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Mathematical Problems in Engineering
Volume 2015, Article ID 727218, 13 pages
http://dx.doi.org/10.1155/2015/727218
Research Article

Research on Solving Systems of Nonlinear Equations Based on Improved PSO

1College of Materials Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China
2College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China

Received 5 May 2015; Accepted 15 July 2015

Academic Editor: Valery Sbitnev

Copyright © 2015 Yugui Li et al. 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.

Abstract

Solving systems of nonlinear equations is perhaps one of the most difficult problems in all of numerical computations, especially in a diverse range of engineering applications. The convergence and performance characteristics can be highly sensitive to the initial guess of the solution for most numerical methods such as Newton’s method. However, it is very difficult to select reasonable initial guess of the solution for most systems of nonlinear equations. Besides, the computational efficiency is not high enough. Aiming at these problems, an improved particle swarm optimization algorithm (imPSO) is proposed, which can overcome the problem of selecting reasonable initial guess of the solution and improve the computational efficiency. The convergence and performance characteristics of this method are demonstrated through some standard systems. The results show that the improved PSO for solving systems of nonlinear equations has reliable convergence probability, high convergence rate, and solution precision and is a successful approach in solving systems of nonlinear equations.