## 4 Model Development
### Ica-Ann  
To achieve an ICA-ANN model of the highest quality, the ICA parameters need to be completely investigated, but first, the architecture of ANN must be fully determined. The performance of the ANN models depends strongly on the suggested architecture of the network [89; 90; 91]. Therefore, determination of the optimal architecture is required to design an ANN model. The network architecture is defined as the number of hidden layer(s) and the number of nodes in each hidden layer(s). According to various researchers (e.g., [92; 93; 94]), one hidden layer can solve any complex function in a network. Hence, in this study, one hidden layer was selected to construct the ANN models. In addition, determining the neuron number(s) in the hidden layer is the most critical task in the ANN architecture, as mentioned by [PERSON] et al. [95]. It was performed through a trial and error procedure, which finally resulted in the fact that an architecture of \(3\times 5\times 1\) (or a model with five hidden neurons) can offer optimum results. Thus, the above architecture was considered for the best ANN model as well as for all hybrid ANN-based models (as a confirmed initial ANN model) developed in this study. More information on obtaining ANN structures can be found in previous articles [96; 97; 98; 99; 100]. As noted previously, the key parameters in ICA are N\({}_{\text{decade}}\), N\({}_{\text{country}}\), and N\({}_{\text{imp}}\). To set the N\({}_{\text{imp}}\) value, lots of models were designed by means of different values of this parameter ranging from 15 to 40 with an incremental step of five. In these models, N\({}_{\text{country}}\) was set to 200, and N\({}_{\text{decade}}\) was set to 150. The results obtained from such a parametric research confirmed that when N\({}_{\text{imp}}\) is set to 25, a higher performance capacity can be achieved. On the other hand, for the purpose of choosing an optimal value for N\({}_{\text{decade}}\), as can be seen in Figure 7, different models were created with N\({}_{\text{country}}\) values ranging  
Figure 6: Modeling procedures of hybrid artificial neural network (ANN)-based techniques in predicting Brazilian tensile strength (BTS). between 50 and 400, with an incremental step of 50. The models' performance was then tested based on their RMSE. The RMSE results did not change any more after N\({}_{\text{decade}}\) = 550. Finally, with the two parameters of N\({}_{\text{imp}}\) = 25 and N\({}_{\text{decade}}\) = 550, different numbers of countries were taken into account, and their ICA-ANN models were configured. Required evaluations were done on the models on the basis of the performance indices (PIs), i.e., RMSE values and the coefficient of determination (R\({}^{2}\)) (see Table 1). To select the hybrid models of the highest quality in this research, [PERSON] et al. 's [101] ranking method was adopted. This technique is fully explained by [PERSON] et al. [101], based on which a rank value was allocated to each PI in its group (training and testing). For instance, values of 0.865, 0.871, 0.853, 0.899, 0.857, 0.861, 0.874, and 0.894 were obtained for the R\({}^{2}\) values of training datasets of models 1 to 8, respectively, and values of 4, 5, 1, 8, 2, 3, 6, and 7 were set to their ranks, respectively. This process was also done in the case of the RMSE results. Afterwards, a summation value of rating of the R\({}^{2}\) train, RMSE train, R\({}^{2}\) test, and RMSE test was computed and allocated to each model, according to which model 4 (N\({}_{\text{country}}\) = 200) with a total rank of 30 was found to be the best ICA-ANN model. An evaluation of the best ICA-ANN results is presented in the next sections. All the models were configured by means of a ratio of 80 to 20 for the training and testing datasets, respectively. In this study, a certain color was dedicated to each row of the models.