## 4 Experimental Results
### Effect of Local Search Procedure  
The local search procedure (LS-Seq) of the EA-ILS hyper-heuristic was compared with the VND-style local search, tagged LS-VND, commonly used in the FS-ILS hyper-heuristic and NR-FS-ILS. The purpose was to experimentally investigate the effect of the local search component of the EA-ILS hyper-heuristic on its performance. Two representative instances were selected for each problem domain for experimentation. The control hyper-heuristic was constructed by replacing LS-Seq with LS-VND in the EA-ILS hyper-heuristic. The comparative results are presented in Table 14, wherein a shaded cell means the set-up has a better objective function value than the alternative set-up in the adjacent cell. The \(\alpha\) and \(\beta\) set-ups were run in an overlapped manner such that when a single run or trial is completed on a sample instance for a set-up, the run of the next set-up on the same instance immediately follows. Moreover, both set-ups start with the same random number seed for each run throughout the entirety of the sample instances. This mechanism ensures fairness in the experiment. The meaning of the column names in Table 14 along with other important information are described as follows: The column name \(\alpha\) represents the EA-ILS hyper-heuristic with the LS-Seq procedure as the intensification module while \(\beta\) is the control hyper-heuristic with the LS-VND procedure as the intensification module. \(\alpha\_\)iter is the number of iterations covered by \(\alpha\) while solving a problem instance during a run. \(\beta\_\)iter is the number of iterations covered by \(\beta\) while solving a problem instance during a run. \(\alpha\_\)lsi is the average number of calls to local search heuristics per iteration by \(\alpha\). \(\beta\_\)lsi is the average number of calls to local search heuristics per iteration by \(\beta\). The numbers of local search heuristics on the KP, QAP, and MAC domains are 6, 2, and 3, respectively. The ofv of each run from the two set-ups were normalized to values in the range [0, 1] using the maximum and minimum ofvs over five trials completed for each sample instance to perform the [PERSON] signed rank sum test. The reported \(p\)-value was 0.2249 at a 0.05 level of significance. The obtained \(p\)-value indicates that across the entire set of 30 data points, there is no significant difference between the performances of the two experimental set-ups of the EA-ILS hyper-heuristic. This finding can be attributed to the performance of the EA-ILS hyper-heuristic with the VND style of local search in the QAP domain. It was highly competitive or even slightly better than the EA-ILS hyper-heuristic with LS-Seq in the two instances of the QAP domain. In fact, after the removal of 10 data points that corresponded to the performance in QAP0 and QAP7 instances, a \(p\)-value of **0.01962** was returned from the [PERSON] signed rank sum test. This would suggest a significant difference in the performances of the two set-ups. The sum of ranks for the entire set of data points for which the EA-ILS hyper-heuristic with LS-Seq outperformed the control algorithm of the EA-ILS hyper-heuristic with LS-VND is 291 while the sum of ranks of the opposite outcome is 173. A careful observation of the \(\alpha\_\)iter and \(\beta\_\)iter values indicates that the first set-up completes a better diversification-intensification cycle than the control set-up in the KP instances. Peradventure this is the reason for the huge difference in the performances of the two set-ups. The LS-Seq set-up was able to visit many search areas and had leverage to escape the local optima over the alternative set-up because of the invocation of local search heuristics. The local search calls per iteration did not pose a challenge for the LS-VND set-up in the QAP domain based on its performance relative to that of LS-Seq. This observation may be attributed to the low number of local search heuristics available for the problem domain.