# 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} \hline \hline
**Problem** & \(m\) & \(\mathcal{MM}\)**AS** + \(\mathrm{LK}\) & \(\mathcal{MM}\)**AS** + \(\mathrm{US}\) & **HULK** \\
**Instance** & \(m\) & \(\mathcal{MM}\)**AS** + \(\mathrm{LK}\) & \(\mathcal{MM}\)**AS** + \(\mathrm{US}\) & **HULK** \\ \hline KROA100.atsp & 0.05 & 20,279.1 (1.5) & 20,058.4 (0.4) & **19,981.4** \\  & 0.1 & 20,051.2 (0.4) & 20,120.6 (0.3) & **19,975.4** \\  & 0.2 & 20,050.9 (0.9) & 20,038.6 (0.8) & **19,875.4** \\  & 0.4 & 20,090.3 (1.5) & 19,978.9 (0.9) & **19,802.0** \\ \hline KROA150.atsp & 0.05 & 25,447.8 (1.3) & 25,236.0 (0.5) & **25,109.0** \\  & 0.1 & 25,277.0 (0.8) & 25,291.1 (0.8) & **25,083.7** \\  & 0.2 & 25,451.3 (2.6) & 25,062.8 (1.0) & **24,808.1** \\  & 0.4 & 25,268.0 (2.5) & 24,907.7 (1.0) & **24,651.8** \\ \hline KROA200.atsp & 0.05 & **28,110.2** & 28,183.5 (0.3) & 28,131.3 (0.1) \\  & 0.1 & 28,170.0 (0.9) & 27,988.0 (0.3) & **27,910.7** \\  & 0.2 & 28,326.1 (2.6) & **27,595.1** & 27,626.3 (0.0) \\  & 0.4 & 28,433.7 (3.6) & 27,796.9 (1.3) & **27,453.0** \\ \hline di98.atsp & 0.05 & 14,582.0 (5.5) & 14,999.4 (8.6) & **13,815.4** \\  & 0.1 & 14,489.4 (5.3) & 14,831.4 (7.8) & **13,761.6** \\  & 0.2 & 14,236.4 (2.9) & 14,842.6 (7.3) & **13,834.8** \\  & 0.4 & 13,789.3 (6.3) & 14,578.9 (12.4) & **12,967.4** \\ \hline lin318.atsp & 0.05 & 41,768.9 (2.6) & 41,924.9 (3.0) & 40,700.7 \\  & 0.1 & 41,615.0 (3.0) & 42,168.5 (4.4) & **40,394.4** \\  & 0.2 & 41,587.3 (3.7) & 42,457.0 (5.8) & **40,111.2** \\  & 0.4 & 41,314.8 (3.5) & 42,675.8 (6.9) & **39,928.6** \\ \hline pcb442.atsp & 0.05 & 51,549.2 (3.2) & 50,997.1 (2.1) & **49,970.9** \\  & 0.1 & 51,763.4 (2.9) & 51,543.3 (2.5) & **50,305.6** \\  & 0.2 & 51,694.0 (3.0) & 51,844.5 (3.3) & **50,175.4** \\  & 0.4 & 51,471.9 (3.3) & 52,153.3 (4.6) & **49,846.4** \\ \hline u574.atsp & 0.05 & 37,363.4 (2.0) & 38,305.9 (4.6) & 36,620.7 \\  & 0.1 & 36,893.0 (0.8) & 38,369.8 (4.0) & 36,587.3 \\  & 0.2 & 36,775.8 (2.9) & 38,385.6 (4.4) & **35,727.4** \\  & 0.4 & 36,437.0 (2.8) & 38,383.5 (5.3) & 35,442.5 \\ \hline rat783.atsp & 0.05 & 8678.9 (1.1) & 8722.9 (1.6) & 8586.5 \\  & 0.1 & 8649.5 (2.6) & 8800.3 (4.4) & **8431.1** \\  & 0.2 & 8567.1 (2.0) & 8790.2 (4.7) & 8395.5 \\  & 0.4 & 8491.7 (2.5) & 9103.6 (9.8) & **8288.3** \\ \hline pcb1173.atsp & 0.05 & 60,343.1 (2.4) & 61,194.5 (3.9) & **58,920.1** \\  & 0.1 & 60,197.8 (2.7) & 61,655.1 (5.1) & **58,636.8** \\  & 0.2 & 60,027.8 (2.6) & 62,008.5 (6.0) & **58,515.8** \\  & 0.4 & 59,639.9 (2.3) & 62,706.6 (7.6) & **58,270.7** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Experimental results regarding the average offline performance of the presented methods, asymmetric DTSPs. The number between brackets means the distance in percentage from the current value to the best value, in boldface. To visualize and understand the behavior of the compared methods, we plotted for the last twenty environmental changes the dynamic average offline performance of the presented hyper-heuristic (HULK), \(\mathcal{MMAS}\) + US and \(\mathcal{MMAS}\) + \(\mathtt{LK}\), and see Figure 5 for symmetric, and Figure 6 for asymmetric dynamic changes. The problems plotted are rat783 and pcb1173, and we can observe that for the symmetrical change case all methods are competitive with an advantage to HULK and \(\mathcal{MMAS}\) + \(\mathtt{LK}\), but when we turn to the asymmetrical change case we can see the consistently better performance of HULK proving that the combination of two powerful LSOs can achieve much better solutions. We can also trace the following observations from the computational results.