## 5 Test Verification
### Test Results and Comparative Analysis from ARP  
Based on an actual ARP scene, this study employed four advanced optimization algorithms to refine the parking reference trajectory for improved performance. Specifically, the following algorithms were applied: the improved directional mutation moth-flame algorithm via gene modification (IDMMO-GM) proposed in this study, an enhanced immune MFO algorithm according to gene correction (IIMPO-GC) [24], an improved particle swarm optimization algorithm (IPSO) [20], and an enhanced immune shark smell optimization algorithm (IISSO) [21]. Additionally, these algorithms uniformly employed fuzzy proportional-integral-derivative (PID) control to achieve precise reference trajectory tracking. To ensure an impartial comparison, the ARP reference trajectory optimization model utilizing the aforementioned algorithms all employed identical parameter settings, as detailed in Table 2. The parameter settings for IDMMFO-GM applied in the ARP reference trajectory optimization model are presented in Table 3.  
To achieve a fair comparison of the four optimization algorithm, three designated fixed-point regions (\(A_{10}\), \(A_{7}\), \(A_{4}\)) were selected, where \(y(P_{10})\in[2.35,2.40]\), \(y(P_{7})\in[4.55,4.65]\), and \(y(P_{4})\in[6.10,6.25]\). The detailed results of ARP optimization and tracking control are presented in Tables 4-7. The specific optimization trajectories and tracking control curves for the ARP system, as monitored by the host computer, are depicted in Figures 8 and 9. The designated fixed-point regions' curves for ARP trajectory optimization and tracking control, as determined by the host computer monitoring, are presented in Figures 10 and 11. An actual unmanned aerial image of the fixed-point regions for ARP trajectory tracking control is shown in Figure 12.  
As illustrated in Figure 8, compared with the three optimization algorithms used for comparison, IDMMFO-GM shows superior optimization performance in obtaining an ideal reference trajectory, and it exhibits a shorter path length and a smaller expected berthing tilt angle in its reference trajectory. As depicted in Figure 9, the IDMMFO-GM algorithm demonstrates higher tracking control performance when employing the fuzzy PID tracking algorithm. Consequently, the resulting trajectory exhibits a reduced path length and a smaller actual berthing tilt angle. As shown in Figure 10, compared with the three optimization algorithms used for comparison, the IDMMFO-GM algorithm exhibits better optimization performance in generating an optimal reference trajectory. The trajectory produced by IDMMFO-GM not only approaches the garage's boundary line more closely but also results in a reduced expected berthing tilt angle. As displayed in Figures 11 and 12, the IDMMFO-GM algorithm describes enhanced tracking control performance when using the fuzzy PID algorithm. The resulting trajectory is nearer to the garage's boundary line and exhibits a smaller actual berthing tilt angle. In Figure 11, the IDMMFO-GM algorithm aligns the vehicle toward the right side of the parking garage. Specifically, the x-axis coordinate of the vehicle's final parking position is greater compared to that achieved by other algorithms. Consequently, with the same initiating region, the IDMMFO-GM algorithm demands the least land area, significantly minimizing the construction and operational costs associated with parking facilities. On the other hand, a more to the right position results in a shorter path length. As the vehicle maintains an approximately steady speed while parking, this indicates that the vehicle will require less stopping time, thus enhancing the users' overall experience.