## 4 Optimization Results and Discussion  
After the key structural parameters were identified from the factorial design, GA was employed for optimization. The GA optimizer setup included maximum number of generations (10,000), number of individuals for parents (30), number of mating pools per individual (30), number of individuals for children (30), number of survivors (10), and selection pressure for the next generation (10). For the reproduction setup, a uniform distribution mutation type was utilized with 0.1 uniform mutation probability, 0.5 individual mutation probability, 0.2 variable mutation probability, and 0.05 standard  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multicolumn{10}{c}{**The Unit for the Parameters Is mm**} & \multicolumn{1}{c}{**Return**} & \multicolumn{1}{c}{**Bandwidth**} & \multicolumn{1}{c}{**Maximum**} \\ \hline
**A** & **b** & **c** & **d** & **tl** & **tw** & **ga** & **gb** & **gc** & **gd** & **Loss (dB)** & **(GHz)** & **EMI (V/m)** \\ \hline
0.5 & 1 & 0.75 & 0.75 & 12.75 & 4.5 & 16.5 & 1.5 & 12.5 & 0.45 & \(-\)41.7 & 8.47 & 15.54 \\ \hline
1.5 & 1 & 0.25 & 2.25 & 12.75 & 4.5 & 5.5 & 1.5 & 37.5 & 0.15 & \(-\)34.2 & 8.51 & 15.78 deviation [33]. These GA set up values were taken from [33], which also employed GA to optimize antenna design parameters with highly accurate results. The optimized values of the parameters are shown in Table 3. Figure 5 shows the optimal design of the antenna in comparison with the initial antenna design. Figure 6 shows the EMI results for the nominal initial antenna design and the optimized design. We can see that in the frequency range covered by the antenna (shown in Figure 7 where the return loss is less than \(-10\) dB), EMI was reduced by about 1 V/m. The initial antenna design covers a frequency range from 7.84 to 16.44 GHz, while the optimized antenna covers a frequency range from 7.72 to 17.25 GHz In Figure 7, the major change can be seen in the frequency at which the return loss is at a minimum. The antenna was excited using a wave port excitation at 10.3 GHz frequency and it was observed that the maximum surface current distribution concentrated at the excited port, and this is depicted in Figure 8. Surface current distribution was reduced for the same excitation in the optimized antenna, by almost half of that of the initial antenna. Lower current density points towards lower power consumption of the antenna. Figure 6: EMI for the 1 m spherical environment from the antenna. Figure 7: Return loss of antenna. The 2-D and 3-D radiation patterns obtained in the E-fields and H-fields of the initial and optimized antennas at 10 GHz (operating frequency) was simulated and depicted in Figure 9. The antenna was simulated in the xz-plane orientation, where red and violet color patterns in Figure 9a and b represent radiation patterns for phi angles of 0\({}^{\circ}\) and 90\({}^{\circ}\), respectively, and the theta angle is 0\({}^{\circ}\). 3-D radiation patterns help to study the spread from the antenna into the environment. It is noticed that both the initial and optimized antennas achieved omnidirectional radiation patterns at a central frequency. Figure 8: Surface current distribution. Figure 9: \(Cont\). Peak gain was plotted with respect to the operating frequency of the antenna as shown in Figure 10. An increase in peak gain was observed with the increase in operating frequency: 0.7 dB to 4.95 dB was the average peak gain of the initial antenna design, whereas 0 dB to 5 dB was the average peak gain for the optimized antenna for the given frequency range (where return loss was less than \(-10\) dB). The advantage of stubs is that it helps to achieve small peak gains at lower operating frequencies [34]. A small variation of 0.05 dB found in the peak gain of an antenna is because of the reduced ground plane [34]. Figure 9: Radiation patterns for the initial and optimized antennas: (**a**,**b**) show 2-D radiation patterns and (**c**,**d**) show 3-D radiation patterns.