## 5 Computational Experiment
### Computational Results of the Panel Block Assembly Line  
Table 4 presents the computational results of six baseline methods and our approach, in which the time unit of _makespan_ is hours, as shown by the character h in brackets in the title of the table. We test five groups of instances of different planar segments. By comparing them, we can conclude that our method yields a smaller _makespan_ than all the baseline methods in all cases. Compared with the two models of reinforcement learning, our method can save 1-2% time, and it can save 10% time compared with LPT. To visually demonstrate the differences between our model and the baseline methods, we showcase the disparities by taking the differences between the baseline methods and our model's results in Table 5. Additionally, we depict a line graph in Figure 6 that intuitively illustrates how the magnitude of differences varies with the problem scale. From Table 5 and Figure 6, it can be observed that our model consistently outperforms the other methods across all problem instances. The metaheuristic algorithm shows superior performance compared to the heuristic algorithm, but the NEH algorithm and the metaheuristic algorithm perform similarly, with the NEH algorithm even slightly outperforming the metaheuristic algorithm. Overall, the reinforcement learning algorithm surpasses the other baseline methods. However, when compared to other reinforcement learning algorithms, such as DDQN and PPO, which do not use disjunctive graph representation for states, our algorithm achieves lower _makespan_. For instance, compared with the DDQN method, our method can save 3.3 h of processing time when the segment count is 15 and 14.6 h when the segment count is 125. Therefore, in real shipbuilding scenarios, our approach can significantly enhance the efficiency of panel block assembly. With the increase in problem scale, it is evident that the disparity between other algorithms and the algorithm proposed in this paper in terms of _makespan_ is also growing. The advantages of our method are even more pronounced. For instance, compared to the PPO algorithm that does not incorporate disjunctive graph representation for states, the time saved by our algorithm has expanded from 1.9 h to 10.3 h. This signifies that in practical applications, as ship sizes grow and the demand for panel blocks increases, our algorithm will save even more time. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of Blocks**} & \multicolumn{2}{c}{**Heuristic**} & \multicolumn{2}{c}{**Metaheuristic**} & \multicolumn{2}{c}{**Reinforcement Learning**} & \multirow{2}{*}{**Ours**} \\ \cline{2-2} \cline{4-7}  & **LPT** & **NEH** & **GA** & **TS** & **DDQN** & **PPO** & \\ \hline
25 & 180.5 & 162.7 & 164.6 & 163.4 & 160.7 & 159.3 & 157.4 \\
50 & 327.7 & 299.8 & 301.3 & 299.6 & 295.1 & 293.4 & 289.7 \\
75 & 457.5 & 419.4 & 421.7 & 420.9 & 414.3 & 412.2 & 407.1 \\
100 & 613.7 & 564.6 & 566.5 & 564.7 & 561.6 & 557.6 & 550.4 \\
125 & 753.3 & 696.1 & 698.4 & 694.1 & 689.5 & 685.2 & 674.9 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Makespan_ of each algorithm on the panel block assembly line (h). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Number of Blocks**} & \multicolumn{2}{c}{**Heuristic**} & \multicolumn{2}{c}{**Metaheuristic**} & \multicolumn{2}{c}{**Reinforcement Learning**} & \multirow{2}{*}{**Ours**} \\ \cline{2-2} \cline{4-7}  & **LPT** & **NEH** & **GA** & **TS** & **DDQN** & **PPO** & \\ \hline
25 & 23.1 & 5.3 & 7.2 & 6 & 3.3 & 1.9 & 0 \\
50 & 38 & 10.1 & 11.6 & 9.9 & 5.4 & 3.7 & 0 \\
75 & 50.4 & 12.3 & 14.6 & 13.8 & 7.2 & 5.1 & 0 \\
100 & 63.3 & 14.2 & 16.1 & 14.3 & 11.2 & 7.2 & 0 \\
125 & 78.4 & 21.2 & 23.5 & 19.2 & 14.6 &To provide a more comprehensive reflection of the model's performance, we further compared the computation times of each algorithm, as shown in Table 6, in which the time unit of computation time is seconds, as shown by the character s in parentheses in the title of the table.