## 4 Methodology
In this table, we present the name, variation parameters, and tuning parameters of these simple heuristics. The variation parameters concern those that drastically alter the nature of the operator. Meanwhile, tuning parameters hone the searching process. Besides, we also obtained the selectors from the metaheuristics mentioned above. It is worth mentioning that we also dedicated some words in Appendix A for documenting the finalisers commonly utilised in MH implementation. Since we have described the problem and solution domains, we can now specify how they were employed to study the proposed model. Recall that we are studying 'unfolded' metaheuristics (uMHs) represented by heterogeneous heuristic sequences (cf. Figure 2). Thus, the number of iterations \(t_{\text{max}}\) is given by the sequence length or cardinality \(\varpi\), i.e., \(t_{\text{max}}=\varpi\). In detail, we planned the experiments using a population size (N) of 30 for each unfolded metaheuristic with two cardinality limits. The first cardinality range is between 1 and 100, and the second one between 1 and 500. We selected these values to analyse the influence over the performance of a tight or a loose imposition in the sequence length. Due to this, we allowed SOs to appear more than once in the sequence. Thus, for controlling the actions that search over the heuristic space, we implemented the well-known Simulated Annealing (SA) using the Single-agent SV heuristics documented in Table 2 and Appendix A.2.1. Particularly, we utilised an initial dimensionless temperature (\(\Theta_{0}\)) of 1.0, a minimal dimensionless temperature (\(\Theta_{\min}\)) of \(10^{-6}\), and a cooling rate (\(\delta\)) of \(10^{-3}\). A maximal number of steps (\(s_{\text{max}}\)) of 200 was set for \(\varpi_{\text{max}}=100\), and 500 steps were allowed for \(\varpi_{\text{max}}=500\). We refer henceforth to these two configurations as Experiments 1 and 2, respectively. Subsequently, to assess the performance of each uMH (say, \(\vec{h}\)) when solving a given problem, we ran each candidate \(N_{r}=50\) times and recorded the last fitness values. Then, we estimated its performance using  
\[Q(\vec{h})\approx-(\text{med}+\text{iqr})(\{\forall\ \vec{x}_{s,r}\in X_{s}|f( \vec{x}_{s,r})\}), \tag{5}\] \begin{table}
\begin{tabular}{c c c} \hline \multicolumn{2}{c}{**Role**} \\ \hline \multicolumn{2}{c}{**Solver**} & \multicolumn{1}{c}{**Problem**} \\ \hline \multirow{4}{*}{High} & Search Space: PF Heuristics, \(H_{PF}\subseteq\mathfrak{H}^{3}\) & Domain: Heuristics, \(H_{PF}\subseteq\mathfrak{H}^{\varpi}\) \\  & Individual: Metaheuristic, & Individual: Sequence, \(\vec{h}=(h_{1},\dots,h_{\varpi})^{\intercal}\in H_{PF}\) \\  & \(\text{MH}_{\varpi}\triangleq\langle\eta_{i},\eta_{\varpi},\eta_{f}\rangle\in H _{SV}\) & Image: \(Q(\vec{h}|\vec{x}):H\times\vec{x}\mapsto\mathbb{R}\) \\  & Procedure: \((\eta_{f}(\eta_{\varpi})\circ\eta_{i})\{(H_{PF},Q)\}\) & Objective: Maximisation, \(\max_{\vec{h}}Q(\vec{h}|\vec{x},f)\) \\ \hline \multirow{4}{*}{Low} & Search Space: Continuous, \(\vec{x}\subseteq\mathbb{R}^{D}\) & Domain: Continuous, \(\vec{x}\subseteq\mathbb{R}^{D}\) \\  & Individual: Unfolded metaheuristic, & Individual: Position, \(\vec{x}=(x_{1},\dots,x_{D})^{\intercal}\in\vec{x}\) \\ \cline{1-1}  & \(\vec{h}=(h_{1},\dots,h_{\varpi})^{\intercal}\in H_{PF}\) & Image: Cost function, \(f(\vec{x}):\vec{x}\mapsto\mathbb{R}\) \\ \cline{1-1}  & Procedure: \((h_{\varpi}\circ\dots\circ h_{1})\{(\vec{x},f)\}\) & Objective: Minimisation, \(\min_{\vec{x}}f(\vec{x})\) \\ \hline \end{tabular}
\end{table} 
Table 1: Description of the domains utilised in this work according to their level of abstraction and role. PF and SV stand Population-based Fixed-dimension and Single-agent Variable-dimension heuristics. where med and iqr are the median and interquartile range operators, respectively, applied to the fitness values \(f(\vec{x}_{*,r})\). The symbol '\(\approx\)' indicates that the estimation depends on the \(N_{r}\) samples \(X_{*}\) obtained from a stochastic process.