## 5 Conclusions  
The evolutionary algorithm-based iterated local search (EA-ILS) hyper-heuristic developed in this study is a highly effective tool for solving COPs. Hyper-heuristics are search methodologies for solving numerous forms of computational search problems with manifold applications in complex social problems affecting humanity. The EA-ILS hyper-heuristic recorded impressive performance when compared to the competitive hyper-heuristics for solving the QAP domain. It has obtained the best median ofv across several problem instances. The overall performance consolidates the observation that the EA-ILS hyper-heuristic obtained the best median ofv in 27 out of the available 30 instances across three supplementary problem domains. The reason that the EA-ILS hyper-heuristic generally obtained the best performance against FS-ILS and NR-FS-ILS is explained as follows: The algorithm has the potential to pair perturbative LLHs when it is necessary. However, FS-ILS and NR-FS-ILS lack the feature of pairing two heuristics to visit a deeper search space because they are designed to operate based on the traditional perturbative LLH plus local search LLHs obtained in a typical ILS-based implementation. The EA-ILS hyper-heuristic utilizes an evolutionary algorithm to automatically learn sequences of perturbative LLHs with the capability of pairing two heuristics for a deeper solution space search. The EA-ILS hyper-heuristic has been presented in this paper as a high-performance tool for solving COPs with a focus on knapsack, quadratic assignment, and maximum-cut problems. The EA-ILS hyper-heuristic has a different local search module that automatically learns the promising sequences of local search heuristics during the intensification phase of the algorithm. This study has made significant contributions to the existing discipline  
Figure 8: Analysis of two KP and two MAC instances. of combinatorial optimization and achieved the purpose of designing a hyper-heuristic for performance improvement. The extension of the existing ILS framework has been effective considering the dominating performance that the EA-ILS hyper-heuristic had over the existing hyper-heuristics according to the experimental results in QAP, KP, and MAC instances. The implementation of the EA-ILS hyper-heuristic has been able to correct the weaknesses of the ILS-based methods in the extended HyFlex domains by performing consecutive perturbations when necessary and utilizing a faster local search procedure, especially for problem domains such as personnel scheduling with slow heuristics. The EA-ILS hyper-heuristic did not completely dominate across the instances of HyFlex v1.0 but was able to outperform the FS-ILS hyper-heuristic across the six problem domains. In addition, it ranked ahead of the TS-ILS hyper-heuristic in the problem domains of PS and PFS in terms of effectiveness. Reviewing the performance of the EA-ILS hyper-heuristic in the initial problem domains of HyFlex, it is evident that it struggled to quickly evolve effective perturbative heuristics for some instances. Some domains where the EA-ILS hyper-heuristic struggled with evolving effective heuristic sequences include SAT, especially in SAT5 and SAT10, and TSP, especially in the TSP8 instance. This is because of the large amount time it takes the LLH to finish its operation on the TSP8 instance, while for the other instances, it could be the result of extreme criteria used for allowing an operation sequence into an archive. This backdrop opens up the need for more research efforts on the EA-ILS hyper-heuristic. A possible area of improvement could be to combine multiple criteria for archive entries, using the acceptance of solutions with the improvement of the best global solution instead of only the latter as employed in this study. Although the EA-ILS hyper-heuristic was competitive in both HyFlex 1.0 and HyFlex 2.0 problem domains, further improvement can be realized by combining an evolutionary algorithm to create heuristic sequences with effective selection mechanisms.