Multi-Objective Fitness Functions with Non-Linear Switching for Antenna Optimizations

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.