Antenna arrays can enhance the performance and reduce the overhead of the wireless communication systems. However, the beam pattern synthesis of antenna arrays are difficult problems since the optimization properties are usually trade-offs that affect each other. In this paper, we formulate a multiobjective beam pattern optimization problem (MBPOP) to simultaneously reduce the maximum sidelobe level (SLL) and achieve the nulls of the antenna array beam pattern. The multiobjective evolutionary algorithm based on decomposition (MOEA/D) is a general and effective algorithm to solve the MOPs. However, it may be easy to lose population diversity and converge to local optimum. To overcome the issues above, we propose an improved MOEA/D (IMOEA/D) to deal with the formulated MBPOP. IMOEA/D introduces the normal distribution crossover operator (NDX), Lévy flight strategy and Euclidean distance-based solution selection mechanism to enhance the performance of conventional MOEA/D to make it more suitable to solve the formulated MBPOP. Experiments are conducted and the results indicate that the proposed IMOEA/D has a better performance in terms of the convergence rate and population diversity compared to other algorithms for solving the formulated MBPOP.

中文翻译：

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一种改进的基于分解法的多目标进化算法及其在天线阵列波束图合成中的应用

天线阵列可以提高无线通信系统的性能并降低其开销。然而，天线阵列的波束图合成是一个难题，因为优化特性通常是相互影响的权衡。在本文中，我们制定了一个多目标波束图优化问题 (MBPOP)，以同时降低最大旁瓣电平 (SLL) 并实现天线阵列波束图的零点。基于分解的多目标进化算法(MOEA/D)是求解MOPs的通用有效算法。然而，可能很容易失去种群多样性并收敛到局部最优。为了克服上述问题，我们提出了一种改进的 MOEA/D (IMOEA/D) 来处理制定的 MBPOP。IMOEA/D 引入了正态分布交叉算子 (NDX)，Lévy 飞行策略和基于欧几里得距离的解选择机制，以增强常规 MOEA/D 的性能，使其更适合求解公式化的 MBPOP。进行了实验，结果表明，与用于求解公式化 MBPOP 的其他算法相比，所提出的 IMOEA/D 在收敛速度和种群多样性方面具有更好的性能。