## 3 Application
### Comparisons and Discussions  
To compare the predictive performance of developed four predictive models and verify the optimization capability of PSO, the predictive performance of these models was compared by using Figure 8 and a ranking method provided by [PERSON] [81] (see Figure 9). Figure 6: Performance of the \(GP\) model. Figure 7: Performance of the PSO-GP model. As shown in Figure 8, predicted results provided by PSO-GP are most consistent with the actual measurement results, and the best predictive performance was also proved by the highest total ranking values of 24 by using [PERSON]'s method. For a better understanding of roadways broken rock zone (BRZ), a sensitivity analysis using cosine amplitude method [82] was carried out here to determine the influenced factors of these input variables on broken rock thickness. The sensitivity factor was obtained by using the following equations:  
\[ED=\{97,125,125,\cdots,780\} \tag{8}\]  
\[DS=\{2.6,2.8,2.8,\cdots,3.0\} \tag{9}\]  
\[RS=\{11.2,13.3,13.3,\cdots,70.6\} \tag{10}\]  
\[JI=\{3,3,2,\cdots,1\} \tag{11}\]  
\[BRT=\{1.20,1.30,0.70,\cdots,0.65\} \tag{12}\]  
\[S_{ED\text{-}BRZT}=\frac{\sum_{i=1}^{154}ED_{i}\cdot BRZT_{i}}{\sqrt{\sum_{i=1 }^{154}ED_{i}^{2}}\cdot\sqrt{\sum_{i=1}^{154}BRZT_{i}^{2}}} \tag{13}\]  
\[S_{DS\text{-}BRZT}=\frac{\sum_{i=1}^{154}DS_{i}\cdot BRZT_{i}}{\sqrt{\sum_{i=1 }^{154}DS_{i}^{2}}\cdot\sqrt{\sum_{i=1}^{154}BRZT_{i}^{2}}} \tag{14}\]  
\[S_{RS\text{-}BRZT}=\frac{\sum_{i=1}^{154}RS_{i}\cdot BRZT_{i}}{\sqrt{\sum_{i= 1}^{154}RS_{i}^{2}}\cdot\sqrt{\sum_{i=1}^{154}BRZT_{i}^{2}}} \tag{15}\]  
Figure 7:0  
Figure 7:1 Predictive results of the four predictive models. Figure 7:2 Histogram of the ranking values of four predictive models. After calculating, the influenced factors of \(ED\), \(DS\), RMS and \(JI\) to \(BRZT\) are, respectively, 0.9384, 0.9162, 0.6651 and 0.9711, and it can be concluded that the joint index (\(JI\)) has the most influence on broken rock zone thickness (\(BRZT\)) prediction under the collected database. In this study, four predictive models for roadway the broken rock zone (BRZ) prediction, including MLR model, ANN model, \(GP\) model and PSO-GP model were proposed and can provide the nice predictive performance of that engineering problem. However, some limitations can be found as follows:  
1. Due to the difference in mechanical behavior between shallow and deep mining, this paper focuses on shallow mining and can just be used in the prediction of roadway broken rock zone (BRZ) with depth less than 800 m.
2. A large-scale and comprehensive comparison with various artificial intelligence models for a specified engineering problem and the same database is meaningful and can provide a guide for the on-site application. Although MLR, ANN, \(GP\) and PSO-GP were utilized in this paper, other methods, such as random forest (RF), support vector machine (SVM), extreme learning machine (ELM) and gene expression programming (GEP) were not analyzed, and other optimization algorithms, such as artificial bee colony algorithm (ABC), Salp Swarm algorithm (SSA), Harris Hawks optimization algorithm (HHO) and cuckoo search algorithm (CS), were not utilized. 3. Although it is now possible to use some methods, such as borehole camera, geophysical detecting radar and ultrasonic detection, to measure the broken rock zone, it is still hard to develop a big enough database with enough datasets and enough factors. Though the authors tried the best to collect datasets, only 181 datasets were found, and that database is far from the big data level. Some studies [83; 84] show that the broken rock zone is quite complex issue and is affected by many factors, such as rock beds gradient, divrage in the fold, seismic activity, goafs, divrage with blasting, etc. A qualified database should contain as many mine data as possible, due to the different conditions of each mine, we failed for developing a big enough database with various factors, so only four factors were utilized in this paper.