (PS), genetic algorithms (GAs), simulated annealing (SA), active-set technique (AST), interior-point technique, sequential quadratic programming and their hybrid forms based on GA–AST, PS–AST and SA–AST. Numerical results show that the designed solvers provide a reasonable precision and efficiency with minimal computational cost. The efficacy of the proposed computing strategies is also investigated through a descriptive statistical analysis by means of histogram illustrations, probability plots and one-way analysis of variance.

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Acknowledgements

The authors want to thank the anonymous referees for their careful reading of the manuscript and their comments, which greatly improved the final result.

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Authors and Affiliations

  1. Department of Mathematics, University of Gujrat, Gujrat, Pakistan

    Iftikhar Ahmad

  2. Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliou, 64002, Yunlin, Taiwan, ROC

    Muhammad Asif Zahoor Raja

  3. Department of Electrical and Computer Engineering, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Asif Zahoor Raja

  4. Department of Applied Mathematics, University of Salamanca, Salamanca, Spain

    Higinio Ramos

  5. Faculty of Science and Technology, University of Malaysia Pahang, Pekan, Malaysia

    Muhammad Bilal

  6. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock, 43600, Pakistan

    Muhammad Shoaib

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  1. Iftikhar Ahmad
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  2. Muhammad Asif Zahoor Raja
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  3. Higinio Ramos
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  4. Muhammad Bilal
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All authors contributed equally to this manuscript.

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Correspondence to Higinio Ramos.

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Ahmad, I., Raja, M.A.Z., Ramos, H. et al. Integrated neuro-evolution-based computing solver for dynamics of nonlinear corneal shape model numerically. Neural Comput & Applic 33, 5753–5769 (2021). https://doi.org/10.1007/s00521-020-05355-y

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  • DOI: https://doi.org/10.1007/s00521-020-05355-y

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