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Mathematical Problems in Engineering
Volume 2013, Article ID 256180, 15 pages
Research Article

Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches

Department of Business Administration, Lunghwa University of Science and Technology, No. 300, Section 1, Wanshou Road, Guishan, Taoyuan County 33306, Taiwan

Received 7 September 2012; Revised 3 December 2012; Accepted 4 December 2012

Academic Editor: Baozhen Yao

Copyright © 2013 Jui-Yu Wu. 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.


Stochastic global optimization (SGO) algorithms such as the particle swarm optimization (PSO) approach have become popular for solving unconstrained global optimization (UGO) problems. The PSO approach, which belongs to the swarm intelligence domain, does not require gradient information, enabling it to overcome this limitation of traditional nonlinear programming methods. Unfortunately, PSO algorithm implementation and performance depend on several parameters, such as cognitive parameter, social parameter, and constriction coefficient. These parameters are tuned by using trial and error. To reduce the parametrization of a PSO method, this work presents two efficient hybrid SGO approaches, namely, a real-coded genetic algorithm-based PSO (RGA-PSO) method and an artificial immune algorithm-based PSO (AIA-PSO) method. The specific parameters of the internal PSO algorithm are optimized using the external RGA and AIA approaches, and then the internal PSO algorithm is applied to solve UGO problems. The performances of the proposed RGA-PSO and AIA-PSO algorithms are then evaluated using a set of benchmark UGO problems. Numerical results indicate that, besides their ability to converge to a global minimum for each test UGO problem, the proposed RGA-PSO and AIA-PSO algorithms outperform many hybrid SGO algorithms. Thus, the RGA-PSO and AIA-PSO approaches can be considered alternative SGO approaches for solving standard-dimensional UGO problems.