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Evolutionary algorithms(EAs) are global, parallel, search and optimization methods, based on the principles of natural selection (Darwin, C. 2004) and population genetics (Fisher, R. A. 1958), and which are found a wide range of applications in various fields of science and engineering (Dasgupta, D., & Michalewicz, Z. (Eds.). 2013, Fleming, P. J., & Purshouse, R. C. 2002). EAs have been widely employed for solving antenna problems since the early 1990s (Altshuler, E. E., & Linden, D. S. 1997, Linden, D. S., & Altshuler, E. E. 1996), generally, antenna design problems are modeled as constrained optimization problems (COPs) (Hu, C., et al. 2019, Liu, B., et al. 2013, Liu, Z., Zeng, S., Jiang, Y., Li, C., & Ouyang, N. 2013, Jia, L., et al. 2011, Wang, Y., & Cai, Z. 2012,). Such as, Genetic Algorithm (GA) (Goldberg, D. E., & Holland, J. H. 1988) is usually selected as an optimization tool for the antenna design in (Altshuler, E. E., & Linden, D. S. 1997, Chou, H. T., & Cheng, D. Y. 2016, Linden, D. S., & Altshuler, E. E. 1996, Makki, B., Ide, A., Svensson, T., Eriksson, T., & Alouini, M. S. 2016, Wen, Y. Q., Wang, B. Z., & Ding, X. 2015). Differential Evolution (DE) (Storn, R., & Price, K. 1997) is used frequently in the field of antenna design (Hu, C., et al. 2019, Cui, C. Y., Deb, A., Roy, J. S., & Gupta, B. 2014, Ding, Y., Jiao, Y. C., Zhang, Jiao, Y. C., & Zhang, L. 2017, L., & Li, B. 2014). Particle Swarm Optimization (Eberhart, R., & Kennedy, J. 1995) is used for antenna design (Jin, N., & Rahmat-Samii, Y. 2007, Robinson, J., & Rahmat-Samii, Y. 2004). Evolution Strategy (ES) (Rechenberg, I. 1994) is used usually in the antenna optimization (Chen, Y., Yang, S., & Nie, Z. 2008, Choi, K., et al. 2015), and other evolutionary techniques.
Microstrip patch antennas with low profile, conformable to planar and nonplanar surfaces, easy realization and inexpensive to manufacture using modern printed circuit technology, have been widely researched in recent years (Colles, D., & Arakaki, D. 2014, Dwivedi, S., Yadav, S. G., & Singh, A. K. 2014, Radavaram, S., & Pour, M. 2018, Pozar, D. M. 1992, Wang, H., Huang, X. B., Fang, D. G., & Han, G. B. 2007), and pay an important role in developing the mobile radio, wireless communication, high-performance aircraft, and satellite engineering application. The patch shapes with ellipse that have a good demand and fame for their feed line flexibility and multiple frequency operation are usually considered in microstrip patch antennas design. On top of that, elliptical microstrip patch antennas that can give dual resonant frequency owing to two modes, even and odd mode (Agrawal, A., Vakula, D., & Sarma, N. V. S. N. 2011, Long, S., Shen, L., Schaubert, D., & Farrar, F. 1981). Therefore, there are many researchers have interested in elliptical patch microstrip antennas (Jung, H., & Seo, C. 2002, Saxena, P., Ranjan, R., & Gupta, K. 2016, Tasnim, N., Inum, R., Khatun, H., & Khan, M. A. G. 2019).