## 5 Computational Experiment  
In this section, we present the computational results of our method on instances of various scales. We demonstrate the effectiveness of our model through two validation approaches. Firstly, we conduct tests using real shipyard data, and secondly, we evaluate our model using the publicly available Taillard benchmark dataset [45]. To assess the performance of the proposed model, we compare it to six baseline methods, considering both the minimization of the maximum completion time and the training time of each algorithm.  
Datasets: In this study, we trained our model using real processing data of ship hull blocks on a panel block assembly line. The dataset comprises 40 types of blocks, totaling 287, with their respective processing data across seven workstations. As shown in Table 2, we randomly selected six blocks to illustrate their processing times at each workstation in the assembly line. We use a random sampling method to select 50 blocks from several panel blocks to train our model. Subsequently, the trained model was tested on instances with 25, 50, 75, 100, and 125 planar segments, totaling five cases. To evaluate the effectiveness of our approach, the trained model was also subjected to nine test sets ranging from 20 \(\times\) 5 to 100 \(\times\) 20 using the Taillard benchmark.  
Baseline methods: In the two test cases, our model is compared to heuristic algorithms LPT, NEH, and metaheuristic algorithms GA, TS. Additionally, to demonstrate the effectiveness of our introduced disjunctive graph state representation approach, we contrast it with DDQN and DRL algorithm PPO which employs traditional state representation methods. Detailed descriptions of the six baseline methods are provided in Appendix A.  
Experimental Settings: Our experiments were conducted entirely in Python 3.8, running on a computer equipped with an AMD Ryzen 7 5800H/3.20 Ghz CPU and an NVIDIA RTX3050 Ti GPU. The selection of appropriate parameters plays a crucial role in the success of our experiments. Table 3 presents the parameters utilized during the training process of our model.  
Evaluation metrics: We employ the metrics of _makespan_ and the computational time of the model to assess the performance of our method and the baseline approaches.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Workstation**} & \multicolumn{6}{c}{**Block Number**} \\ \cline{2-7}  & **Block1** & **Block2** & **Block3** & **Block4** & **Block5** & **Block6** \\ \hline Plate assembling & 2.7 h & 3.0 h & 3.0 h & 3.0 h & 3.0 h & 2.7 h \\ Bottom plate welding & 4.6 h & 4.8 h & 4.8 h & 4.5 h & 4.5 h & 4.6 h \\ Longitudinal bone assembly & 2.6 h & 2.4 h & 2.4 h & 2.5 h & 2.5 h & 2.6 h \\ Longitudinal bone welding & 3.3 h & 3.0 h & 3.0 h & 3.4 h & 3.4 h & 3.3 h \\ Ribbed longitudinal Truss assembly & 3.8 h & 3.5 h & 3.5 h & 3.6 h & 3.6 h & 3.8 h \\ Ribbed longitudinal Truss welding & 5.8 h & 5.4 h & 5.4 h & 5.8 h & 5.8 h & 5.8 h \\ Inspection and shipping out & 2.5 h & 3.2 h & 3.2 h & 2.5 h & 2.5 h & 2.5 h \\ \hline \hline \end{tabular}
\end{table}
Table 2: The processing times of randomly selected blocks at each workstation.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline Batch size & 128 \\ Learning rate & \(10^{-4}\) \\ Learning rate decay factor & 0.98 \\ Learning rate decay step & 3000 \\ Optimizer & Adam \\ The clipping parameter & 0.2 \\ The policy loss coefficient & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Hyperparameter configuration.