## 4 Performance Evaluation
### Result of Solutions  
In Section 4.1, we observed the trained models get better performance in terms of reward and number of steps. In this section, we will verify the performance of the trained models applied to unseen problems. The trained models and baseline methods solved 1000 problems per problem type. The types of problems are discussed in the first paragraph of Section 4. We calculated the average value based on the profits of the selected items in the solutions. Tables 1-3 show the profit of selected items divided by the profit of total items. The optimal result of each instance represents the maximum feasible profit ratio in each knapsack and capacity. Tables 4-6 show the percentage of profit derived from each algorithm over the profit of the optimal solution. The percentage of each field represents how close the derived solution is to the optimal solution. Tables 7-9 show the total profit of the selected items. Tables 10-12 represent the average profits of the selected items per  
Figure 4: DRL training information of step in episodes. (**a**) Step of RI; (**b**) Step of LI; (**c**) Step of QI. Figure 3: DRL training information of reward in episodes. (**a**) Reward of RI; (**b**) Reward of LI; (**c**) Reward of QI. capacity. Each field of them is an average value of the aggregate profit of the selected items in all knapsacks for a given capacity. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(M\) & \(N\) & **Capacity** & **Random** & **Greedy** & **Proposed** & **Optimal** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{50} & 10 & 0.1507 & 0.1727 & 0.1727 & 0.1743 \\  & & 20 & 0.2064 & 0.2652 & 0.2652 & 0.2672 \\  & & 40 & 0.3002 & 0.3960 & 0.3958 & 0.3979 \\  & & 80 & 0.4638 & 0.5853 & 0.5853 & 0.5873 \\  & & 100 & 0.5354 & 0.6553 & 0.6551 & 0.6573 \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{50} & 10 & 0.2786 & 0.3230 & 0.3256 & 0.3376 \\  & & 20 & 0.4016 & 0.4855 & 0.4876 & 0.4995 \\  & & 40 & 0.6138 & 0.7165 & 0.7166 & 0.7293 \\  & & 80 & 0.9285 & 0.9678 & 0.9678 & 0.9738 \\  & & 100 & 0.9952 & 0.9985 & 0.9985 & 0.9993 \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{50} & 10 & 0.3665 & 0.4235 & 0.4268 & 0.4530 \\  & & 20 & 0.5449 & 0.6323 & 0.6323 & 0.6609 \\ \cline{1-1}  & & 40 & 0.8239 & 0.9029 & 0.9030 & 0.9218 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Profit ratio of selected items for RI set. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(M\) & \(N\) & **Capacity** & **Random** & **Greedy** & **Proposed** & **Optimal** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{50} & 10 & 0.0467 & 0.0483 & 0.0483 & 0.0488 \\  & & 20 & 0.0848 & 0.0893 & 0.0893 & 0.0901 \\  & & 40 & 0.1587 & 0.1664 & 0.1664 & 0.1675 \\  & & 80 & 0.3060 & 0.3153 & 0.3156 & 0.3170 \\  & & 100 & 0.3798 & 0.3893 & 0.3894 & 0.3911 \\ \hline \multirow{4}{*}{3} & \multirow{4}{*}{50} & 10 & 0.1238 & 0.1244 & 0.1263 & 0.1299 \\  & & 20 & 0.2347 & 0.2377 & 0.2398 & 0.2442 \\  & & 40 & 0.4522 & 0.4555 & 0.4581 & 0.4638 \\  & & 80 & 0.8720 & 0.8642 & 0.8665 & 0.8830 \\  & & 100 & 0.9914 & 0.9917 & 0.9929 & 0.9964 \\ \hline \multirow{4}{*}{5} & \multirow{4}{*}{50} & 10 & 0.1956 & 0.1920 & 0.1920 & 0.2061 \\  & & 20 & 0.3776 & 0.3751 & 0.3784 & 0.3920 \\ \cline{1-1}  & & 40 & 0.7240 & 0.7191 & 0.7208 & 0.7438 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Profit ratio of selected items for LI set.