## 3 Simulation Models
### Hybrid Model Development  
This section describes the implementation of the new IWO-ANN model. A review of the literature revealed that no study has been already conducted integrating ANN and IWO, though this new model is implemented in the same way as the parallel models. The above-mentioned IWO algorithm is indeed an innovative optimization algorithm applicable to different problems. This algorithm involves different parameters among which the key ones include the seeds' initial population and the number of iterations. A number of parameters in this regard exert less effect upon the finally obtained results and they can be achieved through a trial-and-error approach. As a result, such parameters are determined at the beginning of the algorithm operation. For instance, the minimum (Smin) and maximum (Smax) number of seeds were examined in a range between 0 and 30. It was found that the Smin value \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**The Best R\({}^{2}\)**} \\ \cline{3-4}  & & **Training** & **Testing** \\ \hline S1 & 6-1-1 & 0.8571 & 0.8600 \\ S2 & 6-2-1 & 0.8708 & 0.8924 \\ S3 & 6-3-1 & 0.9231 & 0.8874 \\ S4 & 6-4-1 & 0.8962 & 0.9053 \\ S5 & 6-5-1 & 0.8862 & 0.9113 \\ S6 & 6-6-1 & 0.9055 & 0.8813 \\ S7 & 6-7-1 & 0.8834 & 0.9075 \\ S8 & 6-8-1 & 0.9017 & 0.8825 \\ S9 & 6-9-1 & 0.8876 & 0.9175 \\ S10 & 6-10-1 & 0.8668 & 0.8925 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of various ANN models with activation function Sine. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**The Best R\({}^{2}\)**} \\ \cline{3-4}  & & **Training** & **Testing** \\ \hline E1 & 6-1-1 & 0.8460 & 0.8391 \\ E2 & 6-2-1 & 0.9025 & 0.8954 \\ E3 & 6-3-1 & 0.9257 & 0.9261 \\ E4 & 6-4-1 & 0.9059 & 0.9064 \\ E5 & 6-5-1 & 0.8648 & 0.8660 \\ E6 & 6-6-1 & 0.8813 & 0.8956 \\ E7 & 6-7-1 & 0.9103 & 0.9213 \\ E8 & 6-8-1 & 0.9052 & 0.9149 \\ E9 & 6-9-1 & 0.8666 & 0.8926 \\ E10 & 6-10-1 & 0.8860 & 0.8722 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of various ANN models with activation function Exponential. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model No.**} & \multirow{2}{*}{**Structure**} & \multicolumn{2}{c}{**The Best R\({}^{2}\)**} \\ \cline{3-4}  & & **Training** & **Testing** \\ \hline L1 & 6-1-1 & 0.8513 & 0.8643 \\ L2 & 6-2-1 & 0.8757 & 0.8875 \\ L3 & 6-3-1 & 0.8521 & 0.8432 \\ L4 & 6-4-1 & 0.8852 & 0.8946 \\ L5 & 6-5-1 & 0.9023 & 0.8904 \\ L6 & 6-6-1 & 0.8938 & 0.8849 \\ L7 & 6-7-1 & 0.8759 & 0.9009 \\ L8 & 6-8-1 & 0.9052 & 0.8944 \\ L9 & 6-9-1 & 0.8707 & 0.8712 \\ L10 & 6-10-1 & 0.8802 & 0.8934 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of various ANN models with activation function Logistic. Figure 6 shows the iteration changes for different models. As can be seen, the two models with the repetition of 300 and 400 provide the best case for seepage rate prediction. Here, by examining the testing section, it can be seen that the performance of the model is reduced by 400 iterations. This indicates that the model is over-fitting, indicating that the model does not have the capability to handle new data. For this reason, the model with 300 iterations provides greater flexibility due to the close proximity of both training and testing sections. As a result, this model is chosen. The RMSE results of the models are also shown in Figure 7. As can be seen, the RMSE of model with 300 and 400 iterations is less than other models, but since the system with 400 iterations has increased errors against new data (testing dataset), it excludes the selected options. Finally, by examining Figures 9 and 10 and considering the different operating conditions of the models, the model with the repetition  
Figure 8: The R\({}^{2}\) changes of hybrid models, investigating seed numbers. Figure 9: The RMSE changes of hybrid models, investigating seed numbers. of 300 is chosen as the main model.