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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

There is abundant literature on response surface methodology about how the Nelder–Mead simplex search (NMSS) procedure can be applied to the determination of optimum operating conditions for deterministic response surface functions. However, searching for the optima of stochastic functions seems a more realistic task for many practical situations. This is particularly true when the response surface functions have not been fitted or the physical models may not even exist, so gradient information is not available. In such cases, it might be interesting to employ simplex-search-type methods ‘on-line’ to sequentially optimize the actual response of interest. Toward that end, an enhanced NMSS is proposed in this article to explore the terrains of empirical (or experimental) optimization adaptively where the known response surface function incorporates additional white-noise errors. Internal modifications to basic operations in NMSS are made primarily according to some statistical process control statistics in estimating response variation and confidence bands for mean responses. A series of graphical illustrations are presented to give an insight into the way the new simplex-search-type approach accurately anchors the true optimum point in noisy environments. As evidenced by a wide variety of simulation studies on the published response functions, the new method proves to perform much better than two recent modifications of NMSS in solution quality achieved while applied to the stochastic response surface optimization problems. [ABSTRACT FROM AUTHOR]