## 1 Introduction
The selection of a heuristic to apply was based on its record of successes and failures when applied to a given problem. If the combined effect of a perturbative heuristic and a local search heuristic (when applied in an iteration) leads to a new best global solution, the \"success\" count of the heuristics is incremented; otherwise, the \"failure\" count is incremented, which makes it a reinforcement learning scheme. The TSHH implemented an improving-or-equal (IE) acceptance mechanism and finished second behind the AdapHH using the F1 ranking. The hyper-heuristic outperformed other competitors in personnel scheduling (PS), PFS, and TSP and underperformed in SAT and VRP. [PERSON] et al. [23] proposed different settings of a multi-armed bandit scheme for heuristic selection, with the best version being able to only do well on VRP problems, which the authors blamed on the hyper-parameter settings. The HyFlex framework was extended in [24] by introducing three new problem domains of the knapsack problem (KP), quadratic assignment problem (QAP), and maximum-cut problem (MAC). The experimental procedure in the work pitted FS-ILS against a no-restart version of FS-ILS (NR-FS-ILS), AdapHH, evolutionary programming hyper-heuristic (EPH), a competitor in CHeSC 2011, and two other simple random procedures that differ in their acceptance mechanisms. EPH is based on the principle of evolutionary programming and co-evolution that concomitantly maintains a population of solutions with a population of low-level heuristic sequences that are applied to the solutions [11]. The AdapHH emerged as the winner on these new domains and the random procedure that accepts all moves surprisingly finished second while FS-ILS finished fifth among the six hyper-heuristics compared. In addition, the SSHH was tested on these three new problem domains [25] and its performance was compared with those of others presented for the extended HyFlex framework [24]. sequence-based selection hyper-heuristic (SSHH) and AdapHH emerged as the best two hyper-heuristics based on the experimental results. The new problem domains were used in two other works [26; 27] that tuned a memetic algorithm, but only [27] compared the proposed hyper-heuristic with others that were tested on the domains, using 15 out of the entire set of 30 benchmarking instances. This study was inspired by the inherent weaknesses exhibited by ILS hyper-heuristics on the extended HyFlex suite to design an evolutionary algorithm-based iterated local search (EA-ILS) hyper-heuristic. The following two critical points are highlighted as areas of concern for ILS hyper-heuristics. First, ILS hyper-heuristics utilizing a typical local search invocation based on VNS may not be effective when solving problems that require deep search space and are time-consuming [28]. Therefore, designing an improved local search is worth exploring [29]. Second, although hyper-heuristic methods are generally not exact, an alternative for covering a deeper search space for performance enhancement could be to design ILS-based hyper-heuristics to perturb solutions more than once before the local search invocations. This will depend on how effective these multiple perturbations can be for solving a COP. Since the perturbation strength is prime to the performance of ILS [30; 31], designing a hyper-heuristic with an option to perturb solutions more than once is very viable. The introduced hyper-heuristic algorithm works on the principles of the basic ILS and evolutionary algorithms. It uses a novel mutation operator to construct LLH sequences with the possibility of multiple perturbations that ultimately end with a local LLH search. The ILS is widely used in the literature for solving a wide range of COPs such as orienteering [32], inventory routing [33], classical knapsack [34], vehicle routing [35; 36; 37], and course timetabling [38; 39; 40]. The metaheuristic appears to be a versatile method that has been frequently combined with other optimization algorithms to solve COPs.