# Optimization Method of Customized Shuttle Bus Lines under Random Condition
## 4 Numerical Example  
In this section, we analyze travel demands for the customized shuttle bus in an area served by a depot. We optimize the customized shuttle bus route in the decision period. The area is presented in Figures 2 and 3. The K-means clustering analysis is adopted to analyze the travel demand and the result is shown in Figure 4. Passengers get on customized shuttle bus vehicles mainly in residential areas, while their destinations are mainly government agencies, hospitals, the central business district, enterprises, and creative industry parks. The number of pairs of origin-destination is 200 and this paper has not listed them all due to the limited space. There is a line between any two stops. The distances matrices are given in Tables 1 and 2. The travel time depends on the traffic condition. The arrival time and dwell time are given by Table 3. \(d_{v}^{+}\) and \(d_{v}^{-}\) are normally distributed, while the  
We adopt the following parameter values: The number of iterations is 1000, the number of clone operator times is 500, and the population size is 1200. The time for the calculation is 1.5 s. The optimized customized shuttle bus lines are shown in Figure 4. Two customized shuttle bus lines are obtained (2-4-5-6-7, 2-1-3-8-9-10) and 90% demands can be satisfied. To verify the practical effect of the model and algorithm, we compare the results for different travel demands, as shown in Tables 4 and 5. In the case of the same random time, compared with the traditional simulated annealing algorithm (the cooling rate is 0.98, the initial temperature is 1000, the end temperature is 0.001, and the chain length \(L\) of the Metropolis is 500), the proposed hybrid intelligent optimization algorithm can improve the solving efficiency of the model, especially when there is a large travel demand. The advantage of the proposed hybrid intelligent optimization algorithm is obvious in terms of the solving speed. The proportion of passengers served will be improved with the increasing of the travel demand. The simulated annealing algorithm works as follows: \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \(\mathbf{v_{1}}\) & \(\mathbf{v_{2}}\) & \(\mathbf{v_{3}}\) & \(\mathbf{v_{4}}\) & \(\mathbf{v_{5}}\) & \(\mathbf{v_{6}}\) & \(\mathbf{v_{7}}\) & \(\mathbf{v_{8}}\) & \(\mathbf{v_{9}}\) & \(\mathbf{v_{10}}\) & \(\mathbf{v_{11}}\) & \(\mathbf{v_{12}}\) \\ \hline \(v_{1}\) & 0 & 4 & 1 & 6 & 11 & 15 & 18 & 5 & 8 & 10 & 4 & 6 \\ \(v_{2}\) & 4 & 0 & 5 & 2 & 7 & 10 & 13 & 9 & 12 & 14 & 4 & 3 \\ \(v_{3}\) & 1 & 5 & 0 & 7 & 12 & 15 & 18 & 4 & 7 & 9 & 5 & 7 \\ \(v_{4}\) & 6 & 2 & 7 & 0 & 5 & 8 & 11 & 11 & 14 & 16 & 6 & 5 \\ \(v_{5}\) & 11 & 7 & 12 & 5 & 0 & 3 & 6 & 16 & 19 & 21 & 11 & 10 \\ \(v_{6}\) & 15 & 10 & 15 & 8 & 3 & 0 & 3 & 19 & 22 & 24 & 14 & 13 \\ \(v_{7}\) & 18 & 13 & 18 & 11 & 6 & 3 & 0 & 22 & 25 & 27 & 17 & 16 \\ \(v_{8}\) & 5 & 9 & 4 & 11 & 16 & 19 & 22 & 0 & 3 & 5 & 9 & 11 \\ \(v_{9}\) & 8 & 12 & 7 & 14 & 19 & 22 & 25 & 3 & 0 & 2 & 12 & 14 \\ \(v_{10}\) & 10 & 14 & 9 & 16 & 21 & 24 & 27 & 5 & 2 & 0 & 14 & 16 \\ \(v_{11}\) & 4 & 4 & 5 & 6 & 11 & 14 & 17 & 9 & 12 & 14 & 0 & 3 \\ \(v_{12}\) & 6 & 6 & 7 & 5 & 10 & 13 & 16 & 11 & 14 & 16 & 3 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distance matrix among stops (km). Figure 4: Schematic diagram of the customized shuttle bus routes planning. and algorithm is verified by the numerical example with different travel demand sizes. On the basis of the minimum cost, it can maximize the demand of the customized shuttle bus (90%), and ensure the travel time demand of passengers. This method can improve the efficiency of the customized shuttle bus line planning effectively, which is nearly 10 times faster than the traditional simulated annealing algorithm. By optimizing the customized bus routes, it can continuously improve the service quality and efficiency, promote the diversification of urban public transit, and improve the sharing of urban public transit.