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.
Highlights
Solving systems of nonlinear equations is one of the main concerns in a diverse range of engineering applications such as computational mechanics, weather forecast, hydraulic analysis of water distribution systems, aircraft control and petroleum geological prospecting
Mo et al [5] presented a combination of the conjugate direction method (CD) and particle swarm optimization (PSO) for solving systems of nonlinear equations
This paper presents a new meta-heuristic algorithm, called Soccer League Competitions (SLC), for solving Equation (2)
Summary
Solving systems of nonlinear equations is one of the main concerns in a diverse range of engineering applications such as computational mechanics, weather forecast, hydraulic analysis of water distribution systems, aircraft control and petroleum geological prospecting. Many previous efforts have been made to find a solution for systems of nonlinear equations. Results of these studies comprise some theories and algorithms [1,2,3,4]. Frontini and Sormani [6] proposed a third-order method based on a quadrature formula to solve systems of nonlinear equations. Luo et al [12] solved a system of nonlinear equations using a combination of chaos search and Newton-type methods. Mo et al [5] presented a combination of the conjugate direction method (CD) and particle swarm optimization (PSO) for solving systems of nonlinear equations
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