## 4 Comparison and Analysis
### Comparison and Analysis of Numerical
The results of \(L_{3}\), \(\theta_{1}\), and \(\theta_{2}\) fluctuate relatively consistently, especially the length of the  
Figure 8: The best \(SOS\) calculated 20 times by IRMO: Series 4 in Table 2.  
Figure 9: Trajectories after searching 20 times by IRMO: Series 4 in Table 2.  
central segment \(L_{3}\). The optimization of \(L_{3}\) tends to the lower limit of its initial range (as shown in Table 1) with no difference in the 20 searches, which indicates that a shorter \(L_{3}\) is beneficial to the trajectory fitting. The results of \(\theta_{1}\) and \(\theta_{2}\) fluctuate only in the range of \(0.5^{\circ}\) (Figure 10), with standard deviations of 0.29313 and 0.212049, respectively. However, the optimization results of \(L_{1}\), \(R_{2}\), and \(R_{4}\) contrast obviously with the former findings. This shows that the fluctuations in the fitting are less correlated with \(L_{1}\), \(R_{2}\), and \(R_{4}\). Figure 11: The fluctuations of \(R_{2}\) and \(R_{4}\) for 20 calculations. Figure 10: The fluctuations of \(\theta_{1}\) and \(\theta_{2}\) for 20 calculations. [PERSON] et al. [19] suggested fixing the length of the central segment \(L_{3}\) and narrowing the ranges of the other parameters to further optimize the five-segment trajectory in a smaller solution space. The final optimization is clearly to be applied in practice. However, the optimization result that he obtained is one among numerous possible results. In this study, to achieve more precise and stable results of parameters, we narrowed the parameter limitations according to the volatility ranges and set the _Fitness_L_(Equation (8)) as the purpose to search the shortest trajectory to reduce the costs associated with the length of trajectory. The narrowed ranges are concluded in Table 5, and the parameters of the IRMO algorithm are: N = 50, M = 6, and generation = 250. After searching 20 times by IRMO in the narrowed optimization ranges above, the total length of the trajectory is obviously shortened (Figure 13) compared with Figures 6 and 9, although the fitting degree is lower. The values of the shortest length searched 20 times are shown in Figure 14. The standard deviation is only 0.05813, in which the maximum decrease is 16.92 m, the minimum decrease is 10.62 m, and the average decrease is 14.53 m. The Figure 15 shows the convergence of the total length when the iteration of the IRMO is set as 250. The global optimum t  
Figure 7:0 The fluctuations of \(L_{1}\) and \(L_{3}\) for 20 calculations. \begin{table}
\begin{tabular}{l} \hline \hline \multicolumn{1}{c}{**The Narrowed Optimization Ranges of Trajectory Parameters**} \\ \hline Length of the entry straight segment, \(L_{1}\)\(\in\)[60, 110] m; \\ Length of the central straight segment, \(L_{3}\)\(\in\)[100, 120] m; \\ Radius of curved segments, \(R_{2}\)\(\in\)[2500, 3000] m, \(R_{4}\)\(\in\)[1800, 2400] m; \\ Inclination angle of the entry straight segment, \(\theta_{1}\)\(\in\)[\(-\)10, \(-\)8] \({}^{o}\); \\ Inclination angle of the exit straight segment, \(\theta_{2}\)\(\in\)[6, 8] \({}^{o}\); \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The narrowed optimization ranges of trajectory parameters. Figure 14: Optimal length of trajectories by searching 20 times. Figure 13: The shortest total length trajectories after searching 20 times by IRMO. Figure 15: The convergence progress of searching optimal length after 250 iterations. A set of trajectory parameters before and after optimization is compared in Table 6. The results after optimization of \(\theta_{1}\) and \(\theta_{2}\) are smaller than before, while the results after optimization of \(R_{2}\), \(R_{4}\), \(L_{1}\), and \(L_{3}\) are larger. Moreover, the length of the exit straight segment \(L_{5}\) is exhibited, which demonstrates that the optimization effect of the total length is mainly contributed by the exit straight segment \(L_{5}\). Figures 16-21 show the convergence of six parameters over 250 iterations in searching.