## 4 Case Study
### Comparison Results of Passenger Flow Prediction
\[MAPE=\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{y_{i}-\hat{y}_{i}}{y_{i}}\right| \tag{60}\]  
where \(y_{i}\) is the actual passenger flow data and \(\hat{y}_{i}\) represents the predicting data. As shown in Figure 12, it can be seen that the MAPE of ARMA-RBFNN, LAG-LSTM and MQ-RNN are 2.23%, 6.38% and 7.88%. Table 4 shows that the prediction error of ARMA-RBFNN was the smallest, superior to other algorithms. Therefore, the ARMA-RBFNN algorithm can be used to improve the prediction accuracy of passenger flow in URT systems. side slope, curve radius (2000 m) and speed limit (80 km/h), are also selected. The station spacing is shown in Table 5.
* Selection Operator  
The selection operator is changed without changing other operators. The relationship between the fitness function value and the number of iterations is shown in Figure 13.  
Figure 11: _Cont_. Figure 11: RBFNN algorithm parameters selection and performance results. (**a**) The prediction results of four different stations; (**b**) ARMA-RBFNN performance results; (**c**) ARMA-RBFNN training state results; (**d**) ARMA-RBFNN regression results. Figure 13 shows that the number of iterations required when the fitness function value tends to be stable decreases as the selection probability increases. When the selection probability value is 0.75, the fitness function value tends to be stable in the 26 th generation. When the selection probability value is 0.85, the fitness function value tends to be stable in the 22 th generation. When the selection probability value is 0.95, the fitness function value tends to be stable in the 8 th generation. Thus, when the selection probability is between [0.80, 0.95], the convergence speed of GA is improved. * Crossover Operator  
The crossover operator is changed without changing other operators. The relationship between the fitness function value and the number of iterations is shown in Figure 14.  
Figure 14 shows that the number of iterations of the algorithm has little effect on the stability of the fitness function value based on changing the crossover operator. However, the function value has the effect of tending to the optimal value. The values of the crossover \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **ARMA-RBFNN** & **LAG-LSTM** & **MQ-RNN** \\ \hline \textless{}10\% & 93.78\% & 73.06\% & 69.07\% \\ 10-15\% & 6.22\% & 20.16\% & 18.65\% \\ 15-20\% & – & 7.25\% & 5.18\% \\ \textgreater{}20\% & – & 0.52\% & 3.11\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison prediction error of MAPE. Figure 12: MAPE comparative analysis results. operator are between 0.7 and 0.8, and the fitness function value is close to the optimal value. When the values of the crossover operator are between 0.8 and 0.9, the fitness function value is far from optimal, with a large error. Therefore, a crossover operator value between [0.75, 0.85] can improve the evolution effect of GA. The mutation operator is changed without changing other operators. The relationship between the fitness function value and the number of iterations is shown in Figure 15.  
Figure 15 demonstrates that the variance probability is taken as 0.003; the value of the fitness function tends to be smooth in the 6 th generation. When the variance probability is taken as 0.004, the value of the fitness function tends to be smooth in the 11 th generation. When the variance probability is taken as 0.005, the value of the fitness function tends to be smooth in the 16 th generation, and at the value of 0.004, the value of the fitness function is closer to the optimal value. Therefore, the algorithm evolves better when the variation probability is taken between [0.003, 0.005]. In summary, the selection operator, crossover operator and mutation operator are determined. The GA is run, and the optimal fitness value is related to the number of iterations, as shown in Figure 16.  
Figure 16 shows that when the number of iterations is about 53, the fitness curve tends to be stable.