## 3 Results  
Matlab_R2019a was used to solve the double-cycling model. First, we randomly generated a container scheduling sequence. In this work, a queue was formulated for each QC or YC. The task points were arranged in queues according to the container's transportation order of the container scheduling sequence. The waiting time of the task points and the number of task points that did not meet the LTQ were calculated according to the relationship among the task points in the queue. Then, the scheduling sequence with the least number of task points that did not meet the LTQ and the least AGV waiting time were obtained using an HPSO algorithm. We then analyzed some critical parameters. Corresponding waiting areas were set up at the quayside and the yard for storing AGVs that needed to wait. AGVs in the waiting area could turn off the engine or keep the engine on for waiting according to the estimated waiting time. The waiting time of the AGV that remained after starting the engine was a key to be considered in the double-cycling model. Table 5 show the data obtained in Qingdao Port from our field investigation. Figure 4: AGV double-cycling algorithm. \begin{table}
\begin{tabular}{l c} \hline Speed of QC & 50 m/min \\ Speed of QC spreader & 240 m/min \\ Grasping speed of QC spreader & 180 m/min \\ Average time for QC to transport containers & 60 s \\ Average travel time from the quayside to the yard & 30 s \\ Speed of YC & 270 m/min \\ Speed of YC spreader & 180 m/min \\ Grasping speed of YC spreader & 60 m/min \\ Average time for YC to transport containers & 74 s \\ Speed of AGV & 3 m/s \\ AGV travel time between two YCs & 15 s \\ AGV travel time between two QCs & 15 s \\ \hline \end{tabular}
\end{table} 
Table 5: The data obtained in Qingdao Port. Table 6 show experimental results considering the total waiting time of the AGVs (Total Waiting Time), the number of task points that did not conform to LTQ (Not-Conform LTQ), the number of task points that did not conform to double-cycling (Not-Conform Double-cycling), and the fitness value. First, a time disturbance that conformed to the Gaussian distribution was added to the QC operation time. We randomized the assignment according to the Gaussian distribution, so the results were not the same each time. In the double-cycling model, the experimental results showed that most scheduling sequences satisfy both double-cycling and LTQ. This work simulated the time disturbance existing in the QC operation, so a few experimental results failed to satisfy LTQ at all task points on the basic constraint of double-cycling. The number of task points that did not conform to LTQ was significantly higher in the last experiment than in other experiments. This situation was generally caused by the significant difference in the QC operation time in the last experiment and other experiments' QC operation time, resulting in a severe phenomenon of AGV delays. The QC operator caused the time disturbance of QC operating time. Therefore, we think that the AGV could not reach the quayside in time due to the operator's operation error. This part of the data should be discarded or recalculated. However, according to the experimental results in Table 6, there exists the phenomenon that some AGVs' scheduling sequence was empty in the optimal scheduling sequence, which led to resource waste. To further improve the efficiency of the double-cycling system, this work continued to consider the influence of the number of AGVs on the efficiency of the double-cycling system. Tables 7-11 show the experimental results of changing the number of AGVs under a different number of task points on the base constraint of double-cycling, including the total waiting time of AGV and the number of task points that do not conform to LTQ. We selected three experimental results for each number of AGVs.