## 3 Driver-Inspection Vehicle Automatic Scheduling Method
### Dynamic Automatic Scheduling Algorithm Based on Multi-Objective Optimization
Notably, the multi-objective optimization algorithm achieved convergence after only tens of iterations, highlighting its efficiency. Figure 3 illustrates the convergence curves of the algorithm under different iteration counts. As shown, the improved PSO algorithm exhibits significant enhancements in both computational efficiency and convergence speed compared to traditional algorithms. The results indicate that the proposed method can effectively balance multiple objectives, optimizing the scheduling process while reducing vehicle waiting times and improving resource utilization. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Scenario Content**} & \multirow{2}{*}{**Objective Indicator**} & **Manual Scheduling Algorithm** & **Simple Heuristic Algorithm** & **Proposed Method** \\ \hline
1 & & Vehicle Waiting Time (min) & 21.04 & 19.15 & 17.59 \\ \hline
2 & & Relocation Path Length (m) & 2325.24 & 2298.25 & 2017.29 \\ \hline
3 & & Resource Utilization (\%) & 76.32 & 78.24 & 80.41 \\ \hline
4 & Berth 11 to & Driver Workload Balance (h) \({}^{*}\) & 1.28 & 1.18 & 0.89 \\ \hline
5 & & Relocation Time (min) & 38.89 & 34.28 & 30.07 \\ \hline
6 & & System Throughput (/h) & 328.24 & 344.28 & 375.36 \\ \hline
7 & & Scheduling Uncertainty (min) & 18.25 & 17.58 & 16.38 \\ \hline
8 & & Vehicle Scheduling Consistency (min) & 9.24 & 8.68 & 8.04 \\ \hline
9 & & Vehicle Waiting Time (min) & 16.52 & 15.21 & 14.21 \\ \hline
10 & & Relocation Path Length (m) & 1208.26 & 1106.32 & 1028.57 \\ \hline
11 & & Resource Utilization (\%) & 80.56 & 83.24 & 84.29 \\ \hline
12 & & Driver Workload Balance (h) \({}^{*}\) & 0.85 & 0.78 & 0.69 \\ \hline
13 & & Relocation Time (min) & 24.89 & 23.92 & 21.08 \\ \hline
14 & & System Throughput (/h) & 369.69 & 402.98 & 415.26 \\ \hline
15 & & Scheduling Uncertainty (min) & 13.25 & 12.06 & 10.88 \\ \hline
16 & & Vehicle Scheduling Consistency (min) & 10.85 & 9.25 & 8.85 \\ \hline \hline \end{tabular}

* Calculated as variance of work time.

\end{table} 
Table 1: Comparison of objective function values. Figure 3: Convergence curve of algorithm proposed. The proposed multi-objective optimization algorithm exhibits a rapid convergence feature in optimizing vehicle waiting time. In the early iterations, the objective function value drops sharply, indicating that the algorithm can quickly identify better solutions during the initial optimization phase. As the iterations progress, the convergence curve smoothens, approaching the optimal solution, which demonstrates good stability. Similarly, the convergence curve of the relocation path length also showcases a fast initial convergence speed, marked by a significant decrease in the objective function value during the early iterations. This indicates that the algorithm is effective in reducing vehicle relocation path length. In the subsequent optimization process, the convergence curve maintains a high degree of smoothness without significant fluctuations, underscoring the algorithm's robustness across multiple experimental runs. The convergence curve for optimizing resource utilization shows the clear advantages of the proposed algorithm during the convergence process. The algorithm rapidly improves resource utilization in the early iterations, demonstrating a strong global search capability. As the number of iterations increases, the proposed algorithm gradually approaches the Pareto front, and the curve stabilizes, indicating a good convergence performance and solution quality. The convergence curve for optimizing driver workload balance shows a rapid decrease in the objective function value during the initial iterations, signifying the algorithm's ability to find better solutions early on. This decline is steep in the early stage. In the middle iterations, the curve begins to flatten, indicating that the algorithm is progressively approaching the Pareto front, with solution quality steadily improving.