Advertisement

Simplex Bat Algorithm for Solving System of Non-linear Equations

  • Gengyu Ge
  • Xuexian Ruan
  • Pingping Chen
  • Aijia Ouyang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10954)

Abstract

In consideration of the fact that bat algorithm (BA) is sensitive to the initial values and simplex algorithm (SA) could often easily fall into local optimal, simplex - bat algorithm is put forward in this paper to solve system of non-linear equations based on the respective advantages of both algorithms. Such a combined algorithm does not only give full play to BAs global searching ability but also make full use of SA local searching ability. The results of simulation experiments show that this combined algorithm can be used to find the roots of all sorts of systems of non-linear equations with high accuracy, and moreover, with strong robustness and fast convergence rate, and therefore, it is indeed an effective method to solve system of non-linear equations.

Keywords

System of non-linear equations Simplex Algorithm Bat Algorithm Hybrid Algorithm 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.
    Qiuruchen, K.R.: An accelerated simplex method. J. Nanjing Univ. Sci. Technol. 27(2), 209–213 (2003)Google Scholar
  2. 2.
    Ning, X.: Graph simplex method for solution of maximum flow problem in a network. Trans. Nanjing Univ. Aeronaut. Astronaut. 28(5), 626–630 (1996)zbMATHGoogle Scholar
  3. 3.
    De Wolf, D., Smeers, Y.: The gas transmission problem solved by an extension of the simplex algorithm. Manage. Sci. 46(46), 1454–1465 (2000)CrossRefGoogle Scholar
  4. 4.
    Karim, M.R., Mal, A.K., Bar-Cohen, Y.: Inversion of leaky lamb wave data by simplex algorithm. J. Acoust. Soc. Am. 88(1), 482–491 (1990)CrossRefGoogle Scholar
  5. 5.
    Xiao, H.H., Duan, Y.M.: Research and application of improved bat algorithm based on de algorithm. Comput. Simul. 31(1), 272–277 (2014)Google Scholar
  6. 6.
    Rodrigues, D., Nakamura, R.Y.M., Costa, K.A.P., Yang, X.S.: A wrapper approach for feature selection based on bat algorithm and optimum-path forest. Expert Syst. Appl. Int. J. 41(5), 2250–2258 (2014)CrossRefGoogle Scholar
  7. 7.
    Sambariya, D.K., Prasad, R.: Robust tuning of power system stabilizer for small signal stability enhancement using meta heuristic bat algorithm. Int. J. Electr. Power Energy Syst. 61(61), 229–238 (2014)CrossRefGoogle Scholar
  8. 8.
    Alihodzic, A., Tuba, M.: Improved bat algorithm applied to multilevel image thresholding. Sci. World J. 2014, 16 (2014)CrossRefGoogle Scholar
  9. 9.
    Sathya, M.R., Ansari, M.M.T.: Load frequency control using bat inspired algorithm based dual mode gain scheduling of pi controllers for interconnected power system. Int. J. Electr. Power Energy Syst. 64(64), 365–374 (2015)CrossRefGoogle Scholar
  10. 10.
    Iztok Fister, J., Fong, S., Brest, J., Fister, I.: A novel hybrid self-adaptive bat algorithm. Sci. World J. 2014(1–2), 709738 (2014)Google Scholar
  11. 11.
    Yu, L.I., Liang, M.A., Management, S.O.: Bat-inspired algorithm: a novel approach for global optimization. Comput. Sci. 40(9), 225–229 (2013)Google Scholar
  12. 12.
    Ouyang, A.J., Zhang, W.W.: Hybrid global optimization algorithm based on simplex and population migration. Comput. Eng. Appl. 46(4), 29–30 (2010)Google Scholar
  13. 13.
    Sun, J.Z.: Solving nonlinear systems of equations based on social cognitive optimization. Comput. Eng. Appl. 44(28), 42–43 (2008)Google Scholar
  14. 14.
    Zhang, A.L.: Hybrid quasi-newton/particle swarm optimization algorithm for nonlinear equations. Comput. Eng. Appl. 44(33), 41–42 (2008)Google Scholar
  15. 15.
    Sui, Y., Zhao, W.: A quadratic programming method for solving the NSE and its application. Chin. J. Comput. Mech. 19(2), 245–246 (2002)Google Scholar
  16. 16.
    Mo, Y., Chen, D.Z., Hu, S.: A complex particle swarm optimization for solving system of nonlinear equations. Inf. Control 35(4), 423–427 (2006)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Gengyu Ge
    • 1
  • Xuexian Ruan
    • 1
  • Pingping Chen
    • 1
  • Aijia Ouyang
    • 1
  1. 1.School of Information EngineeringZunyi Normal UniversityZunyiChina

Personalised recommendations