# Learning-Based Branching Acceleration for Unit Commitment with Few Training Samples
## 5 Numerical Studies
### Generalization Capability Analysis of the Enhanced Pruning Policy  
The generalization capability of ML models is a key factor that determines their practical value and impact, making it a critical area of focus in ML research. To evaluate the generalization capability of the enhanced pruning policy model proposed in this paper, including the generalization capability for scenarios involving systems with larger or smaller numbers of units. This subsection evaluates policy models trained on the 24-unit standard testing system and the 10-unit practical testing system under varying systems. The number of training daily load profiles is 30, and the number of testing daily load profiles is 50. The results are presented in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Standard Testing System**} & \multicolumn{3}{c}{**Practical Testing System**} \\ \cline{2-6}
**No. of Units for Training** & \multicolumn{3}{c}{**24**} & \multicolumn{3}{c}{**10**} \\ \cline{2-6}
**No. of Units for Testing** & **12** & **36** & **5** & **12** & **15** \\ \hline Average node count in B\&B tree & 45 & 313 & 24 & 46 & 62 \\ Average calculation time (s) & 11.56 & 145.67 & 7.39 & 13.93 & 21.62 \\ Speedup & 2.21\(\times\) & 11.86\(\times\) & 5.36\(\times\) & 13.11\(\times\) & 13.71\(\times\) \\ Optimality gap & 0.08\% & 0.05\% & 0.96\% & 0.06\% & 0.08\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Generalization capability of the enhanced pruning policy.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Standard Testing System**} & \multicolumn{3}{c}{**Practical Testing System**} \\ \cline{2-6}
**No. of Units** & **12** & **24** & **36** & **5** & **10** & **12** & **15** \\ \hline Average node count in B\&B tree & 31 & 63 & 209 & 26 & 51 & 64 & 77 \\ Average calculation time (s) & 8.38 & 27.86 & 97.44 & 7.48 & 14.79 & 18.32 & 26.20 \\ Speedup & 3.21\(\times\) & 10.90\(\times\) & 17.75\(\times\) & 5.11\(\times\) & 15.58\(\times\) & 9.36\(\times\) & 11.01\(\times\) \\ Optimality gap & 0.11\% & 0.08\% & 0.04\% & 0.64\% & 0.05\% & 0.04\% & 0.04\% \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance of branching acceleration for UC with 30 training daily load profiles.  
As shown in Table 6, the proposed policy models exhibit excellent generalization capability in scenarios with larger or smaller numbers of units. While the performance shows a slight decline compared to re-trained policy models in Table 5, the results remain highly satisfactory. Based on the data in Table 6 and the analysis provided in Section 5.2, the following conclusions can be drawn:  
* When testing the enhanced pruning policy model for performance and generalization capability on the 12-unit standard testing system and the 5-unit practical testing system, it becomes evident that the acceleration effect is somewhat less pronounced compared to other systems. This discrepancy occurs because the B&B algorithm generates a relatively small number of search tree nodes, leaving less space for pruning acceleration. As a result, in these cases, the speedup metric does not fully capture the excellent acceleration effect of branching acceleration for UC.
* The performance and generalization capability evaluations of the 5-unit practical testing system reveal suboptimal results for the optimality gap metric. This can be attributed to the fact that systems with smaller total unit generator capacities and corresponding loads tend to have lower costs and greater cost volatility. Even a minor cost difference is reflected in a more significant optimality gap metric.