# Multi-Objective Order Scheduling via Reinforcement Learning
## 5 Experiments
### Results on Public Benchmarks  
In order to ensure the validity of our experimental results, we carefully selected the DMU dataset and divided it into eight groups based on dataset size. Our team then generated policies for three of these groups, while the remaining five groups were used as the test set. The purpose of this experimental setup was to evaluate the performance of our policies against a baseline in a variety of dataset scenarios. In this way, we were able to determine the effectiveness of our policies in improving the performance of the DMU dataset. The results of our experiments, shown in Table 4, clearly demonstrate that our policies outperformed the baseline in all of the tested scenarios. This indicates that our policies have the potential to significantly improve the performance of similar datasets in the future.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Size** & **Instance** & **SPT** & **MWKR** & **FDD/WKR** & **Ours** \\ \hline \multirow{8}{*}{\(30\times 20\)} & dmu01 & 6241 & **5837** & 5948 & 5917 \\  & dmu02 & 6487 & 6610 & 6035 & **5271** \\  & dmu03 & 6978 & 6363 & 5863 & **5553** \\  & dmu04 & 5767 & 6385 & 5424 & **6360** \\  & dmu05 & 6910 & 6472 & 6444 & **4791** \\  & dmu1 & 7698 & 7930 & 8248 & **6887** \\  & dmu42 & 7746 & 7063 & 7694 & **6913** \\  & dmu3 & 7269 & 7708 & 7601 & **7063** \\  & dmu44 & 7114 & 7335 & 7490 & **6489** \\  & dmu45 & **6212** & 6844 & 7101 & 7085 \\ \hline \multirow{8}{*}{\(50\times 15\)} & Time(s) & 0.721 & 0.731 & 0.731 & 1.804 \\ \cline{1-1}  & dmu31 & 8869 & 8147 & 7899 & **7433** \\ \cline{1-1}  & dmu32 & 7814 & 8004 & 7316 & **7305** \\ \cline{1-1}  & dmu33 & 8114 & 7710 & **7262** & 7774 \\ \cline{1-1}  & dmu34 & 7625 & 7709 & 7725 & **7385** \\ \cline{1-1}  & dmu35 & 8626 & 7617 & **7099** & 7240 \\ \cline{1-1}  & dmu71 & **9594** & 9978 & 10,889 & 10,828 \\ \cline{1-1}  & dmu72 & **9882** & 10,135 & 11,602 & 10,144 \\ \cline{1-1}  & dmu73 & 9953 & 9721 & 10,212 & **9625** \\ \cline{1-1}  & dmu74 & 9866 & 10,086 & 10,659 & **9473** \\ \cline{1-1}  & dmu75 & 9411 & 9953 & 10,839 & **9270** \\ \hline \multirow{8}{*}{\(50\times 20\)} & Time(s) & 2.403 & 2.323 & 2.524 & 4.972 \\ \cline{1-1}  & dmu36 & 9911 & 8090 & **8084** & 8433 \\ \cline{1-1}  & dmu37 & 8917 & 9685 & 9433 & **8774** \\ \cline{1-1}  & dmu38 & 9384 & 8414 & 8428 & **8385** \\ \cline{1-1}  & dmu39 & 9221 & 9266 & 8177 & **7801** \\ \cline{1-1}  & dmu40 & 9406 & 8261 & 7773 & 8256 \\ \cline{1-1}  & dmu76 & 11,677 & 10,571 & 11,576 & **10,114** \\ \cline{1-1}  & dmu77 & 10,401 & 11,148 & 11,910 & 11,564 \\ \cline{1-1}  & dmu78 & 10,585 & **10540** & 11,464 & 11,345 \\ \cline{1-1}  & dmu79 & 11,115 & 11,201 & 11,035 & **10,828** \\ \cline{1-1}  & dmu80 & 10,711 & 10,894 & 11,116 & **11,033** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results on generated instances compared to the algorithm without convex hull.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Size**} & \multicolumn{2}{c}{**Without Convexhull [12]**} & \multicolumn{2}{c}{**Ours**} \\ \cline{2-5}  & **Time** & **Cost** & **Distance** & **Time** & **Cost** & **Distance** \\ \hline \(10\times 10\) & 1466.24 & 548.67 & 390.14 & 1138.67 & 464.38 & 396.67 \\ \(15\times 15\) & 2012.84 & 811.77 & 813.63 & 1633.5 & 655.72 & 643.99 \\ \(20\times 15\) & 2375.15 & 909.56 & 917.10 & 1971.35 & **727.28** & **879.7** \\ \(20\times 20\) & 2417.89 & 893.47 & 1131.72 & 2369.32 & **873.75** & **1009.42** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison with traditional algorithms.