# Hyper-Heuristic Based on ACO and Local Search for Dynamic Optimization Problems +
## 4 Computational Tests
### Experimental Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Problem Instance**} & \multirow{3}{*}{\(m\)} & \multicolumn{4}{c}{**Symmetric**} & \multicolumn{4}{c}{**Asymmetric**} \\ \cline{3-8}  & & **HULK** & **HULK** & **\(\mathtt{ALK}\)**vs.** & **HULK** & **HULK** & **\(\mathtt{ALK}\)**vs.** \\  & & **vs.** & \(\mathtt{ALK}\) & **vs.** & \(\mathtt{AUS}\) & **\(\mathtt{AUS}\)**vs.** & \(\mathtt{AUS}\) & **\(\mathtt{AUS}\)**vs.** \\ \hline KROA100 & 0.05 & \(+\) & \(\sim\) & \(-\) & \(+\) & \(+\) & \(-\) \\  & 0.1 & \(+\) & \(+\) & \(-\) & \(+\) & \(+\) & \(\sim\) \\  & 0.2 & \(+\) & \(+\) & \(-\) & \(+\) & \(+\) & \(\sim\) \\  & 0.4 & \(+\) & \(+\) & \(-\) & \(+\) & \(+\) & \(-\) \\ \hline KROA150 & 0.05 & \(+\) & \(+\) & \(-\) & \(+\) & \(+\) & \(-\) \\  & 0.1 & \(++\) & \(+\) & \(-\) & \(+\) & \(+\) & \(\sim\) \\  & 0.2 & \(++\) & \(+\) & \(-\) & \(++\) & \(+\) & \(-\) \\  & 0.4 & \(++\) & \(+\) & \(-\) & \(++\) & \(+\) & \(-\) \\ \hline KROA200 & 0.05 & \(++\) & \(\sim\) & \(--\) & \(\sim\) & \(+\) & \(+\) \\  & 0.1 & \(++\) & \(\sim\) & \(--\) & \(+\) & \(+\) & \(-\) \\  & 0.2 & \(++\) & \(\sim\) & \(--\) & \(++\) & \(\sim\) & \(--\) \\  & 0.4 & \(++\) & \(+\) & \(--\) & \(++\) & \(+\) & \(--\) \\ \hline d198 & 0.05 & \(-\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.1 & \(--\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.2 & \(--\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.4 & \(--\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\ \hline lin318 & 0.05 & \(+\) & \(++\) & \(++\) & \(++\) & \(++\) & \(+\) \\  & 0.1 & \(+\) & \(++\) & \(++\) & \(++\) & \(++\) & \(+\) \\  & 0.2 & \(\sim\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.4 & \(\sim\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\ \hline pcb442 & 0.05 & \(-\) & \(+\) & \(+\) & \(++\) & \(++\) & \(-\) \\  & 0.1 & \(-\) & \(+\) & \(+\) & \(++\) & \(++\) & \(-\) \\  & 0.2 & \(-\) & \(+\) & \(++\) & \(++\) & \(++\) & \(+\) \\  & 0.4 & \(-\) & \(+\) & \(++\) & \(++\) & \(++\) & \(+\) \\ \hline u574 & 0.05 & \(++\) & \(++\) & \(--\) & \(+\) & \(++\) & \(++\) \\  & 0.1 & \(++\) & \(++\) & \(--\) & \(+\) & \(++\) & \(++\) \\  & 0.2 & \(++\) & \(+\) & \(--\) & \(++\) & \(++\) & \(++\) \\  & 0.4 & \(++\) & \(+\) & \(--\) & \(++\) & \(++\) & \(++\) \\ \hline rat783 & 0.05 & \(+\) & \(++\) & \(++\) & \(+\) & \(+\) & \(+\) \\  & 0.1 & \(+\) & \(++\) & \(++\) & \(++\) & \(++\) & \(+\) \\  & 0.2 & \(\sim\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.4 & \(+\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\ \hline pcb1173 & 0.05 & \(-\) & \(++\) & \(++\) & \(++\) & \(++\) & \(+\) \\  & 0.1 & \(-\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.2 & \(+\) & \(++\) & \(++\) & \(++\) & \(++\) & \(++\) \\  & 0.4 & \(++\) & \(++\) & \(--\) & \(++\) & \(++\) & \(++\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Statistical results regarding the average offline performance of the presented methods on symmetric DTSPs (upper half) and asymmetric DTSPs (lower half), where \(\mathcal{MMAS}\) + \(\mathtt{LK}\) and \(\mathcal{MMAS}\) + \(\mathtt{US}\) are replaced by \(\mathtt{ALK}\) and \(\mathtt{AUS}\), respectively. Considering the symmetric environmental changes (Table 3), HULK performs better in 66.7% of test cases and \(\mathcal{MMAS}\) + LR performs better in the rest, but there are two where \(\mathcal{MMAS}\) + US wins. In terms of numbers, HULK wins in 24 out of 32 instances; in seven the percentage difference is less than 1.0%, and for the other five the percentage difference remains between 1.0% and 3.1%. There are situations where \(\mathcal{MMAS}\) + US outperforms \(\mathcal{MMAS}\) + LR, e.g., u57.tsp and the entire KROA family, but there are only two cases where \(\mathcal{MMAS}\) + US outperform HULK. We can also observe Table 5, which shows that HULK always has a similar or superior quality compared with \(\mathcal{MMAS}\) + US and in some cases loses to \(\mathcal{MMAS}\) + LR.