In a multi-objective optimization process, several goals are traditionally combined into a single fitness function. In such cases, the choice of the objective function is critical, as it should accurately represent the desired optimization goals. Here, we introduce a new class of multi-objective functions with non-linearity and switching behavior, and also provide a method for objective function engineering. Notably, the proposed objective functions introduce versatile forms of fitness growth during the optimization, and provide a systematic approach for integrating the expertise in antenna design with the optimization process. The proposed optimization processes are applied in antenna optimization to demonstrate their enhanced performance. Our optimization examples consider problems based on both analytical electromagnetic models and full-wave simulation. Specifically, we consider the designs of an end-fire array, a pyramidal horn antenna, a Yagi-Uda array, and a wideband patch antenna. Our results suggest that, with minimum computation effort, the proposed non-linear fitness functions produce better performing designs when compared to a linear summation-based fitness function, e.g., 12% higher forward gain for the Yagi-Uda array, 9.3% lower side lobe level for the horn antenna, 23.38% higher directivity for the end-fire array, and approximately 1.5 times higher bandwidth for the wideband patch antenna.

中文翻译：

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用于天线优化的具有非线性切换的多目标适应度函数

在多目标优化过程中，传统上将几个目标组合成一个适应度函数。在这种情况下，目标函数的选择至关重要，因为它应该准确地表示所需的优化目标。在这里，我们介绍了一类新的具有非线性和切换行为的多目标函数，也为目标函数工程提供了一种方法。. 值得注意的是，所提出的目标函数在优化过程中引入了多种形式的适应度增长，并提供了一种将天线设计专业知识与优化过程相结合的系统方法。建议的优化过程应用于天线优化，以展示其增强的性能。我们的优化示例考虑了基于解析电磁模型和全波仿真的问题。具体来说，我们考虑了端射阵列、金字塔喇叭天线、八木-宇田阵列和宽带贴片天线的设计。我们的结果表明，与基于线性求和的适应度函数相比，所提出的非线性适应度函数以最少的计算工作量产生更好的性能设计，例如，八木宇田阵列的前向增益提高了 12%，9。