## 1 Introduction  
Hyper-heuristics are search methodologies for solving numerous forms of combinatorial optimization problems (COPs) in routing applications [1; 2], scheduling [3; 4], machine learning [5; 6], generation of solvers [7], and software engineering [8; 9; 10]. They have been applied to several other application domains of combinatorial optimization such as university examination timetabling, university course timetabling, and school timetabling problems [11]. Due to the countless peculiarities and inherent complexity of the different forms of optimization problems, a customized algorithm usually fails to generalize well. Hence, the impetus for studying hyper-heuristics over heuristics and metaheuristics is to address the problem of generality that hyper-heuristics provide across different forms of optimization problems [12]. Meta-learning for offline learning of heuristic sequences was recently described for solving capacitated vehicle routing and graph coloring problems [13]. The study [14] proposed a novel mechanism to create an effective recombination procedure for sub-trees in a genetic programming hyper-heuristic to solve the job-shop scheduling problem. A fuzzy logic-based method for the selection of low-level heuristics was described to solve many instances of the 0/1 knapsack problem [15]. A genetic programming-based hyper-heuristic was described for solving multiple tasks within a dynamic environment [16]. The ability of a generative hyper-heuristic underpinned by an artificial neural network was introduced for creating customized metaheuristics in continuous domains [17]. The study in [18] proposed the use of a double deep Q-network (DDQN) for generating a constructive hyper-heuristic for COPs with uncertainties. Hyper-heuristics can broadly be classified into selection and generation categories. Selection is employed to automatically control the use of low-level heuristics (LLHs) while generation is used to generate new LHHs from the building blocks of previous ones [12]. Manifold hyper-heuristics have been proposed in the literature, but a particular set of them have been developed and their performances benchmarked against others within the hyper-heuristics flexible framework (HyFlex) [19]. The HyFlex framework was initially used for the CHeSC 2011 competition where twenty algorithms were tested and their performances compared on six problem domains. The AdapHH hyper-heuristic [20] emerged as the winner of the competition after obtaining the highest rank in three domains of Boolean satisfiability (SAT), bin packing (BP), and the traveling salesman problem (TSP). The framework eventually became useful for benchmarking the performance of a newly proposed hyper-heuristic. The author of a newly proposed hyper-heuristic algorithm would conventionally compare its performance with the original 20 CHeSC entries. The fair-share iterated local search (FS-ILS) hyper-heuristic utilized a speed-proportional selection scheme (SpeedNew) as the heuristic selection mechanism and accept probabilistic worse (APW) as the solution acceptance mechanism [21]. It selects from a pool of perturbative heuristics during the perturbation phase of the iterated local search (ILS) It applies the local search heuristics in a variable neighborhood descent (VND) fashion on the resultant solution from the perturbation phase until the solution can no longer be improved. The VND is a variant of the variable neighborhood search (VNS) metaheuristic that deterministically explores the neighborhoods in a search space. The FS-ILS outperformed the 20 CHeSC entries in the HyFlex framework by obtaining the highest scores on the Boolean satisfiability (SAT), permutation flow-shop (PFS), and vehicle routing problem (VRP) domains. A Thompson sampling hyper-heuristic (TSHH) was proposed in [22] and uses the Thompson sampling learning algorithm to respectively select perturbative and local search heuristics during the perturbation and intensification phases of the ILS.