## 5 Experiments
### Determination of the Optimal Number of AGVs Under Different Layouts  
In the FISPRLP-LTCC problem, the configuration of transport resources is one of the key factors affecting the overall system performance. There exists a significant correlation between the number of AGVs and the system's makespan: when the number of AGVs is insufficient, the material transport capacity of the system is limited, which tends to increase the waiting time between operations and thus prolong the overall production cycle. Conversely, an excessive number of AGVs may lead to resource waste, increased idle travel rates, and higher operational costs. Therefore, based on the three workshop layouts proposed in Section 5.1, this section conducts a systematic analysis of the performance of each layout under different AGV configurations using the proposed CRGPPO-TKL algorithm, aiming to determine the optimal transport resource configuration for each layout. Each configuration was subjected to 20 independent experimental runs, and the results are presented in Table 6 where bold indicates the best performance and Figure 7. \begin{table}
\begin{tabular}{l c c} \hline \hline \multicolumn{1}{c}{**Symbol**} & **Definition** & **Value** \\ \hline \(\gamma\) & discount factor & 0.99 \\ \(\lambda_{\text{GAE}}\) & GAE coefficient & 0.95 \\ \(\epsilon_{\text{clip}}\) & Policy Shear Threshold & 0.2 \\ \(\epsilon_{\text{min}}/\epsilon_{\text{max}}\) & Shear range & 0.1/0.3 \\ \(T_{\text{KL}}^{\text{target}}\) & KL dispersion threshold & 0.3 \\ \(\alpha_{\text{adjust}}\) & Learning rate adjustment step & 0.05 \\ \(\beta_{\text{entropy}}\) & Entropy regularization factor & 0.01 \\ \(N_{\text{candidates}}\) & Number of candidate actions & 5 \\ \(K_{\text{epoch}}\) & PPO update rounds & 4 \\ \(B_{min}\) & Minimum Batch Size & 128 \\ \(\eta_{\text{actor}}/\eta_{\text{critic}}\) & E-learning rate & \(3\times 10^{-4}/1\times 10^{-3}\) \\ \(T_{\text{train}}\) & Total training time & 500 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Hyperparameter setting of CRGPPO-TKL. Figure 7: Effect of the number of AGVs on completion time in different layouts. (**a**) Effect of different numbers of AGVs on completion time under layout 1. (**b**) Effect of different numbers of AGVs on completion time under layout 2. (**c**) Effect of different numbers of AGVs on completion time under layout 3. Figure 7 illustrates the significant impact of AGV quantity on the makespan across the three layouts. In Layout 1, when the number of AGVs increases from 1 to 6, the average makespan of test sets MK01, MK02, MK05, and MK07 decreases by 227.4, 271.2, 360.7, and 483.1, corresponding to reductions of 82.2%, 83.7%, 63.8%, and 70.7%, respectively. In Layout 2, when the AGV number increases from 2 to 7, the average makespan of test sets MK03, MK04, MK08, and MK09 decreases by 266.2, 148.7, 399.3, and 537.2, with reduction rates of 52.8%, 59.1%, 38.8%, and 56.3%, respectively. In Layout 3, increasing AGVs from 3 to 8 leads to makespan reductions of 302.8 and 427.4 for MK06 and MK10, corresponding to 65.1% and 58.4%, respectively. Furthermore, it can be observed from Figure 6 that as the number of AGVs increases, the improvement in system makespan gradually diminishes. In some test sets, like MK05 and MK07, the shortest makespan is not achieved with the maximum number of AGVs, indicating that the transport capacity has reached saturation. Therefore, to achieve an optimal balance between transport efficiency and resource cost, it is crucial to determine the optimal AGV quantity for each layout. A detailed analysis of the results for the three layouts is presented below:  
In Layout 1, the shortest makespan for test sets MK01, MK02, MK05, and MK07 corresponds to AGV quantities of 6, 6, 3, and 5, respectively. Using these shortest makespans as benchmarks, the ODR for other configurations is calculated, and the same method is applied for Layouts 2 and 3.