## 4 Results and Discussion
### Performance Assessment  
As explained supra, the effect of the applied metaheuristic algorithm is represented by the changes in the results of the typical ANFIS when it is coupled with the LCA. In this regard, the performance error is measured by the RSME and MAE criteria, and the correlation between the observed and modeled SCC is calculated by the R\({}^{2}\) index. As is known, the quality of the training results represents the capability of the model in discerning the relationship between the SCC and influential soil factors. Also, the testing results indicate the generalization potential of the model. In other words, predicting the SCC for unseen soil conditions. Figure 8 demonstrates the results of the training data. The observed values of the SCC vary from 0.0090 to 0.1820, and the products of ANFIS and LCA-ANFIS range in [0.0057, 0.1123] and [0.0109, 0.1105], respectively. It shows that both predictive models have grasped an acceptable pattern of the SCC. In this phase, the RMSE of ANFIS was reduced by 2.31% (i.e., from 0.0130 to 0.0127) as the impact of incorporation with the LCA technique. This improvement indicates that the MF parameters suggested by the LCA performed more promisingly than the regular ANFIS learning method. This claim could be also supported by respective MAEs of 0.0094 and 0.0091 calculated for ANFIS and LCA-ANFIS. The results of the testing data are presented in Figure 9. In addition to the graphical comparisons of the targets and outputs, the error (= target - output) calculated for each sample is depicted. Besides,  
Figure 8: Graphical comparison between the observed and modeled SCC for the (**a**) typical ANFIS and (**b**) LCA-ANFIS in the training phase. the histogram of the errors is also presented showing the frequency of each error value. The observed testing SCCs vary from 0.0100 to 0.1060, and the products of ANFIS and LCA-ANFIS range in [0.0045, 0.1066] and [0.0107, 0.1045], respectively. Referring to the obtained RMSEs of 0.0123 and 0.0117, as well as the MAEs of 0.0097 and 0.0091 (respectively for ANFIS and LCA-ANFIS models), it can be seen that applying the LCA resulted in 4.88% decrease in the RMSE, and more considerably, 6.19% reduction in the MAE criterion. Moreover, standard errors of 0.0123 and 0.0117 indicate a higher consistency of the hybrid ensemble prediction. This increase in the prediction accuracy demonstrates that the LCA technique enables ANFIS to gain a better generalization capability for strange conditions of the problem. Furthermore, the consistency of both training and testing results is graphically evaluated by correlation charts presented in Figure 10. As is seen, the coefficient of determination experienced a rise from 0.7224 to 0.7342 in the training phase, and from 0.7351 to 0.7539 in the testing phase. Therefore, confirming the RMSE and MAE, the SCCs estimated by the LCA-ANFIS were better correlated with actual values in both phases. Figure 9: The testing results of the (**a**) typical ANFIS and (**b**) LCA-ANFIS. Another appreciable point is that the performance of both models for the testing data was more accurate than training ones. It could be also derived by the calculated values of the RMSE and MAE. Due to the extent of data, a possible reason for that could be the wider range of data in the training set (the difference between the maximum and minimum values of SCC is 0.173 and 0.096, respectively for the training and testing data). As Figure 10a,c illustrate, two maximum values of training dataset are 0.182 and 0.148 which have been considerably underestimated as 0.0969 and 0.1052 by ANFIS and 0.0926 and 0.1070 by LCA-ANFIS, respectively. Also, Figure 11 displays four examples of scatter-based comparison between the predicted and actual SCCs belonging to the whole dataset. Each figure plots the SCC (on the \(y\)-axis) versus the LI (on the \(x\)-axis) for a constant value of other influential parameters.