## 5 Conclusions  
In this study, we investigated reportedly the top four online selection hyper-heuristics across eighteen real-world optimization problems. The hyper-heuristics controlled and mixed a set of five low-level MOEAs to produce improved trade-off solutions. The performance of algorithms was also evaluated with a larger set of MOEAs. To the best of the authors' knowledge, this work is the first one which addresses the problem of using real-world problem instances for cross-domain performance evaluation of hyper-heuristics. In particular, we addressed in this paper the following issues: (i) an evaluation of four state-of-the-art online hyper-heuristics (MOABHH, HHRL, HHLA, and HHCF) using exclusively real-world problems; (ii) a harder selection task for these four hyper-heuristics by increasing the number of Low-Level heuristics used: in our work, we used five LLHs, whereas, in previous publications, the number of LLHs used were 3 or 4; (iii) a cross-domain tested formed by eighteen real-world optimization problems (presented in Table 1) in order to evaluate multi-objective hyper-heuristics, which gives a more realistic overview of their performance. As expected, the empirical results showed that individual MOEAs deliver different performances on different problems, making those real-world problem instances very useful for cross-domain performance evaluation of hyper-heuristics. Moreover, our results showed that hyper-heuristics have a better cross-domain performance than single meta-heuristics. This means that, when a new multi-objective optimization problem must be solved, hyper-heuristics are excellent candidates, reducing the user's effort to run repeatedly several meta-heuristics with different parameters settings in order to get a solution. In particular, MOABHH turned out to be the best algorithm delivering the best overall cross-domain performance, beating the other state-of-the-art hyper-heuristics with respect to two quality indicators: IGD+ and Hypervolume. As future work, these hyper-heuristics will be studied across various applications in the discrete multi-objective optimization domain, such as Search-Based Software Engineering Problems [78] and exploring the potential of these algorithms on helping to improve the current pandemic, in terms of diagnosis and treatment [79] and drug discovery [80]. Many objective problems also impose a challenge for researchers and practitioners: some many-objective approaches were recently proposed in the literature. Another research direction would be to study the performance of the top-performing online learning selection hyper-heuristics across problems with more than eight objectives, varying their LLHs. **Author Contributions:** Conceptualization: all authors; Formalization, implementation and experiments: V.R.d.C. ; Supervision: [PERSON] and J.S.S. ; Writing and proofreading the paper: all authors. All authors have read and agreed to the published version of the manuscript. **Funding:** This study was partially supported by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior--Brasil (CAPES)--grant code 001. [PERSON] was also supported by CNPq, Brazil, Grant No. 140974/2016-4. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** MOABHH source code can be found in [[https://github.com/vinixna/MOABHH](https://github.com/vinixna/MOABHH)]([https://github.com/vinixna/MOABHH](https://github.com/vinixna/MOABHH)). HHRL, HHLA, and HHCF code can be found in [[https://github.com/vinixnan/MO](https://github.com/vinixnan/MO)]([https://github.com/vinixnan/MO](https://github.com/vinixnan/MO)) HH-LARILA-Real. All employed problems can be found in [[https://github.com/vinixnan/jMetalHy](https://github.com/vinixnan/jMetalHy)]([https://github.com/vinixnan/jMetalHy](https://github.com/vinixnan/jMetalHy)) perHeuristicHelper, all accessed on 6 August 2021. **Acknowledgments:** We thank [PERSON] by providing MOHH-RILA and mIBEA code.