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Journal of Applied Mathematics
Volume 2012, Article ID 530139, 12 pages
http://dx.doi.org/10.1155/2012/530139
Research Article

A Modified NM-PSO Method for Parameter Estimation Problems of Models

1Department of Computer Science and Information Engineering, St. John’s University, No. 499, Section 4, Tam King Road, Tamsui District, New Taipei City, 25135, Taiwan
2Graduate Institute of Computer and Communication Engineering, National Taipei University of Technology, No. 1, Section 3, Chung-hsiao E. Road, Taipei 10608, Taiwan
3Department of Marketing and Logistics Management, St. John’s University, No. 499, Section 4, Tam King Road, Tamsui District, New Taipei City 25135, Taiwan
4Department of Electrical Engineering, St. John’s University, No. 499, Section 4, Tam King Road, Tamsui District, New Taipei City 25135, Taiwan

Received 9 June 2012; Accepted 9 September 2012

Academic Editor: Alain Miranville

Copyright © 2012 An Liu 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

Ordinary differential equations usefully describe the behavior of a wide range of dynamic physical systems. The particle swarm optimization (PSO) method has been considered an effective tool for solving the engineering optimization problems for ordinary differential equations. This paper proposes a modified hybrid Nelder-Mead simplex search and particle swarm optimization (M-NM-PSO) method for solving parameter estimation problems. The M-NM-PSO method improves the efficiency of the PSO method and the conventional NM-PSO method by rapid convergence and better objective function value. Studies are made for three well-known cases, and the solutions of the M-NM-PSO method are compared with those by other methods published in the literature. The results demonstrate that the proposed M-NM-PSO method yields better estimation results than those obtained by the genetic algorithm, the modified genetic algorithm (real-coded GA (RCGA)), the conventional particle swarm optimization (PSO) method, and the conventional NM-PSO method.