## 5 Antenna Design via HFSS Optimization Tool  
In order to compare the results attained by the SVR method, the HFSS optimization tool was also used in this paper. The required time during the optimization and accuracy of the simulation results from the desired values are selected as the main comparison parameters. HFSS optimization tool includes various types of optimization methods such as gradient- and search-based algorithms. In this study, Genetic Algorithm (GA) [3; 4; 5; 6; 7; 8] and Pattern Search (PS) [63; 64; 65] methods were used as optimizer in the HFSS optimization setup. Goal parameters are selected as the magnitude of S11 in dB values at \(f_{\tau 1}\) = 2.4 GHz, \(f_{\tau 2}\) = 4.7 GHz, and \(f_{\tau 3}\) = 5.3 GHz. Goal values are chosen to be less than or equal to \(-\)10 dB at these resonance frequencies. HFSS optimizer options are given in Table 4 for GA and PS. The same sampling strategy with the SVR model was used in the HFSS optimizer that is given in Table 1.  
It can be observed that at the 715 th iteration, the GA optimizer of HFSS obtained the optimal results. At the end of the optimization process via GA HFSS optimization tool, slot and arc truncation values are obtained as \(sW1\) and \(sW2\) = 1.8 mm, \(sL1\) = 25.5 mm, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **GA** & **PS** \\ \hline number of parents (current gen.) & 30 & - \\ number of mates & 30 & - \\ number of children & 30 & - \\ crossover type & simulated binary & - \\ mutation type & polynomial & - \\ number of survivors & 10 & - \\ number of individuals (next gen.) & 30 & - \\ selection type & roulette & - \\ selection pressure & 10 & - \\ maximum number of iterations & 1000 & 1000 \\ mutation probability & 0.01 & - \\ crossover probability & 0.98 & - \\ cost function norm type & L1 & L1 \\ weights & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: HFSS optimizer options for Genetic Algorithm and Pattern Search. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **MPATSAT** & [55] & [56] & [57] & [58] & [59] & [60] & [61] & [62] \\ \hline number of bands & triple & triple & triple & triple & triple & triple & triple & triple \\ \hline antenna dimensions & & & & & & & & & \\ \(L\times W\) (mm) & 47.5 \(\times\) 38.6 & 27 (radius) & 34 \(\times\) 18 & 20 \(\times\) 21 & 29 \(\times\) 10 & 60 \(\times\) 60 & 40 \(\times\) 50 & 60 \(\times\) 60 & 44 \(\times\) 45 \\ \hline substrate & RT Duroid & RT Duroid & & & & & & & & \\ \(\text{s}\)5870 & 5870 & FR-4 & FR-4 & FR-4 & FR-4 & denim & FR-4 \\ \hline substrate thickness & & & & & & & & & \\ (mm) & 0.787 & 1.5 & 1.6 & 1.57 & 1.6 & 1.56 & 0.8 & 1 & 1.6 \\ \hline resonance (operating) & 2.5 & 1.8 & 2.5 & 1.29 & 2.4 & 2.6 & 1.65 & 2.45 & 2.39 \\ frequencies (GHz) & 4.8 & 2.4 & 3.5 & 2.44 & 3.5 & 4.2 & 1.93 & 3.25 & 3.55 \\  & 5.3 & 5.4 & 5.5 & 3.26 & 5.5 & 4.6 & 2.2 & 5.8 & 4.13 \\ \hline \multirow{3}{*}{bandwidths (MHz)} & 20 & & 300 & 210 & 80 & 580 & 70 & 76 & 196 \\  & 40 & - & 300 & 300 & 420 & 120 & 60 & 156 & 110 \\  & 50 & & 1000 & 1390 & 600 & 100 & 280 & 328 & 220 \\ \hline gains at resonance & 3.1 & 5.5 & 0.28 & 1.29 & \(\sim\)1.75 & 4.4 & 1.08 & 0.025 & 4.05 \\  & 3.8 & 7.8 & 1.42 & 2.44 & \(\sim\)2 & 3.9 & 1.82 & \(-\)1.871 & 2.52 \\  & 7.1 & 7.9 & 4.76 & 3.26 & \(\sim\)2.3 & 3.8 & 2.93 & 3.703 & 2.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of performance characteristics of MPATSAT with several antennas given in the literature. \(sL2=12.75\) mm and \(r=1.36\) mm via HFSS optimization with GA optimizer. Resonance frequencies with these antenna geometric parameters are obtained as 2.37 GHz, 4.52 GHz, and 5.17 GHz by HFSS simulation. The maximum realized antenna gains are 5.9 dB, 3.5 dB, and 6.6 dB, respectively, for these resonance frequencies. PS HFSS optimizer obtained the optimal results at the 625 th iteration. Slot and arc truncation values are obtained as \(sW1\) and \(sW2=3.23\) mm, \(sL1=21.34\) mm, \(sL2=10.67\) mm, and \(r=1.0\) mm via HFSS optimization with PS optimizer.