## 5 Results and Discussion
### Verification of the Improved GA's Ability to Adjust Inter-Unit Distances and Overall Speed  
The improved GA significantly enhances the dynamic optimization of thrust allocation in the MATC system. This ensures stable straight-line sailing by adjusting key parameters such as inter-unit distances and overall speed. This section aims to validate the algorithm's effectiveness in achieving these objectives, highlighting its ability to manage the non-linear dynamics and interactions between the AUV units within the system. Figure 4 illustrates the changes in thrust allocation, inter-unit distance, and overall state of a 5-unit MATC system over time using the improved GA, demonstrating its progression toward stable straight-line sailing. From the Figure 4 results, it can be seen that when using improved GA for thrust allocation, the thrust of each unit stabilizes, the inter-unit distance decreases from 0.13 m to the ideal value of 0.12 m, and the overall speed increases from 1 knot to the target value of 1.5 knots. The specific data are presented in Table 1. As shown, the thrust allocation for each unit varies. At 15 s, the thrust values for units 1, 2, 3, 4, and 5 are 2.314 N, 2.498 N, 2.512 N, 2.401 N, and 2.593 N, respectively. These differences are primarily determined by the initial state of the MATC system. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \(t\) (s) & 0 & 1.500 & 3.000 & 4.500 & 6.000 & 7.500 & 9.000 & 10.500 & 12.000 & 13.500 & 15.000 \\ \hline \(u_{1}\) (N) & 3.915 & 2.088 & 2.306 & 2.377 & 2.270  
Figure 4: The process of a 5-unit MATC system progressing toward stable straight-line sailing when using the improved GA. (**a**) Thrust allocation; (**b**) Inter-unit distances; (**c**) The overall state at 0 s; (**d**) The overall state at 15 s.  
Verification of the Improved GA's Ability to Adjust Inter-Unit Distances Under Ocean Current Disturbances  
This section examines the effectiveness of the improved GA in dynamically adjusting thrust allocation to maintain the desired inter-unit distances despite these external disturbances. By analyzing the system's response, we can evaluate the robustness and adaptability of the algorithm in ensuring stable straight-line sailing under challenging environmental conditions. Figure 5 shows the variation in thrust allocation and inter-unit distances for the 5-unit MATC system under ocean current disturbances as it approaches stable straight-line sailing. Under the improved GA-driven thrust optimization, its thrust continuously adjusts over time to counteract the effects of the disturbance. The inter-unit distances of all units gradually converge from 0.13 m to the ideal 0.12 m.  
Figure 5: The variation results of thrust allocation and inter-unit distances for the 5-unit MATC system under ocean current disturbances. (**a**) Thrust allocation; (**b**) Inter-unit distances. This result demonstrates that the proposed thrust allocation method effectively mitigates the uncertainty caused by ocean current disturbances, ensuring that the units maintain distances close to the ideal value and preventing excessive compression or stretching between the units. Specific data are shown in Table 2.  
The results from the simulation studies clearly demonstrate that the proposed thrust allocation method can effectively handle complex ocean current disturbances. By dynamically adjusting the thrust values to compensate for the varying forces acting on the system, the method ensures the system remains stable and can adapt to real-time changes in the environment. Verification of the Inter-Unit Distance Adjustment Ability of the Improved GA Considering Thrust Constraints  
Thrust constraints are an essential consideration in real-world applications of the MATC system, as they ensure the propulsion system operates within safe and efficient limits. This section evaluates the improved GA's ability to maintain optimal inter-unit distances while respecting these constraints.