International Journal of Intelligence Science, 2014, 4, 7-16 Published Online January 2014 (http://www.scirp.org/journal/ijis ) http://dx.doi.org/10.4236/ijis.2014.41002 OPEN ACCESS IJIS Soccer League Competition Algorithm, a New Method for Solving Systems of Nonlinear Equations Naser Moosavian, Babak Kasaee Roodsari Department of Civil Engineering, Ferdowsi University of Mashhad, Mashhad, Iran Email: naser.moosavian@yahoo.com Received October 9, 2013; revised November 9, 2013; accepted November 15, 2013 Copyright © 2014 Naser Moosavian, Babak Kasaee Roodsari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Naser Moosavian, Babak Kasaee Roodsari. All Copyright © 2014 are guarded by law and by SCIRP as a guardian. 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 posi- tions 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 al- gorithm in solving nonlinear systems of equations demonstrate that SLC converges to the answer more accu- rately and rapidly in comparison with other Meta-heuristic and Newton-type methods. KEYWORDS Soccer League Competition; Nonlinear Equations; Meta-Heuristic Algorithm 1. Introduction Solving systems of nonlinear equations is one of the main concerns in a diverse range of engineering applica- tions such as computational mechanics, weather forecast, hydraulic analysis of water distribution systems, aircraft control and petroleum geological prospecting. Many pre- vious efforts have been made to find a solution for sys- tems of nonlinear equations. Results of these studies comprise some theories and algorithms [1-4]. Among such approaches, Newton’s method is one of the most powerful numerical methods and an important basic me- thod which has a quadratic convergence if the function F is continuously differentiable and if a good initial guess x 0 is provided [5]. Frontini and Sormani [6] proposed a third-order method based on a quadrature formula to solve systems of nonlinear equations. Cordero and Tor- regrosa [7] developed some variants of Newton’s method based on trapezoidal and midpoint rules of quadrature. Also, Darvishi and Barati [8-10] presented some high order iterative methods and Babajee et al. [11] proposed a fourth-order iterative technique. Luo et al. [12] solved a system of nonlinear equations using a combination of chaos search and Newton-type methods. More recently, Mo et al. [5] presented a combination of the conjugate direction method (CD) and particle swarm optimization (PSO) for solving systems of nonlinear equations. The convergence and performance characteristics of Newton-type methods are highly sensitive to the initial guess of the solution supplied to the methods and the algorithm would fail if the initial guess of the solution is improper. However, it is difficult to select a good initial guess for most systems of nonlinear equations [13]. The system of nonlinear equations is considered as follows:       1 1 2 2 1 2 1 2 , , , 0 , , , 0 , , , 0. n n n n f x x x f x x x f x x x               (1) Applying the global optimization methods, the system