# Deriving Situation-Adaptive Policy for Container Stacking in an Automated Container Terminal
## 6 Experimental Results  
We used the algorithm named NTGA for policy optimization, which is the same one as that used in [4] to derive the static stacking policy described in Section 4. Our  
Figure 4: Representation of candidate solution. parameter setting of NTGA is shown in Table 4. Since NTGA requires a random subset of operation scenarios selected from a pool to evaluate each candidate policy, we generated 1000 scenarios to constitute a pool. Each scenario consists of container handling jobs to be completed for three weeks in a block that is 46 days long, 8 rows wide, and 5 tiers high. The job requests are made by the AGVs and ETs that arrive at the seaside and landslide HPs, respectively. They either bring in a container to be stored in the block or ask for a container to be picked up from the block. The average number of AGVs arriving per day is approximately from 220 to 300, and that of ETs is from 70 to 110. More requests are from the AGVs than ETs because there are transshipment containers whose proportion among the containers unloaded from the vessels is about 50% in our scenarios. The average daily workload of the ASCs increases with the number of requests, but the workload continuously changes within a day as the requests are not evenly distributed over time. Using this pool of scenarios, we derived both the static stacking policy of [4] and the dynamic stacking policy proposed in this paper. Then, the two policies were applied to 100 scenarios that were separately generated following the same distribution as that used for generating the scenarios of the above pool. The two weight values \(W_{1}\) and \(W_{2}\) of Equation (4) were empirically set to 50 and 1, respectively, not only when the policies were derived but also when they were tested. The results obtained by measuring the AGV delay and ET waiting time are shown in Table 5. We can see that the proposed policy outperforms the static policy in terms of both AGV delay and ET waiting time. The improvement is 22.3% for AGV delay and 16.3% for ET waiting time. We also confirmed that the proposed policy performs significantly better than the static policy by using a paired \(t\)-test with a confidence level of higher than 99.99%. The data for our experiments and the execution of our program can be found in [26]. To obtain some hints about how the dynamic policy works, we investigated the behaviors of the two boundary policies, i.e., \(\pi_{t}\) for a very low workload and \(\pi_{t_{h}}\) for a very high workload. The two threshold values \(\theta_{t}\) and \(\theta_{h}\) (see Figure 4) found by our search algorithm for distinguishing the very low and very high workloads were 274 s and 1892 s, respectively. Recall that the length of our horizon is 1800 s; the workload of 274 s really looks very low, and that of 1892 s is over the capacity. If we want to quantify the overall stack preference of a boundary policy \(\pi_{b}\) for the \(i\)th container type (see Table 2 for the seven container types), we apply \(\pi_{b}\) to a scenario as if it is a static policy and pay special attention to the moments of stacking the \(i\)th type containers. Whenever we come across such a moment during the simulation, we not only apply \(\pi_{b}\) to stack the container at the \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Setting Value** \\ \hline Population size & 100 \\ Mating pool size & 2 \\ Buffer pool size & 50 \\ Sampling size & 2 (initially 4) \\ Crossover operator & Simulated binary crossover \\ Crossover probability & 0.9 \\ Mutation operator & Polynomial mutation \\ Mutation probability & 0.01 \\ Number of evaluations & 100,000 \\ \hline \end{tabular}
\end{table} 
Table 4: Parameter setting of NTGA in our experiments. \begin{table}
\begin{tabular}{c c} \hline
**Static Policy** & **Dynamic Policy** \\ \hline AGV delay & 80.0 & 62.2 \\ ET waiting time & 285.3 & 238.8 \\ \hline \end{tabular}
\end{table} 
Table 5: Performance comparison of the two policies.