# Hybrid Metaheuristic-Neural Assessment of the Adhesion in Existing Cement Composites
## 3 Results of Training and Testing
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline \multirow{2}{*}{**Models**} & \multicolumn{5}{c}{**ANN Features**} & \multicolumn{5}{c}{**Utilized Initialization**} \\ \cline{2-10}  & **Number** & **Number** & **Number of** & **Number of** & **Number of** & **Number of** & **Number of** & **Number of** & **Number of** \\
**Name** & **Number** & **of Input** & **Output** & **Layer** & **Hidden Layer** & **Function** & **Country** & **Imperialist** & **Decades** \\ \hline
50 GEN\_5 IN & 5 & 1 & 1 & 13 & satlins & 400 & 40 & 50 \\
100 GEN\_5 IN & 5 & 1 & 2 & 5-5 & logsig & 300 & 30 & 100 \\
150 GEN\_5 IN & 5 & 1 & 1 & 9 & purelin & 450 & 45 & 150 \\
200 GEN\_5 IN & 5 & 1 & 3 & 6-4-3 & satlins & 500 & 50 & 200 \\
250 GEN\_5 IN & 5 & 1 & 2 & 6-5 & tansig & 500 & 50 & 250 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of testing and training of the ICA-ANN. Figure 3: The structure of the ICA-ANN used in the analysis. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Testing**} & \multicolumn{2}{c}{**Training**} & \multicolumn{2}{c}{**Errors**} \\ \cline{2-10}  & **Equation** & \(\mathbf{R^{2}}\) & **Equation** & \(\mathbf{R^{2}}\) & **MSE Test** & **MSE Train** & **Best Cost** \\ \hline
50 GEN\_5 IN & \(y=0.482x-0.019\) & 0.215 & \(y=0.273x-0.032\) & 0.084 & 0.131 & 0.152 & 0.152 \\
100 GEN\_5 IN & \(y=0.476x+0.134\) & 0.547 & \(y=0.366x+0.135\) & 0.456 & 0.048 & 0.051 & 0.051 \\
150 GEN\_5 IN & \(y=0.475x+0.120\) & 0.288 & \(y=0.380x+0.115\) & 0.315 & 0.082 & 0.063 & 0.063 \\
200 GEN\_5 IN & \(y=0.002x-0.179\) & 0.001 & \(y=0.001x-0.179\) & 0.041 & 0.289 & 0.226 & 0.226 \\
250 GEN\_5 IN & \(y=0.802x+0.041\) & 0.858 & \(y=0.679x+0.045\) & 0.844 & 0.044 & 0.047 & 0.047 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical results of ICA-ANN errors. As indicated in Tables 3 and 4, in model 5 the values of the determination coefficient \(R^{2}\) for the parameter of \(f_{\rm b}\) at the training and testing stages are equal, respectively, to 0.844 and 0.858. The slope of the straight line for this parameter equals 0.679 and 0.802, which represents the accuracy of the model and less modeling error. According to [61], in this model the nonlinear tan-sigmoid function (TANSIG), which shows the minimal error, was considered as the transfer function:  
\[Tansig(n)=\frac{2}{1+\mathrm{e}^{-2n}}-1 \tag{3}\]  
According to Table 5, the coefficients of \(ME\), \(MAE\), \(MSE\), \(RMSE\), and \(MSRE\) in two training and testing stages for the ANN model with a 1-5-6-5 structure, and also the properties of 500 countries, 50 empires, and 250 repetitions, are less than for all of the other models. This represents lower errors of this ANN in comparison to other models. Therefore, the ICA-ANN model with the title of 250 GEN_5 IN is more accurate than other models of its kind. The result of comparing the selected 250 GEN_5 IN ICA-ANN model with the observation data is presented in Figure 4. The minimum cost and the mean cost diagrams are shown in Figure 5.