## 4 Discussion
### Model Prediction Performance Evaluation  
To better assess the optimization capability of ALO, WVO and GOA, the unoptimized RF model was introduced to compare predictive performance with three hybrid RF models. Figure 7 illustrates the total scores of four evaluation indices for each hybrid model. The larger sector area represents a higher score obtained by a model. In other words, the hybrid model has a superior performance than other models for the ground settlement prediction. Figure 7 displays the cumulative scores of ALO-RF models with population sizes of 10, 20, 50, and 100. It can be obviously observed that the ALO-RF model with 10 population obtains the highest cumulative score. This result indicated that the ALO-RF model with 10 is the best model for the _GS_ prediction than other similar models. Similarly, in Figure 7, the WVO-RF model with a population size of 100 receives the highest score for each evaluated indices, who demonstrates a superior capacity to predict _GS_. The cumulative score of GOA-RF with a population size of 10 was then greater than other models considering other population sizes, thus it is the best prediction model for forecasting the _GS_. To better visualize the performance of each ALO-RF, WVO-RF, and GOA-RF models, the relationships between predicted and measured _GS_ values were depicted in Figure 8. Each sphere in this figure represents the distribution of a set of measured and predicted values. If the sphere lies on the diagonal line, the measured value is equal to the predicted value. Moreover, the histogram of differences located in the upper right corner of the figure represents the distribution of differences between predicted and measured values. The proximity of measured values and predicted values by ALO-RF, WVO-RF, and GOA-RF models to the diagonal dashed line indicates that all hybrid models are effective for predicting the _GS_. By comparison of details, the distribution of GOA-RF (Pop = 10) is more concentrated near the diagonal dashed line than ALO-RF (Pop = 10) and WVO-RF  
Figure 6: The iteration curve of each hybrid model: (**a**) ALO-RF; (**b**) WVO-RF and (**c**) GOA-RF; Pop: population). (Pop = 100) models. In the training set, the MAE of GOA-RF model is significantly lower than that of ALO-RF and WVO-RF models (ALO-RF: 2.9516, WVO-RF: 2.865, GOA-RF: 2.8224); the RMSE of GOA-RF model is also the lowest among three models (ALO-RF: 5.4133, WVO-RF: 5.3441, GOA-RF: 4.93); and the R\({}^{2}\) value of GOA-RF model is higher than ALO-RF and WVO-RF models (ALO-RF: 0.9338, WVO-RF: 0.9409, GOA-RF: 0.9487); the MAPE of GOA-RF model is similar to the WVO-RF model, which are both at a low level (ALO-RF: 50.5681, WVO-RF: 40.3814, GOA-RF: 40.5629). In the test set, the MAE of GOA-RF model is the lowest among three models (ALO-RF: 2.819, WVO-RF: 2.5786, GOA-RF: 2.3507); similarly, the RMSE of GOA-RF model is also the lowest value (ALO-RF: 3.5978, WVO-RF: 3.2843, GOA-RF: 3.1576); and the R\({}^{2}\) of GOA-RF presents is higher than ALO-RF and WVO-RF models (ALO-RF: 0.9055, WVO-RF: 0.9202, GOA-RF: 0.9282); the MAPE of GOA-RF is at a low value as the same as with WVO-RF (ALO-RF: 48.5579, WVO-RF: 38.7341, GOA-RF: 38.7537). This result demonstrated that GOA-RF is the best hybrid model for \(GS\) prediction. In the training phase, the error range of all three hybrid models is primarily concentrated within 10 mm, whereas it is concentrated within 8 mm in the testing phase. It is evident that all hybrid models have an effective error control. Figure 7: Hybrid model comprehensive performance evaluation: (**a**) Comparison of ALO-RF results for populations of 10, 20, 50, 100; (**b**) Comparison of WVO-RF results for populations of 10, 20, 50, 100; (**c**) Comparison of GOA-RF results for populations of 10, 20, 50, 100; (**d**) Comparison of the results of different models.