## 3 Results and Discussion
### Comparison of Models  
Figures 25-27 present a comparison of the above models. As can be seen from these figures, the MLP, RF and SVR models achieved similar results, with best mean RMSEs of 3.6765, 3.6303 and 3.6591, respectively, and best mean MAPEs of 15.0795%, 15.5416% and 15.1239% (see Table 15). In addition, their efficiencies were higher than those of the KNN models (with a best mean RMSE of 3.9694, a best mean MAPE of 15.9617%, and a best MAE of 3.0006). Although these three models gave better performance than the ANN models studied in [6] and the MLR and RT models explored in [19], none of them outperformed the models obtained in this study using the GBR, XGBoost, and WAE methods (see Figure 27). In addition, the comparison of the models treated herein with the models obtained in previous research works [6; 19] also showed that the MLR [19] and KNN models were the worst in terms of predicting the compressive strength of LWAC. KNN showed slightly lower performance than the best tree model in [19] (RMSE = 3.808) and the best ANN model in [6] (RMSE = 3.745). The KNN models based on the Manhattan distance only succeeded in outperforming the MLR models (with a best mean RMSE of 4.332), while the KNN models based on the Euclidean distance, with a best mean RMSE of 4.4808, were worse than the MLR models. A comparison between GBR and XGBoost models showed that the XGBoost models achieved the smallest mean values for the RMSE and MAE on both the training and test datasets (see Figures 25 and 26). With suitable hyperparameter settings, the XGBoost models outperformed GBR models and achieved a mean determination coefficient of approximately 0.8773, a mean RMSE of 3.1396, a mean MAE of 2.4371, and a mean MAPE of 13.6238% (see Table 15 and Figure 27). The mean values of the performance measures for the best machine learning techniques (GBR, XGBoost and WAE) are shown in Table 16. This table and the analysis of the ranking of the best GBR, XGBoost and WAE models in Table 17 indicate that with appropriate values of the weight parameters, the proposed WAE models based on a combination of the RF, SVR, and XGBoost outperformed the GBR and XGBoost models. Note that the overall rank of the WAE model is higher than those of the GBR and XGBoost models. This is also true for the total rank for both the training and test datasets. For the results in Table 16, we  
Figure 27: Ranking of the models of Table 15. **(a)** Discrete ranking; **(b)** continuous ranking. Figure 26: Comparison of the GBR, XGBoost and WAE models (see Table 15 for the \(x\)-axis labels). **(a)** MAE, test dataset; **(b)** MAE, training and all dataset; **(c)** RMSE, test dataset; **(d)** RMSE, training and all dataset; **(e)** MAPE, test dataset; **(f)** MAPE, training and all dataset. used \(\alpha_{2}=0.2\) and \(\alpha_{3}=0.8\). This model gave a mean determination coefficient of 0.8782, a mean RMSE of 3.1272, a mean MAE of 2.4135 and a mean MAPE of 13.3628%. Similar results were obtained for a combination of the SVR and XGBoost models with \(\alpha_{2}\) between 0.15 and 0.2, and \(\alpha_{3}\) between 0.8 and 0.85. An analysis of the importance of each variable on the final predicted response for the different models is shown in Figures 28 and 29. More specifically, Figure 28 compares the importance of each variable in the RF, GBR and XGBoost models using the normalised feature importance based on the mean decrease in impurity. For the RF and GBR models, the most informative variables are the LWA particle density, the LWAC fixed density and the experimental dry density. However, the order of importance of these variables differs between the two models. The number of important features is higher for the XGBoost models, and these are the experimental dry density, the segregation index, the \(P\)-wave velocity, the concrete laying time and the LWA particle density. Figure 29 shows the importance of each variable in the MLP, KNN and SVR models based on feature permutation.