# Spotted Hyena Optimizer and Ant Lion Optimization in Predicting the Shear Strength of Soil
## 4 Results and Discussion  
### Optimizing the MLP using ALO and SHO  
As mentioned supra, this study addressed two novel optimizations of artificial neural networks for counteracting its computational drawbacks in the modeling of the soil shear strength. To optimize the ANN, the ALO and SHO metaheuristic techniques are incorporated with it. However, determining the best structure of the ANN is a prerequisite for this task. Based on the authors' experience, as well as a trial and error process, an MLP neural network with five computational units in the hidden layer was selected as the most suitable structure.  
Next, the ANN was given to the proposed optimization techniques to develop the ALO-ANN and SHO-ANN hybrid ensembles. Note that the computational parameters (i.e., the connecting weights and biases) were the variables of the problem. In other words, the ALO and SHO were performed to find the best values for them. In this way, the number of repetitions was set at 1000, and the RMSE between the actual and predicted SSSs was defined as the objective function. Of note, a population-based trial and error process was also carried out to determine the best-fitted complexity of each ensemble. The models were tested by nine population sizes varying from 10 to 500 (10, 25, 50, 75, 100, 200, 300, 400, and 500), and the RMSE of the latest iteration was recorded. The results are shown in Figure 5a. According to this figure, there is a considerable distinction between the results of the ALO and SHO. As shown, the lowest RMSEs of the models were obtained for the ALO-ANN with population size = 400, and the SHO-ANN with population size = 200 (RMSEs were 0.090138704 and 0.128263102, respectively.) This indicates that the solution suggested by these complexities constructs a more promising ANNS. For more details, Figure 5b,c depicts the convergence curves of the elite structure of the mentioned algorithms.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Features**} & \multicolumn{6}{c}{**Descriptive Index**} \\ \cline{2-9}  & **Mean** & \begin{tabular}{c} **Standard** \\ **Error** \\ \end{tabular} & **Median** & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} &
\begin{tabular}{c} **Sample** \\ **Variance** \\ \end{tabular} & **Skewness** & **Minimum** & **Maximum** \\ \hline Depth of sample (m) & 16.21 & 0.71 & 13.00 & 12.57 & 157.94 & 1.02 & 1.00 & 52.00 \\ Sand (\%) & 8.40 & 0.73 & 2.40 & 13.04 & 169.92 & 1.85 & 0.00 & 57.30 \\ Loam (\%) & 54.01 & 0.70 & 56.10 & 12.46 & 155.30 & \(-\)0.30 & 20.00 & 83.70 \\ Clay (\%) & 37.28 & 0.66 & 37.60 & 11.68 & 136.35 & 0.01 & 10.40 & 63.90 \\ Moisture content (\%) & 48.47 & 1.35 & 49.90 & 23.90 & 571.41 & 0.12 & 17.10 & 90.30 \\ Wet density (g/cm\({}^{2}\)) & 1.77 & 0.01 & 1.69 & 0.21 & 0.05 & 0.09 & 1.47 & 2.15 \\ Liquid limit (\%) & 54.47 & 0.84 & 54.90 & 14.89 & 221.65 & \(-\)0.23 & 21.40 & 79.90 \\ Plastic limit (\%) & 24.72 & 0.30 & 24.40 & 5.39 & 29.05 & 0.02 & 12.90 & 35.90 \\ Plastic Index (\%) & 29.75 & 0.56 & 30.40 & 10.00 & 99.92 & \(-\)0.27 & 6.60 & 49.70 \\ Liquidity index & 0.70 & 0.03 & 0.79 & 0.46 & 0.22 & 0.04 & 0.01 & 1.73 \\ Shear strength (kg/cm\({}^{2}\)) & 0.43 & 0.02 & 0.21 & 0.32 & 0.10 & 0.55 & 0.08 & 1.33 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Descriptive statistics of the used dataset.