## 4 Experimental Results
### Application of EA-ILS Hyper-Heuristic to HyFlex Version 1.0  
The EA-ILS hyper-heuristic was tested on six problem domains of the first version of HyFlex (HyFlex V1.0) to further demonstrate its generality. The problem domains are Boolean satisfiability (SAT), bin packing (BP), personnel scheduling (PS), permutation flow-shop (PFS), traveling salesman problem (TSP), and vehicle routing problem (VRP). Tables 10 and 11 respectively show comparisons of the best and median ofvs of the EA-ILS hyper-heuristic obtained from its 31 runs in each instance against the state-of-the-art hyper-heuristics AdapHH, FS-ILS, and TS-ILS [48]. The values presented in the tables further establish the competitiveness of the EA-ILS hyper-heuristic when compared to the state-of-the-art ones. It is important to note that only algorithms that were run with the updated version of HyFlex v1.0 can be directly compared with the EA-ILS hyper-heuristic 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 & 1.0 & 1.0 & 1.0 & **0.0** \\  & SAT5 & **1.0** & **3.0** & **1.0** & **1.0** \\  & SAT4 & **0.0** & **1.0** & **0.0** & **0.0** \\  & SAT10 & **1.0** & **1.0** & **1.0** & **1.0** \\  & SAT11 & **7.0** & **7.0** & **7.0** & **7.0** \\ \hline \multirow{6}{*}{Bin Packing} & BP7 & **0.01107109** & 0.0131 & 0.01384737 & 0.01569294 \\  & BP1 & 0.00339113 & **0.0028** & 0.00666972 & 0.00306951 \\  & BP9 & 0.00162385 & **0.0004** & 0.01004134 & 0.00049110 \\  & BP10 & 0.10829805 & 0.1083 & 0.10833606 & 0.10827981 \\  & BP11 & 0.00431172 & 0.0031 & 0.01047079 & **0.00115128** \\ \hline \multirow{6}{*}{Scheduling} & PS5 & **15.0** & - & 17.0 & **15.0** \\  & PS9 & **9176.0** & - & 9486.0 & 9291.0 \\  & PS8 & **3136.0** & - & 3148.0 & 3142.0 \\  & PS10 & 1380.0 & - & **1360.0** & 1453.0 \\  & PS11 & **305.0** & - & 325.0 & 315.0 \\ \hline \multirow{6}{*}{Flowshop} & PFS1 & **6210.0** & 6214.0 & 6214.0 & **6210.0** \\  & PFS8 & **26700.0** & 26757.0 & 26743.0 & 26744.0 \\  & PFS3 & **6303.0** & **6303.0** & **6303.0** & **6303.0** \\  & PFS10 & **11308.0** & 11318.0 & 11332.0 & **11308.0** \\  & PFS11 & **26511.0** & 26541.0 & 26547.0 & 26516.0 \\ \hline \multirow{6}{*}{ Travelling Salesman} & TSP0 & **48194.9** & **48194.9** & **48194.9** & **48194.9** \\  & TSP8 & 20732537.2 & 20752853.8 & 20933386.7 & **20662037.2** \\  & TSP2 & 6798.8 & 6797.5 & **6796.5** & 6798.6 \\  & TSP7 & 66017.2 & 66277.1 & 65748.4 & **65592.7** \\  & TSP6 & 52545.2 & 52383.8 & 52385.5 & **52308.7** \\ \hline \multirow{6}{*}{Routing} & VRP6 & 61943.4 & **58052.1** & 63429.7 & 60145.1 \\  & VRP2 & 12270.1 & 13304.9 & 12277.1 & **12266.9** \\ \cline{1-1}  & VRP5 & 143902.4 & 145481.5 & **142481.3** & 142607.9 \\ \cline{1-1}  & VRP1 & 20652.2 & 20652.3 & **20651.6** & 20652.2 \\ \cline{1-1}  & VRP9 & 144030.2 & 146154.1 & 144686.3 & **143479.0** \\ \hline \end{tabular}
\end{table} 
Table 10: Best ofvs Obtained by EA-ILS against three state-of-the-art Hyper-Heuristics. The entries for TS-ILS and FS-ILS were taken from a previous study [48] where both methods were tested on the same machine. The EA-ILS hyper-heuristic comfortably outperformed others on the PS and PFS problem domains. Moreover, it has outperformed the FS-ILS hyper-heuristic on the BP problem but is inferior to others on the SAT according to the median ofvs obtained. The performances of the 20 CHeSC entries, EA-ILS, TS-ILS, and FS-ILS were further analyzed using the F1 ranking test. Table 12 shows the results of the EA-ILS hyper-heuristic versus only the 20 CHeSC entries while Figure 5 shows the results of the EA-ILS hyper-heuristic vs. the 20 CHeSC entries, FS-ILS, and TS-ILS. The overall F1 ranking of the EA-ILS hyper-heuristic based on the total number of algorithms is 3 as observed in Figure 5, behind the TS-ILS and FS-ILS hyper-heuristics. It recorded a total score of 126.25 and a deficit of 4.50 from the score of the FS-ILS hyper-heuristic.