## 3 Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **Number of Task** & **Experiment** & **Total Waiting** & **Not-Conform** \\
**AGVs** & **Points** & **Round** & **Time (s)** & **LTQ** \\ \hline
4 & 40 & 1 & 2689 & 0 \\  & 40 & 2 & 2721 & 5 \\  & & 3 & 2717 & 1 \\ \hline
5 & 40 & 1 & 2498 & 0 \\  & 40 & 2 & 2444 & 0 \\  & & 3 & 2400 & 0 \\ \hline
6 & 40 & 1 & 2679 & 0 \\  & 40 & 2 & 2687 & 0 \\  & & 3 & 2624 & 0 \\ \hline
7 & 40 & 1 & 2634 & 0 \\  & 40 & 2 & 2618 & 0 \\  & 40 & 3 & 2622 & 0 \\ \hline
8 & 40 & 1 & 2584 & 0 \\  & 40 & 2 & 2653 & 0 \\  & 40 & 3 & 2678 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The experimental results of different number of AGVs at 40 task points. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number of** & **Number of Task** & **Experiment** & **Total Waiting** & **Not-Conform** \\
**AGVs** & **Points** & **Round** & **Time (s)** & **LTQ** \\ \hline
5 & 50 & 1 & 3387 & 0 \\
5 & 50 & 2 & 3453 & 2 \\  & & 3 & 3501 & 12 \\ \hline
6 & 50 & 1 & 3398 & 0 \\  & 50 & 2 & 3296 & 0 \\  & & 3 & 3438 & 2 \\ \hline
7 & 50 & 1 & 3420 & 0 \\  & & 2 & 3369 & 0 \\  & & 3 & 3434 & 0 \\ \hline
8 & 50 & 1 & 3333 & 0 \\  & 50 & 2 & 3308 & 0 \\  & & 3 & 3610 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The experimental results of different number of AGVs at 50 task points. double-cycling system. Table 12 show the experimental results under different Gaussian distributions with 30 task points and five AGVs. The smaller the \(\mu\) and \(\sigma\) mean QC operator's operation experience more affluent, and the smaller the time disturbance of the QC operation is. When \(\mu\) = 4, \(\sigma\) = 4, the AGV's waiting time fluctuates around 1814 s, with almost no QC delay. With the increase of \(\mu\) and \(\sigma\), the AGV waiting time fluctuates, and the QC delay becomes more and more frequent. The rise of \(\sigma\) leads to the increase of the time disturbance of QC operation, resulting in the AGV waiting time and the number of task points that do not conform to LTQ fluctuating significantly. The increase of \(\mu\) postpones the time disturbance interval of QC operation, resulting in the AGV waiting time being longer. The experimental results show that the more experienced the QC operator is, the lower the AGV waiting time and QC delay times. According to the model presented and relevant experimental results in this work, as long as the information of the task points set can be obtained, the iterative calculation of the task points set can be carried out in advance. The optimal container scheduling sequence is selected by adjusting the relevant factors, which proves the feasibility of the double-cycling model in practical situations. In the real world, we only need to consider the top layer of containers in the ship to break down the large problem into several small sub-problems. The sizes of the experiments conform to the real situation. To ensure that the HPSO algorithm is excellent, the Simulated Annealing (SA) algorithm and Genetic Algorithm (GA) are designed for comparison in this work. It assumes that the success rate is \(S\) and the total number of experiments is \(E\), where the number of successfully obtaining scheduling sequences that satisfy both LTQ and double-cycling constraints is \(e\). The algorithm's success rate is:  
\[S=\frac{e}{E}\times 100\% \tag{22}\]  
Tables 13-15 show that the three algorithms are compared with the success rate under the different number of task points and the success rate under the different numbers of \(\mu\) and \(\sigma\). Table 15 show the average execution time of the algorithm under the different number of task points. Table 13 show that HPSO has the highest success rate in obtaining effective solutions. Table 14 show that HPSO has the most stable performance under different time disturbances. Table 15 show the HPSO algorithm takes the least time.