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Algorithms 2016, 9(2), 40; doi:10.3390/a9020040

A Direct Search Algorithm for Global Optimization

Instituto de las Tecnologías Avanzadas de la Producción (ITAP), Universidad de Valladolid, Paseo del Cauce 59, 47011 Valladolid, Spain
Centro Tecnológico Cartif, Parque Tecnológico de Boecillo 205, 47151 Bocillo, Spain
Author to whom correspondence should be addressed.
Academic Editor: George Karakostas
Received: 19 January 2016 / Revised: 25 April 2016 / Accepted: 7 June 2016 / Published: 13 June 2016
View Full-Text   |   Download PDF [1262 KB, uploaded 13 June 2016]   |  


A direct search algorithm is proposed for minimizing an arbitrary real valued function. The algorithm uses a new function transformation and three simplex-based operations. The function transformation provides global exploration features, while the simplex-based operations guarantees the termination of the algorithm and provides global convergence to a stationary point if the cost function is differentiable and its gradient is Lipschitz continuous. The algorithm’s performance has been extensively tested using benchmark functions and compared to some well-known global optimization algorithms. The results of the computational study show that the algorithm combines both simplicity and efficiency and is competitive with the heuristics-based strategies presently used for global optimization. View Full-Text
Keywords: global optimization; direct search methods; search space transformation; derivative-free optimization; heuristics-based optimization global optimization; direct search methods; search space transformation; derivative-free optimization; heuristics-based optimization

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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. (CC BY 4.0).

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MDPI and ACS Style

Baeyens, E.; Herreros, A.; Perán, J.R. A Direct Search Algorithm for Global Optimization. Algorithms 2016, 9, 40.

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