• concentric ring array;
  • multiobjective optimization;
  • Pareto front;
  • beam scanning;
  • peak sidelobe level (PSLL)


This paper presents a multiobjective differential evolution (MODE) algorithm for designing concentric ring arrays with three-dimensional (3D) beam scanning. The problem formulation of the concentric ring arrays with 3D beam scanning based on the optimization of the array geometry is a constrained multiobjective optimization problem. To obtain 3D beam scanning, concentric ring array geometries are optimized. The design tradeoffs, namely, the directivity, peak sidelobe level, and the total number of elements of the concentric ring array, are captured by using MODE. MODE adopts an external archive to retain nondominated solutions that are found during the evolutionary process. The method yields the distribution of the objective function values and the corresponding array configurations. In addition, the nondominated sorting genetic algorithm-II (NSGA-II), which is a well-known multiobjective evolutionary algorithm, is also employed to optimize the proposed problems. The comparison with the results of NSGA-II reveals the superiority of the MODE approach and confirms its potential for the array synthesis problems. Copyright © 2012 John Wiley & Sons, Ltd.