## 4 Methodology
Thus, instead of the overall worst case of \(\mathcal{O}(\varpi_{\text{max}}*T_{p})\), we approximated this by accumulating the number of operations done for each simple heuristic from the uMH achieved in the SAHH procedure, i.e., \(\mathcal{O}(\varpi_{\text{max}}*T_{p})\approx\sum_{k=1}^{\infty}T_{p,k}\). Figure 10 displays this information as boxplots, where the effect of the problem dimensionality is evident for both experimental setups. First, it is interesting to note that Experiment 2 allows for more search steps, promoting a more refined heuristic sequence that solves a given problem. Such a fact translates into operation values more concentrated around a specific amount. This has meaningful implications in providing more confidence to the practitioner when implementing the approach proposed in this work. Although, it is not a secret that using this setup instead of the first one would have an additional computing burden. Plus, it is worth mentioning that the order of operations does not increment too dramatically, as we foresaw with the brief theoretical analysis. Likewise, as we expected, the difference between Experiments 1 and 2 (Figure 10a,b, respectively) does not constitute an abyss. Indeed, the overall value is 0.74 \(\pm\) 0.41 with a mean value of 0.70. This is due to the low computational burden that SA imposes on the HH approach. The second setup has 300 and 400 units more in \(s_{\text{max}}\) and \(\varpi_{\text{max}}\) than those for the first setup. In general, we must notice that results for non-differentiable and unimodal functions represent the most expensive procedure for both experimental setups. It is also remarkable that many of the outliers from Figure 10 are mostly situated at data liaised with differentiable (DU = 11 and 10) problems. This is an unusual combination of characteristics since problems from this category exhibit diverse behaviours. Such a fact must be a matter to be considered in further works. ## 6 Conclusions

This work proposed a new heuristic-based solver model for continuous optimisation problems. However, our proposal can be easily extended to other domains. Such a model, which we named 'unfolded' metaheuristic (uMH), comprises a heterogeneous sequence of simple heuristics. This is achieved by delegating the control mechanism in the standard metaheuristic scheme to a high-level strategy. Hence, this implies solving the Metaheuristic Composition Optimisation Problem (MCOP) to tailor a particular uMH that tackles a specific optimisation problem. We carried out a proof-of-concept by utilising the CUSTOMHyS framework, which is publicly available at [[https://github.com/jcrvz/customhys](https://github.com/jcrvz/customhys)]([https://github.com/jcrvz/customhys](https://github.com/jcrvz/customhys)), accessed on 10 May 2021. Through CUSTOMHyS we analyse 107 continuous optimisation problems and a collection of 12 population-based fixed-dimension heuristics, extracted from ten well-known metaheuristics in the literature, to search in the problem domain. Thus, we specified the unfolded metaheuristic model and implemented a Hyper-Heuristic (HH) based on Simulated Annealing (SA), SAHH in short, to solve the MCOPs. For the SAHH, we also incorporated 11 single-agent variable-dimension heuristics to search in the heuristic domain. We considered two main experimental setups. The first one allowed uMHs of up to 100 search operators, with SAHH performing up to 200 steps. The second one considered up to 500 operators and steps. In the manuscript, we refer to the number of search operators in a uMH as its cardinality, \(\varpi\). From the results, we found that our proposed approach represents a very reliable alternative, with low computing cost, for designing optimisation population-based metaheuristics that solve continuous problems. To complement this claim, we shortly summarise several insights extracted from the experiments we carried out.