## 3 Experimental Results and Discussion
### Engineering Problems
#### 3.7.4 Antenna Optimization Problem  
[PERSON] et al. suggested a validated a benchmark test suite for Antenna S-parameter optimization [55]. In the test suite there are unimodal, multimodal, and compositional functions. Each of these functions matches a typical landscape of electromagnetic simulated antenna problems. For this analysis two functions were chosen which can approximate the s-parameter optimization function behavior of two different antennas. Equations (50) and (51) model the single antenna and multi-antenna problems, respectively. Function in Equation (50) is continuous and separable and the landscape has a rose shape which is similar to the patterns of the dual band antenna. Function in Equation (51) is continuous  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **GSLEO-AEFA** & **AEFA** & **PSO** & **DE** & **JAYA** & **SCA** & **CS** \\ \hline x(1) & 0.000 & 2.497 & 1.984 & 3.427 & 1.135 & 4.000 & 1.613 \\ x(2) & 4.000 & 1.998 & 2.758 & 3.992 & 3.908 & 0.000 & 0.0  
non-differentiable and non-separable and its landscape is similar to the reflection pattern of the (multiple input-multiple output) MIMO antenna.  
\[s_{1}(x)=20\log\left(2\left(\sum_{i=1}^{n}\left|\left(\sin\left(\frac{x_{i}}{8} \right)\right)^{2}\right|+\prod_{i=1}^{n}\left|\sin\left(\frac{x_{i}}{8}\right) \right|\right)+1\right) \tag{50}\]  
\[s_{2}(x)=100\sqrt{|x_{2}+1-0.01(x_{1}-10)^{2}|}+0.01|x_{1}| \tag{51}\] \[+20\log(0.01(\sum_{i=1}^{n}|x_{i}|)^{2}(\sin(0.8x_{1})+2)^{4}+1)\]  
We evaluated GSLEO-AEFA and its counterpart algorithms with a population size of 30, iteration of 500 and a dimension set to 8, as recommended by [PERSON] et al. [55], by considering that the s-parameters of most antennas are around 10. The performance of each algorithm after 30 independent runs in Table 11, using average and standard deviation metrics are recorded. Our analysis indicates that GSLEO-AEFA provided the best results for both single-antenna and multi-antenna problems by demonstrating its effectiveness in solving complex optimization problems in this domain, as seen in Table 12.  
To observe the performance of the newly proposed algorithm GSLEO-AEFA, proper analyses and a set of various experiments were conducted. Considering the original AEFA suffers from the insufficient diversification such powerful tools are added to overcome this issue as well as by allowing the algorithm to escape from local optima and to find solutions that are closer to the global optimum. By achieving this equilibrium between exploration and exploitation, high solution quality is achieved. However, there may be some limitations to consider. Since the proposed algorithm is a hybrid one and formed by multiple methods, the computational time of the algorithm is slightly worse than the other algorithms analyzed. It is because of running each of the methods during the optimization process, respectively. However, for the ones who consider the precise solution quality, this limitation might be omitted. It is important to consider these factors carefully and to tailor the used of these techniques to the specific problems being solved.