## 3 Results  
### Scour Depth Prediction by Optimized ANN Models  
Three different metaheuristic algorithms (HHO, PSO, and GA) were applied to train (68 data; 83%) and test (14 data; 17%) an ANN for predicting scour depth around a ski-jump spillway. The controlling parameters of the HHO, PSO, and GA algorithms used in this study are listed in Table 3. Table 4 enlists values of performance metrics (MAE, RMSE, CC, WI, and MAPE) of ANN-HHO, ANN-PSO, ANN-GA, and ANN models during training and testing periods. Table 4 reveals that MAE, RMSE, CC, WI, and MAPE range from 0.1791-0.2657 m, 0.2626-0.3537 m, 0.9557-0.9197, 0.9769-0.9554, and 43.0994-80.9093% during training for ANN-HHO, ANN-PSO, ANN-GA, and ANN models, respectively. Similarly, during testing, MAE, RMSE, CC, WI, and MAPE vary from 0.1760-0.2494 m, 0.2538-0.3152 m, 0.7765-0.7708, 0.8030-0.4597, and 30.5081-51.3543% for the ANN-HHO, ANN-PSO, ANN-GA, and ANN models, respectively. According to the MAE, RMSE, CC, WI and MAPE values, ANN-HHO model has better performance MAE = 0.1791/0.1760 m, RMSE = 0.2626/0.2538 m, CC = 0.9557/0.7765, WI = 0.9769/0.8030, and MAPE = 43.0994/30.5081% during training/testing, respectively. Likewise, the ANN-HHO model follows the criteria of lower values of MAE, RMSE, MAPE, and higher values of CC and WI for both periods and is designated the first (or highest) rank for scour depth prediction. The ANN-PSO model closely follows the ANN-HHO model in both periods for scour depth prediction. The performance of a simple ANN and WM models was found to be the worst in scour depth prediction in this research. The outcomes of ANN optimized by the HHO, PSO, and GA algorithms and traditional ANN and WM models were compared over other studies conducted on SD prediction by employing the simple and hybrid machine learning models [8; 24; 39; 62; 63; 64]. [PERSON] et al. [15] predicted maximum scour depth at seawalls by employing GP, and ANNs models, and compared their results to empirical equations through statistical measures. They found superior outcomes of GP and ANN models over empirical equations. [PERSON] et al. [65] applied support vector machine (SVM), ANN, and ANFIS models to predict scour depth below the river pipeline system. Results of the comparison showed that a better prediction was achieved by SVM models (RMSE = 0.103 and R\({}^{2}\) = 0.94) over the ANN and ANFIS models. [PERSON] et al. [28] optimized ANN with PSO (ANN-PSO) and firefly algorithms (ANN-FFA) to predict scour depths around circular piers and compared them with empirical formulas and the classical ANN model trained with Levenberg-Marquardt (LM) algorithm. Results revealed better outcomes yielded by ANN-PSO and ANN-FFA models than other models (i.e., empirical formulas and classical ANN). These studies also confirmed the supremacy of soft computing techniques in SD prediction. Figure 4a-d to Figure 5a-d displays the comparison among measured (observed) vs. predicted scour depths by the ANN-HHO, ANN-PSO, ANN-GA, and ANN models during training and testing periods. As noted from these figures, ANN-HHO, ANN-PSO, ANN-GA, and ANN models have coefficients of determination (R\({}^{2}\)) = 0.9133, 0.9099, 0.8664 and 0.8459 for training, and 0.6030, 0.6014, 0.5979 and 0.5944 for testing, respectively. Similarly, as can be seen from the figures, ANN optimized by the HHO algorithm has less scattering around the perfect line (1:1 line) than those PSO and GA algorithms as well as the standalone ANN model. Figure 6a-b demonstrates the distribution