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.
Cite this paper
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
 W. R. J. Ortega, “Iterative Solution of Nonlinear Equation in Several Variable,” Academic Press, New York, 1970.
 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
 S. J. J. Nocedal, “Numerical Optimization,” Spring Science + Business Media Inc., Berlin, 1999.
 D. G. Huang and Y. Ma, “Nonlinear Numerical Analysis,” Wuhan University Press, Wuhan, 2000.
 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
 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
 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
 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
 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
 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
 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
 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
 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
 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