This paper presents an automated antenna design and optimization framework employing multi-objective genetic algorithms (MOGAs) to investigate various evolutionary optimization approaches, with a primary emphasis on multi-band frequency optimization. Five MOGA variants were implemented and compared: the Pareto genetic algorithm (PGA), non-dominated sorting genetic algorithm with niching (NSGA-I), non-dominated sorting genetic algorithm with elitism (NSGA-II), non-dominated sorting genetic algorithm using reference points (NSGA-III), and strength Pareto evolutionary algorithm (SPEA). These algorithms are employed to design and optimize microstrip patch antennas loaded with complementary split-ring resonators (CSRRs). A weighted-sum scalarization approach was adopted within a single-objective genetic algorithm framework enhanced with domain-specific constraint handling mechanisms. The optimization addresses the conflicting objectives of minimizing the return loss ($S_{11} < -10$~dB) and achieving multi-band resonance at 2.4~GHz, 3.6~GHz, and 5.2~GHz. The proposed method delivers a superior overall performance by aggregating these objectives into a unified fitness function encompassing $S_{11}$(2.4~GHz), $S_{11}$(3.6~GHz), and $S_{11}$(5.2~GHz). This approach effectively balances all three frequency bands simultaneously, rather than exploring trade-off solutions typical of traditional multi-objective approaches. The antenna was printed on a Rogers RT5880 substrate with a dielectric constant of 2.2 , loss tangent of 0.0009 , and thickness of 1.57~mm . Scalarization approach achieved return loss values of $-21.56$~dB, $-16.60$~dB, and $-27.69$~dB, with corresponding gains of 1.96~dBi, 2.6~dB, and 3.99~dBi at 2.4~GHz, 3.6~GHz, and 5.2~GHz, respectively.

翻译：本文提出了一种采用多目标遗传算法（MOGAs）的自动化天线设计与优化框架，以研究多种进化优化方法，主要侧重于多频段频率优化。本文实现并比较了五种MOGA变体：帕累托遗传算法（PGA）、带小生境的非支配排序遗传算法（NSGA-I）、带精英策略的非支配排序遗传算法（NSGA-II）、使用参考点的非支配排序遗传算法（NSGA-III）以及强度帕累托进化算法（SPEA）。这些算法用于设计和优化加载互补开口环谐振器（CSRRs）的微带贴片天线。在采用特定领域约束处理机制增强的单目标遗传算法框架内，采用了加权和标量化方法。优化处理了最小化回波损耗（$S_{11} < -10$~dB）和在2.4~GHz、3.6~GHz及5.2~GHz实现多频段谐振这两个相互冲突的目标。所提出的方法通过将这些目标聚合为一个包含$S_{11}$(2.4~GHz)、$S_{11}$(3.6~GHz)和$S_{11}$(5.2~GHz)的统一适应度函数，实现了优越的整体性能。该方法有效地同时平衡了所有三个频段，而不是探索传统多目标方法中典型的权衡解。天线印制在介电常数为2.2、损耗角正切为0.0009、厚度为1.57~mm的Rogers RT5880基板上。标量化方法在2.4~GHz、3.6~GHz和5.2~GHz分别实现了$-21.56$~dB、$-16.60$~dB和$-27.69$~dB的回波损耗值，对应的增益分别为1.96~dBi、2.6~dB和3.99~dBi。