# Optimization of Multilayer Absorbers Using the Bald Eagle Optimization Algorithm
## 3 Results  
The BESOA was used to design multilayer electromagnetic absorbers for the microwave frequency band. The materials and thicknesses of layers were considered to minimize the maximum RC in the required FR. [PERSON]'s recursive formula (Equation (1)) was used to calculate the RC of the MMA for both TE and TM polarizations. The optimiza  
\begin{table}
\begin{tabular}{|c c c c c|} \hline \multicolumn{4}{|c|}{Lossy Dielectric Materials (\(\mu^{\prime}=1,\ \mu^{\prime}=0\) )} \\ \multicolumn{2}{|c|}{\(\epsilon=\epsilon^{\prime}-j\epsilon^{\prime}\)} & \(\epsilon^{\prime}(f)=\frac{\epsilon^{\prime}(1\,\mathrm{GHz})}{f^{\prime}}\) & \(\epsilon^{\prime}(f)=\frac{\epsilon^{\prime}(1\,\mathrm{GHz})}{f^{\prime}}\) \\ \hline No: & \(\epsilon^{\prime}(1\,\mathrm{GHz})\) & \(a\) & \(\epsilon^{\prime}(1\,\mathrm{GHz})\) & \(b\) \\ \hline
6 & 5 & 0.861 & 8 & 0.569 \\
7 & 8 & 0.778 & 10 & 0.682 \\
8 & 10 & 0.778 & 6 & 0.861 \\ \hline \multicolumn{4}{|c|}{Relaxation–Type Magnetic Materials (\(\epsilon^{\prime}=15,\ \epsilon^{\prime}=0\) )} \\ \multicolumn{4}{|c|}{\(\mu=\mu^{\prime}-j\mu^{\prime\prime}\)} & \(\mu^{\prime}(f)=\frac{\mu_{m}f_{m}^{2}}{f^{\prime}+f_{m}^{2}}\) & \(\mu^{\prime\prime}(f)=\frac{\mu_{m}f_{m}}{f^{\prime}+f_{m}^{2}}\) & \\ \multicolumn{4}{|c|}{\(f\) and \(f_{m}\) GHz} \\ \hline No: & \(\mu_{m}\) & & \(f_{m}\) \\ \hline
9 & 35 & & 0.8 \\
10 & 35 & & 0.5 \\
11 & 30 & & 1.0 \\
12 & 18 & & 0.5 \\
13 & 20 & & 1.5 \\
14 & 30 & & 2.5 \\
15 & 30 & & 2.0 \\
16 & 25 & & 3.5 \\ \hline \end{tabular}
\end{table}
Table 1: _Cont._  
Figure 4: The Bald Eagle Search Optimization Algorithm (BESOA).  
tions were performed for both normal and oblique incidences. The BESOA was used to build microwave absorbers for a variety of material combinations, several layers, a large FR, and a broad angle of incidence; these MMAs were then compared with existing ones.  
In the optimization process, the population of eagles was set to 50. The dimension, which stands for the layers and their corresponding thicknesses, was considered as two times the number of layers. The maximum layer thickness was set to 1.5 mm to restrict the search boundary. For each design, 20 independent trials were performed with 150 iterations. The best results and their comparison with the recent literature are presented. Sixteen MMA designs with the least maximum RC and the thinnest overall thickness are obtained and compared with 25 different designs. Thirteen of them have lower maximum RCs and thinner overall thickness. The optimum designs are obtained with less than 100 iterations. Referring to the literature, it is seen that the maximum iteration number for DE [16], CFO [10], PSO [11; 13; 18], GSA [10], and LSA [12] is 1000. This value is 650 for DS-ABC, which is 150 is for the first stage and 500 for the second stage. The fewer the iterations, the less the computation time. The optimizations are performed on Intel (R) Core (TM) i7-6700 HQ CPU (2.60 GHz; 2.59 GHz with 16 GB). The execution time for BESOA with a population of 50 is calculated as 798.531 s for 20 trials.  
A FR of 1 to 20 GHz was considered. The MMAs were designed for 2-8 GHz, 12-18 GHz, 2-18 GHz, and 1-20 GHz FRs, and the frequency increment was set to 0.1 GHz. The angle of incidence varied from 0\({}^{\circ}\) to 75\({}^{\circ}\)for a set size of 15\({}^{\circ}\). Here, \(\varphi\)1 and \(\varphi\)2 were considered as 1 and 1000, respectively.