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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.18 n.2 México Apr./Jun. 2014

http://dx.doi.org/10.13053/CyS-18-2-2014-030 

Artículos regulares

 

An Adaptive Random Search for Unconstrained Global Optimization

 

Búsqueda aleatoria adaptiva para problemas de optimizacón global sin restricciones

 

Jonás Velasco1, Mario A. Saucedo-Espinosa1, Hugo Jair Escalante2, Karlo Mendoza1, César Emilio Villarreal-Rodríguez1, Óscar L. Chacón-Mondragón1, and Arturo Berrones1

 

1 Posgrado en Ingeniería de Sistemas, Facultad de Ingeniería Mecánica y Eléctrica, Universidad Autónoma de Nuevo León, Mexico jonasovich2@gmail.com, m.a.saucedo.e@gmail.com, karlo.mendoza@gmail.com, cesarevr@gmail.com, olchacon.uanl@gmail.com, arturo.berrones@gmail.com

2 Departamento de Ciencias Computacionales, Instituto Nacional de Astrofísica, Óptica y Electrónica, Mexico hugo.jair@gmail.com

 

Abstract

Adaptive Gibbs Sampling (AGS) algorithm is a new heuristic for unconstrained global optimization. AGS algorithm is a population-based method that uses a random search strategy to generate a set of new potential solutions. Random search combines the one-dimensional Metropolis-Hastings algorithm with the multidimensional Gibbs sampler in such a way that the noise level can be adaptively controlled according to the landscape providing a good balance between exploration and exploitation over all search space. Local search strategies can be coupled to the random search methods in order to intensify in the promising regions. We have performed experiments on three well known test problems in a range of dimensions with a resulting testbed of 33 instances. We compare the AGS algorithm against two deterministic methods and three stochastic methods. Results show that the AGS algorithm is robust in problems that involve central aspects which is the main reason of global optimization problem difficulty including high-dimensionality, multi-modality and non-smoothness.

Keywords: Random search, Metropolis-Hastings algorithm, heuristics, global optimization.

 

Resumen

El algoritmo del Muestreador Adaptivo de Gibbs (MAG) es una nueva heurística para la optimización global irrestricta. El algoritmo MAG es un método basado en poblaciones que utiliza una estrategia de búsqueda aleatoria para generar un nuevo conjunto de soluciones potenciales. La búsqueda aleatoria combina el algoritmo unidimensional de Metrópolis-Hastings con el multidimensional muestreador de Gibbs, de tal manera que el nivel de ruido se puede controlar adaptativamente de acuerdo al panorama de la función. Existe un buen equilibrio entre la exploración y la explotación en todo el espacio de búsqueda. Una estrategia de búsqueda local puede acoplarse a la búsqueda aleatoria con el fin de intensificar en las regiones prometedoras. Los experimentos se desarrollaron sobre tres problemas conocidos en un rango de dimensiones, con un banco de prueba resultante de 33 instancias. El algoritmo MAG se comparó contra dos métodos deterministas y tres métodos estocásticos. Los resultados muestran que el algoritmo MAG es robusto en problemas que involucran aspectos centrales que determinan principalmente la dificultad de los problemas de optimización global, es decir, de alta dimensionalidad, multimodalidad y la no suavidad.

Palabras clave: Búsqueda aleatoria, algoritmo de Metrópolis-Hastings, heurísticas, optimización global.

 

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Acknowledgements

This work was supported in part by the Mexican National Council for Science and Technology (CONACyT), grant 206705, and by UANL-PAICYT program, grant "Inference based on density estimation".

 

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