## 4 Case Study
### Analysis of Results  
In order to validate the solution algorithm, a hybrid genetic algorithm and conventional genetic algorithm are used to solve the problem separately. Compared to the hybrid genetic algorithm, the conventional genetic algorithm does not perform operations such as simulated annealing perturbation and probabilistic reception of the solution, and the other parameters are kept the same as in the hybrid genetic algorithm compared to the hybrid algorithm. The convergence curves of the fitness functions of the two algorithms are shown in Figures 9 and 10. Comparing the two figures, it can be seen that both algorithms can iterate to obtain the optimal solution of the problem within the maximum number of iterations. From the iteration speed, the starting convergence speed of the hybrid algorithm is significantly improved compared with the conventional genetic algorithm, and the objective function value decreases rapidly within 30 generations. Then, the convergence rate decreases and converges to the optimal value in about 200 generations. From the quality of the solution, the optimal solution obtained by the conventional genetic algorithm is 8.81% higher than that of the hybrid algorithm, indicating that the simulated annealing perturbation operation can be used to make the algorithm eliminate the interference of the local optimal solution to a certain extent, thus obtaining a better evolutionary direction by accepting part of the inferior solution actively and after the cross-variation. At 50 generations, the solution obtained by the hybrid algorithm is better than the final optimization result of  
Figure 10: Convergence curve of conventional genetic algorithm. Figure 9: Convergence curve of the hybrid algorithm. the conventional genetic algorithm, proving that the algorithm has a good practicability in solving this kind of problem. In the optimal scheduling scheme calculated by the hybrid algorithm, the number of bus departures on a single day of the line is 65, and the total cost is CNY 58,144.2. As an example, in the upward direction, the results of the final calculation of the vehicle time-sharing interval and the hybrid algorithm output of the optimal vehicle scheduling program are transformed into the form shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Bus Number** & **Departure Time** & **Arrival Time** & **Running Time** & **Passenger Flow** & **Passenger** & **Average Speed** \\  & & & & **(Person)** & **Service Rate** & **(km/h)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 5: Optimal bus scheduling scenarios from hybrid algorithms. In terms of service capacity, the original total passenger flow of the line in a single day is 5980 and the actual service flow of the program is 5919, with a full-day comprehensive service rate of 98.98%, which is in line with the constraints of the model and the actual operational scenarios. In terms of travel speed, the original scheduling plan has an average speed of 19.7 km/h for the whole day and 18.1 km/h for the peak period, while the optimized scheduling plan has an average speed of 21.6 km/h for the whole day and 20.3 km/h for the peak period, which are improvements of 9.64% and 12.15%. In terms of passengers, the average waiting time for passengers during the whole day is reduced by about 11.07% and the average waiting time for passengers during the peak period is reduced by about 22.15%. Due to the increase in the speed of the buses, the passengers' traveling time will also be shortened. In order to further analyze and evaluate the specific effects of the bus control strategy proposed in this paper, the specific scheduling scheme of some of the buses undergoing stop-skipping or route adjustment is shown in Table 6.  
Analyzing the data in the above table, the following conclusions can be drawn:  
1. The trips for which the stop-skipping control strategy was implemented were concentrated in the morning and evening peak hours, and none of the trips during the weekday peak hours were implemented.