## 4 Experimental Results
### Application of EA-ILS Hyper-Heuristic to HyFlex Version 1.0
It finished fourth, third, first, fifth, and joint third in the SAT, BP, PFS, TSP, and VRP problem domains, respectively. The results of the PS of the EA-ILS, FS-ILS, and TS-ILS hyper-heuristics could not be used for these rankings. This is because of the use of the updated HyFlex library, which was released to correct the errors identified on the PS domain. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Domain** & **Instance** & **EA-ILS** & **AdapHH** & **FS-ILS** & **TS-ILS** \\ \hline \multirow{6}{*}{MAX-SAT} & SAT3 & 4.0 & 3.0 & **2.0** & **2.0** \\  & SAT5 & 5.0 & 5.0 & **3.0** & **3.0** \\  & SAT4 & 2.0 & 2.0 & **1.0** & **1.0** \\  & SAT10 & 6.0 & 3.0 & 2.0 & **1.0** \\  & SAT11 & 9.0 & 8.0 & **8.0** & **8.0** \\ \hline \multirow{6}{*}{Bin Packing} & BP7 & 0.01612590 & **0.01607535** & 0.01851932 & 0.01876799 \\  & BP1 & 0.00354067 & 0.00360372 & 0.00751493 & **0.00350695** \\  & BP9 & 0.00267695 & 0.00356587 & 0.01122520 & **0.00052035** \\  & BP10 & 0.10831818 & **0.10828303** & 0.10840170 & 0.10828402 \\  & BP11 & 0.00755952 & 0.00354259 & 0.01355520 & **0.00142866** \\ \hline \multirow{6}{*}{Personnel} & PS5 & **20.0** & - & 23.0 & 21.0 \\  & PS9 & 9560.0 & - & 9763.0 & **9548.0** \\ \cline{1-1}  & PS8 & **3164.0** & - & 3236.0 & 3181.0 \\ \cline{1-1}  & PS10 & **1550.0** & - & 1635.0 & **1550.0** \\ \cline{1-1}  & PS11 & **325.0** & - & 345.0 & 330.0 \\ \hline \multirow{6}{*}{Flowshop} & PFS1 & **6224.0** & 6240.0 & 6241.0 & 6232.0 \\  & PFS8 & **26769.0** & 26814.0 & 26797.0 & 26785.0 \\ \cline{1-1}  & PFS3 & **6323.0** & 6326.0 & **6323.0** & 6325.0 \\ \cline{1-1}  & PFS10 & 11344.0 & 11359.0 & 11374.0 & **11340.0** \\ \cline{1-1}  & PFS11 & **26583.0** & 26643.0 & 26605.0 & 26601.0 \\ \hline \multirow{6}{*}{Travelling Salesman} & TSP0 & **48194.9** & **48194.9** & **48194.9** & **48194.9** \\ \cline{1-1}  & TSP8 & 21333200.0 & 20822145.6 & 21172591.7 & **20779493.2** \\ \cline{1-1}  & TSP2 & 6805.8 & 6810.5 & 6806.7 & **6805.3** \\ \cline{1-1}  & TSP7 & 66483.8 & 66879.8 & 66415.3 & 66133.0 \\ \cline{1-1}  & TSP6 & 53997.5 & 53099.8 & 52840.8 & 53762.4 \\ \hline \multirow{6}{*}{Vehicle Routing} & VRP6 & 66178.5 & **60900.6** & 65638.8 & 63709.0 \\ \cline{1-1}  & VRP2 & 13286.3 & 13347.6 & **12308.0** & 13292.8 \\ \cline{1-1}  & VRP5 & 146813.7 & 148516.8 & 146871.0 & 145401.5 \\ \cline{1-1}  & VRP1 & **20654.1** & 20656.6 & **20654.1** & 20654.7 \\ \cline{1-1}  & VRP9 & 145765.2 & 148689.2 & 146242.7 & **145205.4** \\ \hline \hline \end{tabular}
\end{table} 
Table 11: Median ofvs Obtained by EA-ILS against three state-of-the-art Hyper-Heuristics. The comparison of three ILS-based hyper-heuristics using a more robust \(\mu\)-norm performance metric [24; 25] was performed across the six domains from HyFlex v1.0. The performance metric normalizes the 31 objective function values obtained by a given hyper-heuristic, thus using the results of all 31 trials per instance as a basis for the evaluation. A fair comparison is possible based on the six domains of HyFlex v1.0 because the results for the PS achieved by the FS-ILS hyper-heuristic and the TS-ILS hyper-heuristic were based on the updated library for the domain. Table 13 summarizes the benchmarking of the performance of the EA-ILS hyper-heuristic with the results obtained by the FS-ILS and TS-ILS hyper-heuristics on the original six problem domains. It is evident from Table 13 that the EA-ILS hyper-heuristic is highly competitive, even in the six domains of HyFlex v1.0. Its weaknesses are evidenced by its application to the SAT and TSP problem domains. Although Table 10 suggests that the hyper-heuristic can find high-quality solutions, it is perhaps the lack of consistency in evol