Soccer League Competition Algorithm, a New Method for Solving Systems of Nonlinear Equations

Abstract

This paper introduces Soccer League Competition (SLC) algorithm as a new optimization technique for solving nonlinear systems of equations. Fundamental ideas of the method are inspired from soccer leagues and based on the competitions among teams and players. Like other meta-heuristic methods, the proposed technique starts with an initial population. Population individuals called players are in two types: fixed players and substitutes that all together form some teams. The competition among teams to take the possession of the top ranked positions in the league table and the internal competitions between players in each team for personal improvements results in the convergence of population individuals to the global optimum. Results of applying the proposed algorithm in solving nonlinear systems of equations demonstrate that SLC converges to the answer more accurately and rapidly in comparison with other Meta-heuristic and Newton-type methods.

Share and Cite:

N. Moosavian and B. Roodsari, "Soccer League Competition Algorithm, a New Method for Solving Systems of Nonlinear Equations," International Journal of Intelligence Science, Vol. 4 No. 1, 2014, pp. 7-16. doi: 10.4236/ijis.2014.41002.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. R. J. Ortega, “Iterative Solution of Nonlinear Equation in Several Variable,” Academic Press, New York, 1970.
[2] S. Krzyworzcka, “Extension of the Lanczos and CGS Methods to Systems of Nonlinear Equations,” Journal of Computational and Applied Mathematics, Vol. 69, No. 1, 1996, pp. 181-190.
http://dx.doi.org/10.1016/0377-0427(95)00032-1
[3] S. J. J. Nocedal, “Numerical Optimization,” Spring Science + Business Media Inc., Berlin, 1999.
[4] D. G. Huang and Y. Ma, “Nonlinear Numerical Analysis,” Wuhan University Press, Wuhan, 2000.
[5] Y. Mo, H. Liu and Q. Wang, “Conjugate Direction Particle Swarm Optimization Solving Systems of Nonlinear Equations,” Computers & Mathematics with Applications, Vol. 57, No. 11-12, 2009, pp. 1877-1882.
http://dx.doi.org/10.1016/j.camwa.2008.10.005
[6] M. Frontini and E. Sormani, “Third-Order Methods from Quadrature Formulae for Solving Systems of Nonlinear Equations,” Applied Mathematics and Computation, Vol. 149, No. 3, 2004, pp. 771-782.
http://dx.doi.org/10.1016/S0096-3003(03)00178-4
[7] A. Cordero and J. R. Torregrosa, “Variants of Newton’s Method for Functions of Several Variables,” Applied Mathematics and Computation, Vol. 183, No. 1, 2006, pp. 199-208. http://dx.doi.org/10.1016/j.amc.2006.05.062
[8] M. T. Darvishi and A. Barati, “Super Cubic Iterative Methods to Solve Systems of Nonlinear Equations,” Applied Mathematics and Computation, Vol. 188, No. 2, 2007, pp. 1678-1685. http://dx.doi.org/10.1016/j.amc.2006.11.022
[9] M. T. Darvishi and A. Barati, “A Fourth-Order Method from Quadrature Formulae to Solve Systems of Nonlinear Equations,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 257-261.
http://dx.doi.org/10.1016/j.amc.2006.09.115
[10] M. T. Darvishi and A. Barati, “A Third-Order NewtonType Method to Solve Systems of Nonlinear Equations,” Applied Mathematics and Computation, Vol. 187, No. 2, 2007, pp. 630-635.
http://dx.doi.org/10.1016/j.amc.2006.08.080
[11] D. K. R. Babajee, et al., “A Note on the Local Convergence of Iterative Methods Based on Adomian Decomposition Method and 3-Node Quadrature Rule,” Applied Mathematics and Computation, Vol. 200, No. 1, 2008, pp. 452-458. http://dx.doi.org/10.1016/j.amc.2007.11.009
[12] Y.-Z. Luo, G.-J. Tang and L.-N. Zhou, “Hybrid Approach for Solving Systems of Nonlinear Equationsusing Chaos Optimization and Quasi-Newton Method,” Applied Soft Computing, Vol. 8, No. 2, 2008, pp. 1068-1073.
http://dx.doi.org/10.1016/j.asoc.2007.05.013
[13] M. Jaberipour, E. Khorram and B. Karimi, “Particle Swarm Algorithm for Solving Systems of Nonlinear Equations,” Computers & Mathematics with Applications, Vol. 62, No. 2, 2011, pp. 566-576.
http://dx.doi.org/10.1016/j.camwa.2011.05.031
[14] B. C. Shin, M. T. Darvishi and C.-H. Kim, “A Comparison of the Newton-Krylov Method with High Order Newton-Like Methods to Solve Nonlinear Systems,” Applied Mathematics and Computation, Vol. 217, No. 7, 2010, pp. 3190-3198. http://dx.doi.org/10.1016/j.amc.2010.08.051

Journals Menu
Follow SCIRP
Contact us
+1 323-425-8868
customer@scirp.org
WhatsApp +86 18163351462(WhatsApp)
Click here to send a message to me 1655362766
Paper Publishing WeChat

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.