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Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.15 n.1 México Jul./Sep. 2011




A Bayesian Estimation of Distribution Algorithm Approach to the Definition of Linear Antenna Arrays Excitations


Un enfoque basado en algoritmos con estimación de distribuciones para el diseño de arreglos lineales de antenas


Julio Isla1 and Alberto Ochoa2


1 Facultad de Ingeniería Eléctrica, Instituto Superior Politécnico José Antonio Echeverría (ISPJAE), Habana, Cuba. E–mail:

2 Departamento de Matemática Interdisciplinaria, Instituto de Cibernética Matemática y Física (ICIMAF), Habana, Cuba. E–mail:


Article received on April 30, 2011.
Accepted on June 30, 2011.



This paper introduces and investigates the family of aperture distributions whose members have the best Side Lobe Ratio (SLR) for a given Inverse Dynamic Range Ratio (IDRR). An optimization approach based on Estimation of Distributions Algorithms is used to find the family instances. The paper shows that the family has limiting distributions with a number of interesting properties, e.g. it has a good tradeoff between beamwidth and SLR and has the best IDRR for a given beamwidth. The numerical results allow us to conclude the following: 1) the IDRR impacts the complexity of the problem, i.e. the larger the IDRR the easier the optimization. 2) linear entropic mutation improves the performance of the algorithms and reduces the population size requirements. 3) the independence model seems to be adequate for very large IDRR but fails dramatically for the other cases.

Keywords: G.1.6:Optimization, G.1.10: Applications, J.2: Physical Sciences and Engineering, antenna arrays, Dolph–Chebyshev distribution, Taylor distribution, dynamic range ratio, estimation of distribution algorithms, side lobe ratio and linear entropic mutation.



Este artículo introduce e investiga la familia de distribuciones de apertura cuyos miembros poseen el menor lóbulo lateral (SLR) para un rango dinámico inverso (IDRR) dado. Un enfoque de optimización basado en algoritmos de estimación de distribuciones es utilizado para encontrar los miembros de la familia. El artículo muestra que la familia presenta distribuciones límites con propiedades interesantes: muestra un buen compromiso entre el ancho del lóbulo central y SLR además del mejor IDRR para un HPBW dado. Los resultados numéricos nos permiten concluir lo siguiente. 1) el IDRR influye en la complejidad del problema: para altos IDRR es más fácil el proceso de optimización. 2) la mutación entrópica lineal mejora el comportamiento de los algoritmos y reduce el tamaño de la población. 3) el modelo de independencia parece resultar adecuado para altos IDRRs pero falla dramáticamente para otros casos.

Palabras clave: G.1.6: Optimización, G.1.10: Aplicaciones, J.2: Ciencias Físicas e Ingeniería, arreglos de antenas, distribución de Dolph–Chebyshev, distribución de Taylor, relación de rango dinámico, estimación de los algoritmos de distribución, relación de los lóbulos laterales y la mutación de entropía lineal.





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