## 3 Improved Sparrow Search Algorithm
### Improved Sparrow Search Algorithm
Figure 12 shows that the designed antennas meet objective \(F_{2}\), and the reflection coefficients are all less than \(-10\) dB in the corresponding frequency band, which can work perfectly. Figure 11: Pareto Front of the planar tri-band antenna. Figure 12: Simulated results of the reflection coefficient of antenna models. \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline  & **W** & **W1** & **W2** & **W3** & **W4** & **L** & **L1** & **L2** & **L3** & **L4** \\ \hline antenna model x (1) & 23.26 & 5.96 & 3.32 & 1.81 & 0.99 & 48.63 & 19.87 & 11.05 & 6.49 & 9.88 \\ antenna model x (2) & 22.55 & 5.64 & 3.09 & 1.64 & 1.49 & 48.28 & 18.90 & 11.25 & 7.09 & 9.33 \\ antenna model x (3) & 24.43 & 5.55 & 3.33 & 2.11 & 1.31 & 49.21 & 19.12 & 11.06 & 6.11 & 9.94 \\ antenna model x (4) & 23.39 & 5.03 & 2.93 & 2.10 & 1.19 & 49.20 & 19.11 & 11.09 & 6.36 & 9.96 \\ antenna model x (5) & 23.46 & 5.07 & 3.37 & 1.86 & 0.75 & 48.73 & 18.73 & 11.63 & 7.04 & 9.97 \\ \hline \end{tabular}
\end{table} 
Table 5: Optimal size parameters of the tri-band antenna (unit: mm). The planar tri-band antenna can meet the antenna design requirements in three frequency bands, less than \(-10\) dB, which are suitable for WLAN wireless networks and high-frequency communication. It can be seen from Figure 13 that in the two-center frequencies of 2.17 GHz and 5.28 GHz, the 3D polar plots of antennas are relatively regular, indicating that the radiation direction is relatively uniform, and the gain is higher than \(-10\) dB. Figure 13: Simulated results from the obtained structure of the tri-band antenna of HFSS: (**a**) 3D polar plot of antenna model x (1) at 2.17 GHz; (**b**) 3D polar plot of antenna model x (1) at 5.28 GHz; (**c**) 3D polar plot of antenna model x (1) at 7.45 GHz; (**d**) 3D polar plot of antenna model x (2) at 2.17 GHz; (**e**) 3D polar plot of antenna model x (2) at 5.28 GHz; (**f**) 3D polar plot of antenna model x (2) at 7.45 GHz; (**g**) 3D polar plot of antenna model x (3) at 2.17 GHz; (**h**) 3D polar plot of antenna model x (3) at 5.28 GHz; (**i**) 3D polar plot of antenna model x (3) at 7.45 GHz; (**j**) 3D polar plot of antenna model x (4) at 2.17 GHz; (**k**) 3D polar plot of antenna model x (4) at 5.28 GHz; (**l**) 3D polar plot of antenna model x (4) at 7.45 GHz; (**m**) 3D polar plot of antenna model x (5) at 2.17 GHz; (**n**) 3D polar plot of antenna model x (5) at 7.45 GHz. 1.8 dB, which meets the design requirements. When the center frequency reaches 7.45 GHz, although the gain of the antenna is enhanced, the directivity becomes worse, resulting in the 3D directional map of the antenna becoming irregular. In general, the reflection coefficient and gain of the designed antenna can meet the requirements of the three-center frequency of 2.17 GHz, 5.28 GHz, and 7.45 GHz. The time comparison between using HFSS electromagnetic simulation software and the method used in this paper to optimize the antenna structure is shown in Table 6. The running time of HFSS electromagnetic simulation software is about 47.70 s per simulation. The optimization of the antenna in this paper by HFSS requires about 1900 simulations, which takes 25.18 h in total. Using the method proposed in the paper to design the antenna, it takes one hundred simulations to build the model, and the total time is 1.55 h, which is only 6.14% of the HFSS method. Finally, we have fabricated the antenna model x (1) in Table 5 and measured the reflection coefficient of the antenna. The real antenna is shown in Figure 14, and the measured results of the reflection coefficient are shown in Figure 15. It is easy to see from Figure 15 that the measured and simulated results of the antenna are very similar. The reflection coefficient is less than \(-10\) dB in the three frequency bands, and the measured results conform to the expected objective. This further illustrates the effectiveness and practicality of the method proposed in this paper.