# Spotted Hyena Optimizer and Ant Lion Optimization in Predicting the Shear Strength of Soil
## 4 Results and Discussion
### Quality Assessment of Predictive Models  
The best-fitted structure of the ANN, ALO-ANN, and SHO-ANN was then used to predict the SSS using the considered input factors. The comparison between the actual and predicted SSSs was made in this section to evaluate the efficiency of the implemented models. Firstly, the RMSE and MAE error criteria were used to measure the error of the performance, and the R\({}^{2}\) was then applied to measure the correlation between the target and output variables. The results of the ANN, ALO-ANN, and SHO-ANN are shown in Figures 6-8, respectively. Evaluating the obtained values' error criteria in the training phase shows that applying the metaheuristic algorithms has effectively helped the ANN to achieve a more reliable analysis of the relationship between the SSS and influential factors. In detail, the RMSE of the ANN decreased by around 37% and 11% (i.e., from 0.1437 to 0.0901 and 0.1282) as a result of the ALO and SHO, respectively. The results of the MAE also agree with the RMSE and experienced a reduction by nearly 47% and 17% (i.e., from 0.1071 to 0.0563 and 0.0892). Comparing the error charts (showing the difference between the actual and predicted values for each sample) also indicates that the ensemble models have trained the ANN better than its regular algorithms. Figure 5: (**a**) The results of the executed trial and error process, (**b,c**) the convergence curve of the elite SHO-ANN and ALO-ANN, respectively. ANN, artificial neural network; ALO, ant lion optimization. The testing results demonstrate that the errors of the ALO-ANN and SHO-ANN are lower than ANN. More clearly, the RMSE levelled off from 0.1603 to 0.1035 (35.43%) and 0.1308 (18.40%). As for the MAE, the ALO and SHO reduced it from 0.1268 to 0.0619 (51.18%) and 0.0874 (31.07%). It points out that the networks constructed by the developed ensembles are more capable than unreinforced ANN in predicting unseen soil conditions. Graphically, part (c) of Figures 6-8 shows that the products of the ensemble models have better agreement with the actual SSSs. As well as the error criteria, the R\({}^{2}\) is used to measure the consistency of the results in terms of the correlation. Figure 9 shows the regression charts of the training and testing data of the implemented models. It can be seen that in both phases, the ALO and SHO enhanced the ANN, due to the higher consistency of their outputs with actual SSSs. The R\({}^{2}\) was raised from 0.8076 to 0.9155 and 0.8371 in the training phase, and from 0.8410 to 0.9348 and 0.8866 in the testing phase. Illustrated in the charts below, the actual training SSSs vary from 0.0843 to 1.3257, while the values predicted by the ANN, ALO-ANN, and SHO-ANN were in the range [0.1296-0.8890], [0.1128-0.9682], and [0.0222-0.9043], respectively. Similarly, the actually tested SSSs vary from 0.1114 to 1.1650, while the values predicted by the ANN, ALO-ANN, and SHO-ANN were in the range [0.0995-0.8426], [0.1170-0.9336], and [\(-\)0.0155-0.8714]. Although the negative values of shear strength do not make sense, one negative value (\(-\)0.0155) was obtained in the testing phase of the SHO-ANN, which is negligible. Considering that this negative value is attributed to one of the lowest values of WD, the reasons for its appearance could be sought in the mean correlation between the SSS and WD (correlation = 0.85). As well as this, the mechanism of neural computing might be another possible reason (which is out of the scope of the current paper). Analyzing the results of the employed models reveals that utilizing both ALO and SHO is helpful for improving the capability of learning and predicting the SSS pattern. The comparison between the accuracy indices obtained for the ALO- and SHO-based ensembles shows that the ALO-ANN performed more promisingly, as it produced the outputs with lower error and a higher correlation with actual SSSs. In other words, the weights and biases suggested by the ALO constructed a more reliable ANN than those found by the SHO.