## 1 Introduction
In [17], [PERSON] tacked the same problem by creating a hyper-heuristic based on FRRMAB [8] and considering the same set of LLHs. Among all these versions, the Choice Function applied together with NSGA-II ([14] version) obtained the best results. Only a few studies focus on online learning hyper-heuristics selecting/mixing multi-objective evolutionary algorithms (MOEAs) for solving multi-objective optimization problems. Among them, [PERSON] et al. [6] proposed the Choice Function Hyper-Heuristic (HHCF) which is an interesting approach employing different quality indicators to evaluate a set of LLHs. In this approach, each LLH executes for some generations, then the resulting population is evaluated based on \(m\) different quality indicators, generating a table \(n\times m\), where \(n\) is the number of LLHs, and \(m\) is the number of quality indicators. Following that, a second table containing the rankings is generated, which is used as input to a choice mathematical function responsible for determining which LLH should execute next. This approach was tested using the Walking Fish Group (WFG) benchmark [18] and on a single real-world problem: the Crashworthiness problem [19]. The authors used the algorithms NSGAII [20], SPEA2 [21], and MOGA [22] as LLHs, and compared their results to Amalgam [23] and to all single MOEAs. The experimental results indicated the success of HHCF outperforming them all. In [24], [PERSON] et al. replaced MOGA by IBEA [25], and evaluated the approach on solving another real-world problem: Wind Farm layout optimization [26]. Although this hyper-heuristic yielded good results, the use of a two-level ranking approach was not justified properly and there was no theoretical background to it. The following studies have employed well-established computational methods within the design of new hyper-heuristics. [PERSON] et al. [3] proposed MOHH-RILA, an online selection hyper-heuristic treating the problem as a learning automata, where the automata action is the selection of an LLH from a set of MOEAs. As _reward_ and _penalty_, they used Hypervolume and Spread indicators (the last in case of ties). Thus, this study can be classified as a Reinforcement Learning based online selection hyper-heuristic. The authors employed IBEA, SPEA2, and NSGAII as LLHs to find solutions for the WFG and DTLZ [27] benchmarks and variants of the crashworthiness problem. The results showed that this approach outperformed HHCF, making it the state-of-the-art online selection hyper-heuristic for multi-objective optimization. [PERSON] et al. [28; 29] proposed the Multi-Objective Agent-Based Hyper-Heuristic (MOABHH), an online selection hyper-heuristic enabling the best performing LLH to have a greater share of the new solutions/offspring. They designed this HH as a multi-agent system by treating all LLH and quality indicators as agents and employed Social Choice Theory [30] voting methods in order to summarize quality indicators preferences for the participation assignment mechanism. In the first study [28], they employed NSGAII, IBEA, and SPEA2 as LLHs and applied MOABHH to the WFG Suite. GDE3 [31] was additionally included within the LLH set in [32]. In the latter [29], they evaluated how MOABHH performs on real-world problems, including the Crashworthiness, Water [33], Car Side Impact [34], and Machining [35]. In [36], the authors evaluated the proposed approach considering different voting criterion considering these four real-world problems and the multi-objective travel salesperson problem [37]. This proposed HH outperformed each individual MOEA and random choice hyper-heuristic; however, MOABHH was not compared to any of the other state-of-the-art hyper-heuristics. Hence, the goal of this paper is to perform a thorough investigation of four reportedly top-ranking hyper-heuristics across an extensive set of problems: (i) MOABHH, which achieved promising results in a previous study; (ii) two variants of MOHH-RILA (HHLA and HHRL); and (iii) HHCF.