# Learning-Based Branching Acceleration for Unit Commitment with Few Training Samples
## 5 Numerical Studies
### Performance of Branching Acceleration for UC  
Obtaining training samples is often difficult and costly, particularly in UC problems, where acquiring a substantial amount of real-world data is hard. Therefore, the number of training samples required to effectively learn a sufficiently robust enhanced pruning policy serves as a critical indicator of the method's quality. In this subsection, a 24-unit standard testing system and a 10-unit practical testing system are first used as examples to evaluate the performance of branching acceleration for UC with a minimal number of training daily load profiles (training samples). The corresponding results are presented in Tables 3 and 4. Subsequently, 30 daily load profiles are utilized to train the enhanced pruning policy models for systems with varying numbers of units. These models are then tested to verify the effectiveness of branching acceleration for UC, with the results summarized in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline No. of training daily load profiles & 20 & 25 & 30 \\ No. of testing daily load profiles & 50 & 50 & 50 \\ Average node count in B\&B tree & 65 & 73 & 51 \\ Average calculation time (s) & 17.96 & 19.77 & 14.79 \\ Speedup & 11.92\(\times\) & 10.64\(\times\) & 15.58\(\times\) \\ Optimality gap & 0.05\% & 0.03\% & 0.05\% \\ \hline \end{tabular}
\end{table} 
Table 4: Performance of branching acceleration for UC with different numbers of training daily load profiles in the 10-unit practical testing system. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **No. of Units** & \
\begin{tabular}{c} **Average Node** \\ **Count in B\&B Tree** \\ \end{tabular} &
\begin{tabular}{c} **Average** \\ **Calculation Time (s)** \\ \end{tabular} \\ \hline Standard & 12 & 99 & 24.07 \\ testing system & 24 & 685 & 289.10 \\
36 & 3716 & 1710.93 \\ \hline \multirow{3}{*}{Practical testing system} & 5 & 131 & 26.38 \\  & 10 & 799 & 186.74 \\ \cline{1-1}  & 12 & 598 & 146.45 \\ \cline{1-1}  & 15 & 852 & 352.20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational metric for the B&B algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline No. of training daily load profiles & 20 & 25 & 30 \\ No. of testing daily load profiles & 50 & 50 & 50 \\ Average node count in B\&B tree & 94 & 82 & 63 \\ Average calculation time (s) & 40.88 & 35.84 & 27.86 \\ Speedup & 7.26\(\times\) & 8.36\(\times\) & 10.90\(\times\) \\ Optimality gap & 0.09\% & 0.06\% & 0.08\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of branching acceleration for UC with different numbers of training daily load profiles in the 24-unit standard testing system. As demonstrated in Tables 3 and 4, branching acceleration for UC exhibits remarkable performance with just 20, 25, or 30 training daily load profiles. In the practical testing system, the method achieves a speedup of over 15 times compared to the B&B algorithm, with an accuracy loss of less than 0.05%. In the standard testing system, although the method's best performance is slightly reduced, it still delivers a speedup of over 10 times, maintaining an accuracy loss of less than 0.08%. As shown in Table 5, the test results demonstrate that the proposed method substantially accelerates the B&B algorithm while incurring minimal accuracy loss in solving the UC problem. Except for the 12-unit standard testing system and the 5-unit practical testing system (further analyzed in Section 5.3), branching acceleration for UC consistently achieves a speedup of over nine times, with an accuracy loss of less than 0.08%. Compared to existing studies that often require thousands or even hundreds of thousands of training samples, the numerical studies in this subsection highlight that branching acceleration for UC achieves excellent performance with a minimal number of training samples. A smaller training dataset offers advantages such as lower computational complexity and reduced training time but results in relatively lower method performance.