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Powell-Based Bat Algorithm for Solving Nonlinear Equations

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Intelligent Computing Methodologies (ICIC 2018)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10956))

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Abstract

As the bat algorithm (BA) has defects such as slow convergence and poor calculation precision, it is likely to result in local extremum, and Powell algorithm (PA) is sensitive to the initial value. To resolve the above defects, advantages and disadvantages of PA and bat algorithm are combined in this paper to solve nonlinear equations. The hybrid Powell bat algorithm (PBA) not only has strong overall search ability like bat algorithm, but also has fine local search ability like Powell algorithm. Experimental results show that the hybrid algorithm can be used to calculate solutions to various nonlinear equations with high precision and fast convergence. Thus, it can be considered a positive method to solve nonlinear equations.

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References

  1. Yang, X.S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29(5), 464–483 (2012)

    Article  Google Scholar 

  2. Ma, W., Sun, Z.X., Li, J.L.: Cuckoo search algorithm based on powell local search method for global optimization. Appl. Res. Comput. 32(6), 1667–1675 (2015)

    Google Scholar 

  3. Mo, Y.B., Liu, H.T., Wang, Q.: Conjugate direction particle swarm optimization solving systems of nonlinear equations. Comput. Math Appl. 57(11), 1877–1882 (2009)

    Article  MathSciNet  Google Scholar 

  4. Luo, Y.Z., Tang, G.J., Zhou, L.N.: Hybrid approach for solving systems of nonlinear equations using chaos optimization and quasi-Newton method. Appl. Soft Comput. 8(2), 1068–1073 (2008)

    Article  Google Scholar 

  5. Krzyworzcka, S.: Extension of the Lanczos and CGS methods to systems of nonlinear equations. J. Comput. Appl. Math. 69(1), 181–190 (1996)

    Article  MathSciNet  Google Scholar 

  6. Hueso, J.L., Martinez, E., Torregrosa, J.R.: Modified Newton’s method for systems of nonlinear equations with singular Jacobian. J. Comput. Appl. Math. 224(1), 77–83 (2009)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The research was partially funded by the science and technology project of Guizhou ([2017]1207), the training program of high level innovative talents of Guizhou ([2017]3), the Guizhou province natural science foundation in China (KY[2016]018), the Science and Technology Research Foundation of Hunan Province (13C333).

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Correspondence to Aijia Ouyang .

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Ge, G., Pu, Y., Zhang, J., Ouyang, A. (2018). Powell-Based Bat Algorithm for Solving Nonlinear Equations. In: Huang, DS., Gromiha, M., Han, K., Hussain, A. (eds) Intelligent Computing Methodologies. ICIC 2018. Lecture Notes in Computer Science(), vol 10956. Springer, Cham. https://doi.org/10.1007/978-3-319-95957-3_90

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  • DOI: https://doi.org/10.1007/978-3-319-95957-3_90

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-95956-6

  • Online ISBN: 978-3-319-95957-3

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