## 4 Numerical Results  
We first considered a perfect conductor concealed in the half-space. Figure 1 shows that an amplitude 1 electromagnetic wave is incident on region 1 with a frequency of 3 GHz and a wavelength of 10 cm. The buried depth at \(y=-a=-10 cm\). The background substance in region 1 is air, i.e., \(\varepsilon_{1}=\varepsilon_{0}\) and \(\sigma_{1}=0\). The background substance in region 2 is the soil with \(\varepsilon_{2}=2.56\,\varepsilon_{0}\) and \(\sigma_{2}=0\). In the numerical simulation, we used three different directions of incident waves (\(\emptyset=-60^{\circ},\,0^{\circ}\) and \(60^{\circ}\)) to show the buried object. There were 20 equally spaced measurement points from \(x=-10\,\,cm\) to \(x=10\,\,cm\) to receive the scattered field along the media \(y=-10\,\,cm\). We aimed to utilize the received scattered field collected from various incident angles for reshaping the object. To investigate the effects of noise, we added a quantity of (b + cj) to each complex scattered field, where b and c are independent random numbers with a uniform distribution over 0 to the noise level times the R.M.S value of the scattered field. The numerical results were obtained with a noise level of 1%. In this research, three inverse scattering examples were investigated using the WOA and SHO. The shape function \(F(\theta)\) was chosen to be \((3+0.4 sin3\theta)\,\,cm\) in the first example. This scatterer was set to a smoother shape. The respective reconstructed shape functions by the WOA and SHO were good, as shown in Figures 2 and 3. Comparing Figures 2 and 3, it can be seen that, although the initial guess of the WOA was poor, it still converged to a better result. It is clear that the backside of the object was not reconstructed well by the SHO. The shape function discrepancies \(DISR\) were defined as:  
\[DISR=\left\{\frac{1}{N^{*}}\sum_{t=1}^{N^{\prime}}[F^{cat}(\theta_{i})-F( \theta_{i})]^{2}\,/F^{2}(\theta_{i})\right\}^{\frac{1}{2}} \tag{36}\]  
where \(N^{\prime}\) was set to 100. The \(DISR\) was about 1.5% and 4.7% using the WOA and SHO, respectively. From the numerical results, it can be seen that the reconstruction of the WOA is better than that of the SHO. The shape function was defined as \(F(\theta)=(3+0.5 cos\theta+1 cos3\theta+1.5 sin3\theta)\,\,cm\) in the second example. The buried object was set to a three-petal shape for example 2. From Figures 4 and 5, it can be observed that the shape functions reconstructed by the WOA and SHO were not bad, although there was some discrepancy on the upper part. This is due to the fact that the backside of the object was more difficult to rebuild. Note that the upper part of the object in the figure corresponds to the back side of the buried object. The \(DISR\) was about 11.6% and 14.0% by the WOA and SHO, respectively. From Figures 4 and 5, it can be seen that the initial guess values of the two algorithms were similar. However, the reconstruction results show that the WOA is better than the SHO. We defined the shape function to be \(F(\theta)=(3+0.9 cos3\theta+0.9 sin2\theta)cm\) in the last example. The buried object was set to be a peanut shape. Figures 6 and 7 show the shape functions reconstructed by the WOA and SHO for the best members, respectively. It can be seen that the initial shape of the WOA is better than that of the SHO for this example. It was found that the shape functions reconstructed by the WOA and SHO had some discrepancies in the upper part, especially on the right-hand side. The _DISR_ was about 12.3% and 14.6% by the WOA and SHO, respectively. From the numerical results, it can be seen that the WOA and SHO were less accurate in reconstructing the concave surface on the back of the peanut. Apparently, the reconstruction performance for the WOA overwhelms that of the SHO.