## 4 Methodology
First, we noticed that SAHH manages to find an unfolded metaheuristic, which deals with the optimisation problem, no matter the imposed design conditions. Naturally, some conditions affect the performance of the outcoming solvers. For example, the cardinality range does not directly affect the uMH performance, but when this range is relaxed, the uMH commonly renders more precise performance values. However, this has the drawback of increasing time complexity (or the number of operations) as a trade-off for a greater chance of balanced exploration and exploitation features. Besides, we found some leads indicating that the dimensionality affects the metaheuristic and hyper-heuristic iterations (i.e., cardinality and steps, respectively) on a scale related to the problem characteristics. The influence of dimensionality over problem hardness acts like a catalyst that amplifies the inherent difficulty given by its characteristics. In such cases, we noted that uMHs with greater cardinality only slightly outperform those with lower \(\varpi\) values, so we must recommend using the low-cost ones in practical implementations. Nevertheless, we have not detected an abysmal difference between the unfolded metaheuristics obtained from the studied setups in the number of operations, i.e., about 0.70 of the median value. This is a great feature due to the heuristic nature of the solvers that our approach generates. Figure 10: Order of the numerical operations carried out for designing unfolded metaheuristics when solving problem domains with different characteristics and dimensionalities. (**a**) Experiment 1. (**b**) Experiment 2. We also studied the nature of the search operators that are automatically selected by SAHH when building uMHs. We remark that SAHH often chooses operators from the Genetic Crossover and Random Search families for two-dimensional problems. However, their frequency seems to be attenuated when increasing the number of dimensions. A similar case was observed with simple heuristics of the Central Force nature, but starting with 5D problems and an evident greater dominance. Conversely, we regard operators from the Gravitational Search and Particle Swarm families correspond to the less frequent ones at the 2D mark, although they become relevant during the dimensionality increment. We attribute this effect to the nature of these families, related to multi-probes intelligent interactions, which performs better on broader search domains. In the end, for the greatest dimensionality, we observed a pretty uniform distribution from almost all the families of search operators. Therefore, we infer that operators slightly sophisticated to the random ones are enough to fulfil the solver requirement for few dimensions. More nature-diverse operators are needed for many variables. Lastly, we carried out a similar experiment using the metaheuristics selected for extracting the search operators used to construct the heuristic space employed by SAHH; we called them basic MHs. We found that our uMHs surmount the average performance of at least one basic metaheuristic for the same problem domain. Such a fact has a tremendous repercussion in the context of the No-Free-Lunch (NFL) theorem, mainly because the practitioner does not have to know which is the excellent metaheuristic for a given problem. Instead, s/he only has to use our approach, and it will indeed find a good one with some particular requirements. Bear in mind that this work does not pretend to violate the NFL theorem. Instead, we are using it in our favour to propose suitable solvers. To the best of our knowledge, this unfolded metaheuristic model has not been previously proposed in the literature. According to our results, it is a model worth considering in practical implementations because it seems to be a very reliable and low-cost computing approach for solving optimisation problems. We know that our model is not a panacea. There are several issues to deal with for further understanding and improvement; some are now commented.