## 4 Comparison and Analysis
### Comparison and Analysis of Numerical
The iterative convergence of the parameters carried by the central particle and the average of each generation of particles are given in the figures simultaneously. We note that the convergence of the central particle and average is relatively more stable (the fluctuation is smaller). This means that for the IRMO algorithm, if the searches for the global optimal value have unstable fluctuations (possibly falling into the local optimum), the central particle could maintain the optimal position to avoid the result becoming stuck in a local optimum (the optimum eventually coincides with the convergence of the central particle). To highlight the optimization trends of parameters, we tagged the upper limit and lower limit (Table 5) in the following figures for each parameter. In Figures 16 and 17, both \(\theta_{1}\) and \(\theta_{2}\) are trending to a lower value of their ranges, which means that the lower inclination of entry or exit straight segments is more conducive to optimizing the total length of the five-segment trajectory. limit to obtain the optimum total length (Figure 19). It could be considered that \(R_{2}\) plays a more influential role in the length optimization. For the length of entry straight segment \(L_{1}\), an obvious convergence can be observed to its upper limit, especially after 100 generations. However, the length of the central straight segment \(L_{3}\) finally trends to nearly 110 m.  
Figure 17: The convergence progress of inclination of exit straight segment: \(\theta_{2}\). Figure 18: The convergence progress of radius of entry curved segment: \(R_{2}\). It is hard to say what are the relations between the lower limit or upper limit with the optimization of \(R_{2}\) and \(L_{3}\) (Figures 18 and 21), but it could be concluded that the determinations of \(R_{2}\) and \(L_{3}\) are not of as much importance as the others. To some extent, their influence on the optimal results is weaker. Therefore, it is advisable to pay more attention to optimizing other parameters, including \(L_{1}\)\(R_{4}\), \(\theta_{1}\), and \(\theta_{2}\), in actual projects. On the other hand, the optimization result of \(L_{3}\) (104.96 m) is larger than the fitting result (100.00 m) (Table 6), which is conducive to the trajectory in practice if there needs to be a longer horizontal crossing. Figure 19: The convergence progress of radius of exit curved segment: \(R_{4}\). Figure 20: The convergence progress of length of entry straight segment: \(L_{1}\). This process of length optimization could certainly reduce the total length of the whole construction, especially when considering the cost associated with the length. As another possibility, it also proves that the trajectory can be designed and optimized with the purpose of minimal total length as in the ACO method [21]. However, for the IRMO method, the outputs of the design parameters are more specific with six parameters available which may help the engineers' judgement. However, in this example, the maximum optimized length is only a fraction of the total length. Its practical value may need to have more practices to be proved in further study. However, it may provide valuable advice for determining certain parameters when those parameters are volatile during fitting.