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A great increase of computational resources to deal with science and engineering problems has happened in the last thirty years. The progress has led to the rapidly development of many advanced numerical algorithms (Arianos et al., 2012). As a kind of the global optimization search method, evolutionary computation methods have been widely applied in the variety of fields, such as Artificial Intelligence (Wang, 2015; Thabit, 2019), engineering (Bilbao, 2015; Yu, 2019), bioinformatics (Pei, Zhou, Chen, Liu, &Wang, 2015), economics (Kim, 2015; Miralles-Pechuán, 2018), and so on. In addition, the further improvement in computational power for the future will strengthen the role of efficient numerical methods for handing complex problems, especially the nonlinear optimization problem.
Since the early 1990s, evolutionary optimization methods had been widely applied to electromagnetics (Weile & Michielssen, 1997). With the development of artificial intelligence for decades, evolutionary algorithms (EAs) such as genetic algorithms (GAs) (Altshuler, 1997; Rogers, 2002; Kerkhoff, 2007), differential evolutions (DEs) (Zheng, 2017; Goudos, 2017), particle swarm optimizations (PSOs) (Jarufe, 2018; Wu, 2019), evolution strategies (ESs) (BouDaher & Hoorfar, 2015), and other evolutionary optimization techniques, are widely employed to deal with antenna design problems. Wire antenna designs were optimized by using GAs in papers (Altshuler, 1997; Smith, 2019). A quadrifilar helical antenna was designed in (Lohn, Kraus & Linden, 2002) where a co-evolutionary GA was applied to optimize the gain and size of the quadrifilar helical antenna. The group further designed an X-Band antennas for NASA's Space Technology 5 Mission (Hornby, Lohn & Linden, 2011). In this research, two EAs were used: the first used a vector of real-valued parameters and the second used a tree-structured generative representation for constructing the antenna, and experimental results show that the proposed method is effective. In paper (Yang &Adams, 2016), a systematic method was presented to the shape optimization of compact, single-aperture MIMO antennas based on characteristic modes and GA. A new approach of controlling antenna radiation power pattern were introduced based on both GA and newly technology 3-D printing of special dielectric materials (Wu, Abdelrahman, Liang, Yu, & Xin, 2017). Dynamic and multi-objective techniques are integrated into EAs to deal with antenna array problems with many local optima (Jiao, Zeng, Alkasassbeh, & Li, 2017). The paper (Ma, Yang, Chen, Qu, & Hu, 2019) proposed an effective optimization approach for the pattern synthesis of 4-D irregular arrays based on the maximum-entropy model and DE. The above researches all deal with the two challenges. The feasible solutions of antenna design problem are hard to be found, because the design constraints are very strange. In addition, the precision of fabricating the antenna maybe can not guarantee. However, the outcomes were very satisfactorily.