## 4 Results and Discussion
### Imperialist Competitive Algorithm-Artificial Neural Network (ICA-ANN)  
Important parameters/coefficients of the ICA-ANN model should be examined for its achievement. Before examining ICA parameters, using a trial and error process, it was found that a 6 \(\times\) 12 \(\times\) 1 architecture (or an ANN with 6 inputs,12 neurons in a hidden layer and one output) yields better results compared to other built models. Therefore, this structure was used for all hybrid intelligent systems in the present study. As noted earlier, N\({}_{\text{country}}\), N\({}_{\text{decade}}\) and N\({}_{\text{imp}}\) are considered as \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Input/Output Variable** & **Category** & **Unit** & **Min** & **Average** & **Max** \\ \hline Wall height (H) & Input & m & 3 & 6.5 & 10 \\ Wall width (B) & Input & m & 0.5 & 0.65 & 0.8 \\ Internal friction angles & Input & Degree & 30 & 37.5 & 45 \\ Soil density & Input & Kg/m\({}^{3}\) & 1700 & 1800 & 1900 \\ Rock density & Input & Kg/m\({}^{3}\) & 2000 & 2426.67 & 2800 \\ peak ground acceleration (PGA) & Input & g & 0.1 & 0.3 & 0.5 \\ Factor of Safety (FOS) & Output & - & 0.027 & 0.568 & 6.476 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: General description of the used database. Figure 4: Dimension model for gravity masonry retaining wall. Figure 5: Distribution of active force for static and dynamic conditions with body forces for soil and Stone blocks. the most important parameters in designing ICA. To assess Nimp, many models were implemented using various quantities of Nimp i.e., 5, 10, 15, 20, 25 and 30. In these models, Ncountry = 300 and Ndecade = 100 were considered. Results of this parametric study indicated that Nimp = 20 gives a higher functional capacity for the system. To choose the best value of Ndecade, as shown in Figure 6, different models were built with various numbers of Ncountry i.e., 25, 50, 75, 100, 150, 200, 250, 300, 350 and 400 and their results are presented based on the root mean square error (RMSE). The results indicated that the RMSE values do not change until the amount of Ndecade arrived at 600. In the last step of modeling, different numbers of countries were considered using Nimp = 5 and Ndecade = 500; and their ICA-ANN models were created. These models were evaluated based on their performance indices (PIs), the coefficient of determination (R\({}^{2}\)) and the RMSE. The changes of the PIs for two sections of training and testing of ICA-ANN models are presented in Figures 7 and 8, respectively  
The proposed ranking technique by [PERSON] et al. [51], was used to select the best hybrid model in the present study. The full version of this technique is available in the original research [51]. Based on this method, a rank was assigned to each PI in its group (train and test). For instance, values of 0.7782, 0.8676, 0.8917, 0.8832, 0.9194, 0.8987, 0.8724, 0.8944, 0.9248 and 0.9120 were respectively obtained for R\({}^{2}\) datasets of the training group of models 1 to 10; and then values of 1, 2, 5, 4, 9, 7, 3, 6, 10 and 8 were respectively considered as their ranks (see Table 2). The method was also performed for the obtained results of RMSE. The sums of R\({}^{2}\) and RMSE rank values for the training and testing groups were obtained and assigned as the total rank of each model. On this basis, Model 9 (N\({}_{\text{country}}\) = 350) with a total score of 40 was selected as the best ICA-ANN model. The performance evaluation of the best results of ICA-ANN is described later for the prediction of SF values. For design of the models, 80% and 20% of dataset were assigned to training and testing sections, respectively. In this study, the authors decided to utilize a technique of classification namely the color intensity ranking (CIR) suggested by [PERSON] et al. [33] for each row of Table 2. According to this method, intensity of the color increases by increasing the rank values and similarly, it decreases by decreasing the rank values.