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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2006.06.034 Byline: Shu-Kai S. Fan, Erwie Zahara Keywords: Simplex search method; Particle swarm optimization; Unconstrained optimization; Metaheuristics Abstract: This paper proposes the hybrid NM-PSO algorithm based on the Nelder-Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder-Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization. Author Affiliation: Department of Industrial Engineering and Management, Yuan Ze University, 135 Yuan-Tung Road, Chung-Li, Taoyuan County 320, Taiwan, ROC Article History: Received 22 December 2003; Accepted 5 June 2006

Abstract: Constrained optimization problems are very important in that they frequently appear in the real world. A constrained optimization problem consists of the optimization of a function subject to constraints, in which both the function and constraints may be nonlinear. Constraint handling is one of the major concerns when solving constrained optimization problems by hybrid Nelder–Mead simplex search method and particle swarm optimization, denoted as NM–PSO. This paper proposes embedding constraint handling methods, which include the gradient repair method and constraint fitness priority-based ranking method, in NM–PSO as a special operator to deal with satisfying constraints. Experiments using three benchmark function and three engineering design problems are presented and compared with the best known solutions reported in the literature. The comparison results with other evolutionary optimization methods demonstrate that NM–PSO with the embedded constraint operator proves to be extremely effective and efficient at locating optimal solutions. [Copyright &y& Elsevier]

Abstract: Data clustering helps one discern the structure of and simplify the complexity of massive quantities of data. It is a common technique for statistical data analysis and is used in many fields, including machine learning, data mining, pattern recognition, image analysis, and bioinformatics, in which the distribution of information can be of any size and shape. The well-known K-means algorithm, which has been successfully applied to many practical clustering problems, suffers from several drawbacks due to its choice of initializations. A hybrid technique based on combining the K-means algorithm, Nelder–Mead simplex search, and particle swarm optimization, called K–NM–PSO, is proposed in this research. The K–NM–PSO searches for cluster centers of an arbitrary data set as does the K-means algorithm, but it can effectively and efficiently find the global optima. The new K–NM–PSO algorithm is tested on nine data sets, and its performance is compared with those of PSO, NM–PSO, K–PSO and K-means clustering. Results show that K–NM–PSO is both robust and suitable for handling data clustering. [Copyright &y& Elsevier]