## 5 Experimental Results
### Comparison of NewKLS_FVS with Other Algorithms
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Instance** & **Best** & **Worst** & **Average** & **Instance** & **Best** & **Worst** & **Average** \\ \hline \hline  & 104 & 97 & 100 & queen12\_12.col & 20 & 19 & 19 \\  & 126 & 123 & 124 & queen13\_13.col & 21 & 21 & 21 \\  & 65 & 60 & 62 & queen14\_14.col & 23 & 22 & 22 \\  & 65 & 60 & 63 & queen15\_15.col & 25 & 24 & 24 \\  & 153 & 149 & 151 & queen16\_16.col & 26 & 25 & 25 \\  & 139 & 136 & 137 & school1.col & 76 & 72 & 73 \\  & 76 & 73 & 74 & school1\_nsh.col & 69 & 66 & 67 \\  & 70 & 67 & 68 & zeroin.i.1.col & 137 & 137 & 137 \\  & 80 & 80 & 80 & zeroin.i.2.col & 160 & 159 & 159 \\  & 43 & 43 & 43 & zeroin.i.3.col & 155 & 154 & 154 \\  & 27 & 27 & 27 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._ \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Instance** & **Best** & **Worst** & **Average** & **Instance** & **Best** & **Worst** & **Average** \\ \hline anna.col & 110 & 107 & 109 & miles1000.col & 15 & 14 & 14 \\ david.col & 58 & 56 & 56 & miles1500.col & 10 & 9 & 9 \\ DSJC125.1.col & 42 & 40 & 41 & mulsol.i.1.col & 39 & 36 & 37 \\ DSJC125.5.col & 12 & 11 & 11 & mulsol.i.2.col & 50 & 46 & 48 \\ DSJC125.9.col & 6 & 6 & 6 & mulsol.i.3.col & 49 & 46 & 47 \\ fpsol2.i.1.col & 78 & 73 & 76 & mulsol.i.4.col & 50 & 46 & 47 \\ fpsol2.i.2.col & 123 & 118 & 120 & mulsol.i.5.col & 50 & 46 & 47 \\ fpsol2.i.3.col & 120 & 112 & 115 & myciel3.col & 8 & 8 & 8 \\ games120.col & 37 & 36 & 36 & myciel4.col & 16 & 16 & 16 \\ homer.col & 336 & 324 & 329 & myciel6.col & 43 & 41 & 41 \\ huck.col & 47 & 46 & 46 & myciel7.col & 56 & 54 & 55 \\ inithx.i.1.col & 131 & 123 & 127 & queen5\_5.col & 7 & 7 & 7 \\ inithx.i.2.col & 144 & 137 & 140 & queen6\_6.col & 9 & 9 & 9 \\ inithx.i.3.col & 142 & 136 & 138 & queen7\_7.col & 11 & 11 & 11 \\ jean.col & 58 & 57 & 57 & queen8\_8.col & 12 & 12 & 12 \\ latin\_square\_10.col & 7 & 7 & 7 & queen8\_12.col & 15 & 14 & 14 \\ le450\_5a.col & 61 & 59 & 60 & queen9\_9.col & 14 & 13 & 13 \\ le450\_5b.col & 62 & 59 & 60 & queen10\_10.col & 15 & 14 & 14 \\ le450\_5c.col & 41 & 38 & 39 & queen11\_11.col & 16 & 15 & 15 \\ le450\_5d.col & 41 & 39 & 40 & queen12\_12.col & 17 & 17 & 17 \\ le450\_15b.col & 54 & 52 & 52 & queen13\_13.col & 19 & 18 & 18 \\ le450\_15c.col & 30 & 28 & 28 & queen14\_14.col & 19 & 19 & 19 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results for VNS2 with \(k_{max}=2\) and a CPU-time limit of 30 min for 15 runs. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Instance** & **Best** & **Worst** & **Average** & **Instance** & **Best** & **Worst** & **Average** \\ \hline le450\_15b.col & 53 & 51 & 52 & queen13\_13.col & 19 & 18 & 18 \\ le450\_15c.col & 30 & 27 & 28 & queen14\_14.col & 19 & 19 & 19 \\ le450\_15d.col & 29 & 27 & 28 & queen15\_15.col & 21 & 20 & 20 \\ le450\_25a.col & 59 & 57 & 57 & queen16\_16.col & 22 & 21 & 21 \\ le450\_25b.col & 57 & 55 & 55 & school1.col & 27 & 25 & 25 \\ le450\_25c.col & 31 & 29 & 29 & school1\_nsh.col & 27 & 25 & 25 \\ le450\_25d.col & 30 & 29 & 29 & zeroin.i.1.col & 47 & 44 & 45 \\ miles250.col & 64 & 62 & 63 & zeroin.i.2.col & 66 & 61 & 64 \\ miles500.col & 32 & 31 & 31 & zeroin.i.3.col & 66 & 61 & 63 \\ miles750.col & 21 & 20 & 20 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: _Cont._