## 3 Driver-Inspection Vehicle Automatic Scheduling Method
### Dynamic Automatic Scheduling Algorithm Based on Multi-Objective Optimization
Within the first 40 iterations, the algorithm's objective function value decreases quickly, approaching the optimal solution area, indicating that it can effectively find optimization solutions in a short period. The convergence curves of NSGA-II and MOEA/D are also relatively rapid in the early stages, and all three algorithms tend to stabilize after the 100 th iteration. However, the proposed algorithm maintains better stability compared to NSGA-II and MOEA/D, which experience local oscillations. This suggests that those algorithms have slightly inadequate search capabilities in complex multi-objective scenarios. The proposed algorithm reaches a stable state more quickly, reflecting its advantage in global optimization. Regarding the optimization goal of scheduling uncertainty (Objective 6), Figure 4f demonstrates the superiority of the proposed algorithm. In the early iteration phase (from 0 to 60 iterations), the algorithm quickly finds relatively optimal solutions and gradually stabilizes. This indicates that the proposed algorithm possesses efficient search capabilities and good local exploration abilities in reducing scheduling uncertainty. In contrast, other classical algorithms like NSGA-II and MOEA/D show slight fluctuations in uncertainty optimization, especially in the mid to late iterations, where there are issues with fluctuations in solution quality, indicating that their stability is inferior to that of the proposed algorithm. In the optimization of vehicle scheduling consistency (Objective 7) shown in Figure 4g, the proposed algorithm demonstrates a fast convergence speed, stabilizing in the optimal solution area within the first 60 iterations. In contrast, while the convergence curves of NSGA-II and MOEA/D are also relatively fast, they exhibit significant oscillations during the mid-iteration phase. The proposed algorithm achieves a distribution of solutions concentrated in the high-quality region of the Pareto front across multiple independent experimental runs, indicating that it can effectively enhance vehicle scheduling consistency while also exhibiting good robustness and convergence performance. Regarding the optimization goal of system throughput (Objective 8), Figure 4h highlights the significant advantages of the proposed algorithm. Compared to other algorithms, it quickly converges to a relatively optimal solution in the initial phase and maintains stability in subsequent iterations, demonstrating its strong global optimization capability in improving system throughput. In contrast, the NSGA-II algorithm shows some oscillation in enhancing throughput, particularly after reaching a certain level of optimization, where the slope of the convergence curve varies significantly, indicating a potential trap of local optima. Although MOEA/D performs relatively stably in throughput optimization, the quality of its final solution is slightly inferior to that of the proposed algorithm. Overall, the proposed dynamic automatic scheduling algorithm based on multi-objective optimization outperforms traditional NSGA-II and MOEA/D algorithms in convergence across various objective functions. Its advantages lie in rapid convergence, high solution quality, and robust performance across multiple independent experimental runs. The analysis of the convergence curves indicates that this algorithm is not only suitable for optimizing the automatic scheduling of customs inspection vehicles but also possesses good generalizability and application potential. Considering the real-time requirements of algorithms in practical applications, this study analyzes the computational complexity of multi-objective optimization algorithms across various problems scales. The experimental results evaluate the algorithm's time and space complexity performance under datasets of differing sizes and compare it with classical multi-objective optimization algorithms, such as NSGA-II and MOEA/D.