# Learning Individualized Hyperparameter Settings
## 3 Algorithms and Problems
### Robust Tabu Search and the QAP
This brought the total number of instances to 103 but the added sets being so small, we present in Table 4 the results grouped by size rather than by name. The results of Table 4 were consistent with those of Table 2 in that individualized settings outperformed global settings in all but one row, without reaching statistical significance. The only subset where global settings performed better, modulo the tie-breaking policy, was that of the simplest instances, where both codes could quickly solve all instances. #### 5.2.2 New Instances

In order to better evaluate the abstraction power of the neural adaptation, we generated some new instances either according to the literature generators or based on data distributions that were clearly different from the literature ones. In particular, since we had to generate data matrices for both problems, we generated them according to a gamma distribution, which is both very flexible and possibly very different from the uniform distribution that is usually at the core of the generation of the literature benchmarks. In the case of the GAP, we generated 15 instances structurally similar to [PERSON]'s OR-library ones, 18 similar to [PERSON]'s E ones, and 30 instances based on the gamma distribution. The literature-like instances were generated in order to achieve a clearer significance, while the gamma ones were to assess the abstraction power of the trained networks. All instances are available from [31] and validation results are reported in Table 5.

The table shows that the number of instances better solved with the individualized settings was higher than with the global setting in all rows. In this case, statistical significance at \(\alpha=0.05\) was reached for two subsets, the Yagiura-like and the newly generated gamma. The results for the Yagiura were consistent with those of Table 5, which already bordered significance, but in that case, from the nonsignificance side. The results on the gamma instances confirmed that a setting optimized for a subset of the instance space can be suboptimal when applied to instances from a different subset, and that neural abstraction can help to constrain the problem. Indeed, we see that the significance of the difference was greatly increased on these instances, and we interpreted this result as consistent with the assumption that motivated the generation of these instances, i.e., that a setting optimized for a given instance set can be suboptimal when applied to instances that are structurally very different from those on which it was optimized. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Size** & \(n\) & \(S_{0}\) & \(S_{n}\) & _p (Binomial)_ \\ \hline
12–15 & 19 & 11 & 8 & 0.820 \\
16–20 & 31 & 14 & 17 & 0.360 \\
21–30 & 27 & 9 & 18 & 0.061 \\
31–40 & 19 & 7 & 12 & 0.180 \\
41–50 & 7 & 2 & 5 & 0.227 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: QAP, full literature test sets. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Type** & \(n\) & \(S_{0}\) & \(S_{n}\) & _p (Binomial)_ \\ \hline Beasley & 60 & 23 & 37 & 0.046 \\ Yagiura & 39 & 14 & 25 & 0.054 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: GAP, full literature test sets. Finally, we also generated instances for the QAP, both replicating the generation procedure for the subsets where it was reproducible (i.e., the CHR, NUG, and TAI subsets) and using the gamma generator to generate the QAP matrices. The results are shown in Table 6. Again, compared to the results of their GAP counterpart in Table 5, these results outlined a smaller impact of the individualized approach, and this testified to the robustness of the robust tabu search, i.e., the low sensitivity to parameters as indicated by the name of the method. However, even in that case, the highest significance was achieved on the new gamma instances. This was consistent with the results presented in Table 5, where the gamma instances also had a greater significance.