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A particle swarm pattern search method for bound constrained global optimization

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Abstract

In this paper we develop, analyze, and test a new algorithm for the global minimization of a function subject to simple bounds without the use of derivatives. The underlying algorithm is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the optional search phase of pattern search we apply a particle swarm scheme to globally explore the possible nonconvexity of the objective function. Our extensive numerical experiments showed that the resulting algorithm is highly competitive with other global optimization methods also based on function values.

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Correspondence to A. Ismael F. Vaz.

Additional information

Support for A. Ismael F. Vaz was provided by Algoritmi Research Center, and by FCT under grants POCI/MAT/59442/2004 and POCI/MAT/58957/2004.

Support for Luís N. Vicente was provided by Centro de Matemática da Universidade de Coimbra and by FCT under grant POCI/MAT/59442/2004.

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Vaz, A.I.F., Vicente, L.N. A particle swarm pattern search method for bound constrained global optimization. J Glob Optim 39, 197–219 (2007). https://doi.org/10.1007/s10898-007-9133-5

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