## 3 Driver-Inspection Vehicle Automatic Scheduling Method
### Dynamic Automatic Scheduling Algorithm Based on Multi-Objective Optimization
As the number of iterations increases, the proposed algorithm gradually approaches the Pareto optimal front, with the curve stabilizing, showcasing good convergence performance and solution quality. In contrast, other algorithms converge more slowly in optimizing resource utilization, with a sparser distribution of optimal solutions, remaining in an oscillatory state even after 15 iterations. In terms of optimizing driver workload balance, Figure 4d displays the convergence curves of different algorithms for driver workload balance (Objective 4), reflecting the performance differences between the proposed algorithm and classical algorithms (NSGA-II and MOEA/D) in achieving balanced workload goals. As shown in Figure 4d, the proposed multi-objective optimization algorithm exhibits a clear rapid convergence characteristic in optimizing driver workload balance. In the first 30 iterations, the algorithm's objective function value decreases rapidly, indicating that it can effectively find better solutions during the initial search process, with a steep downward trend in this phase. In contrast, while NSGA-II and MOEA/D also demonstrate relatively fast decreases in the same number of iterations, their progress is unstable, suggesting that their global search capability in the early search phase is relatively weak and fails to effectively explore the high-quality solution space. In the stable convergence phase, during the mid-iteration (from the 30 th to the 120 th iteration), the convergence curve of the proposed algorithm flattens, indicating that the algorithm is gradually approaching the Pareto front and that the quality of solutions is steadily improving. At this point, the algorithm has begun local exploration near high-quality solutions to ensure further optimization. The NSGA-II algorithm shows some oscillation during this stage, suggesting fluctuations in solution quality across multiple experimental runs, indicating instability. In comparison, while the convergence curve of MOEA/D tends to be smooth relative to NSGA-II, its improvement in solution quality is slower, possibly stagnating in local optimal traps. In the final convergence stage, during the later iterations (from the 80 th to the 150 th iteration), the convergence curve of the proposed algorithm approaches stability, nearing the Pareto optimal front and demonstrating the excellence and stability of the solutions. Across multiple experimental runs, the quality of solutions clusters within a high-quality region, showing good robustness. In contrast, the final convergence performance of the NSGA-II algorithm remains unstable, with some solutions failing to reach the optimal solution region, indicating its slightly inadequate performance in high-dimensional multi-objective optimization problems. Although MOEA/D can achieve a certain level of optimal solution quality, its lack of solution diversity is detrimental to achieving a comprehensive balance in optimizing driver workload. Overall, as shown in Figure 4d, the proposed algorithm significantly outperforms traditional NSGA-II and MOEA/D algorithms in optimizing driver workload balance. Its advantages are reflected in a rapid initial convergence, minimal oscillation during iterations, high quality of final solutions, and concentrated distribution of solutions. These characteristics demonstrate that the proposed algorithm can effectively handle complex multi-objectiveoptimization problems. Additionally, while maintaining driver workload balance, the proposed algorithm can effectively reduce scheduling conflicts and prevent excessive concentration of workload, fully utilizing existing resources and further optimizing the vehicle scheduling process. From Figure 4e, it can be seen that the proposed algorithm exhibits a more stable and rapid convergence characteristic in optimizing relocation time (Objective 5).