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Evolutionary multi‐objective design of non‐uniform circular phased arrays

Marco A. Panduro (Unidad Académica Reynosa‐Rodhe, Universidad Autónoma de Tamaulipas, Reynosa, México)
Carlos A. Brizuela (CICESE Research Center Km. 107 Carretera Tijuana‐Ensenada, Ensenada, México)



The purpose of this paper is to present the application of an efficient genetic algorithm to deal with the problem of computing the trade‐off curves for non‐uniform circular arrays. In order to answer questions related to the performance of the non‐uniform circular phased arrays, two criteria are considered to evaluate the design: the criteria of minimum main beam width and minimum side lobe level (SLL) during scanning.


The design of non‐uniform circular arrays is modeled as a multi‐objective optimization problem. The Non‐dominated Sorting Genetic Algorithm II (NSGA‐II) is employed as the methodology to solve the resulting optimization problem. This algorithm is considered to be one of the best evolutionary optimizer for multi‐objective problems. It is chosen for its ease of implementation and its efficiency for computation of non‐dominated ranks. The method is based on the survival of the fittest paradigm, where each individual in the population represents a feasible solution of the optimization problem being solved. The concept of fitness is adapted to take into account the concept of solution quality in multi‐objective problems. This evolutionary method can be used effectively for computing the trade‐off curves between the SLL and the main beam width.


The NSGA‐II algorithm can effectively compute the trade‐off curve of different non‐uniform circular arrays. The simulation results presented in this paper show design options that maintain a low SLL and main beam width without pattern distortion during beam steering. Moreover, these trade‐off curves provide a more realistic approach to the solution of the design problem.


The design problem is set to determine which are the best design configurations or separations between the antenna elements and the best amplitude excitations when a circular structure is employed. Owing to the complex feasible region and the non‐linear dependence of optimization criteria from the decision variables, simple traditional and more sophisticated mathematical programming approaches will lead us to local optimal solutions in the case we can apply them. To the best of our knowledge, this multi‐objective optimization problem has not dealt with before, when two or more conflicting design criteria are taken into account. Therefore, the solution to this problem constitutes the main contribution of our paper.



Panduro, M.A. and Brizuela, C.A. (2008), "Evolutionary multi‐objective design of non‐uniform circular phased arrays", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 2, pp. 551-566.



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Copyright © 2008, Emerald Group Publishing Limited

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