Advertisement

Powell-Based Bat Algorithm for Solving Nonlinear Equations

  • Gengyu Ge
  • Yuanyuan Pu
  • Jiyuan Zhang
  • Aijia Ouyang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10956)

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.

Keywords

Bat algorithm Powell algorithm Hybrid algorithm Nonlinear equations Optimization 

Notes

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).

References

  1. 1.
    Yang, X.S., Gandomi, A.H.: Bat algorithm: a novel approach for global engineering optimization. Eng. Comput. 29(5), 464–483 (2012)CrossRefGoogle Scholar
  2. 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. 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)MathSciNetCrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 5.
    Krzyworzcka, S.: Extension of the Lanczos and CGS methods to systems of nonlinear equations. J. Comput. Appl. Math. 69(1), 181–190 (1996)MathSciNetCrossRefGoogle Scholar
  6. 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)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gengyu Ge
    • 1
  • Yuanyuan Pu
    • 1
  • Jiyuan Zhang
    • 1
  • Aijia Ouyang
    • 1
  1. 1.School of Information EngineeringZunyi Normal UniversityZunyiChina

Personalised recommendations