## 4 Methodology
Plus, the minus sign in (5) is because HH deals with a maximisation problem (cf. Definition 9), but the objective function \(f(\vec{x})\), at the low-level domain, corresponds to a minimisation problem (cf. Definition 1). We chose this formula mainly because the median and the interquartile range are better descriptors in the presence of outliers. We also based this selection on several a priori results from previous works [31; 44]. Lastly, and for the sake of clarity, we summarised the procedures performed for each problem in Pseudocode 1. In this, we refer to the SV heuristics as actions when they are described along with the PF heuristics to avoid confusion. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Type** & **Simple Heuristic** & **Variation Parameters * & **Tuning Parameters** \\ \hline \multirow{6}{*}{_N_} & Add & – & \(i\sim\mathcal{U}\{1,\varpi+1\}\) \\  & Add Many & – & \(\vartheta\sim\mathcal{U}\{1,\varpi_{u}-\varpi\}\) \\  & Remove & – & \(i\sim\mathcal{U}\{1,\varpi\}\) \\  & Remove Many & – & \(\vartheta\sim\mathcal{U}\{1,\varpi-\varpi_{l}\}\) \\  & Shift & – & \(i\sim\mathcal{U}\{1,\varpi\}\) \\  & Shift Locally & – & \(e\in\mathbb{R}_{++}\), \(\mathcal{D}:\mathfrak{S}\times\mathfrak{S}\mapsto\mathbb{R}_{+}\) \\  & Swap & – & \(i,j\sim\mathcal{U}\{1,\varpi\}\) \\  & Restart & – & – \\  & Mirror & – & – \\  & Roll & – & – \\  & Roll Many & – & \(k\sim\mathcal{U}\{1,\varpi-1\}\) \\ \hline \multirow{6}{*}{_N_} & Random Sample (RX) \({}^{\ddagger}\) & \(\vec{r}\
i r_{i}\sim\mathcal{U}(-1,1)\) & \(\alpha\in[0,1]\) \\  & Random Search (RS) & \(\vec{r}\
i r_{i}\sim\mathcal{U}(-1,1)\) & \(\alpha\in[0,1]\) \\  & Local Random Walk (RW) & \(\vec{r}\
i r_{i}\sim\mathcal{U}(0,1)\) & \(\alpha\in[0,1]\), \(p\in[0,1]\) \\  & Random Flight (RF) & \(\vec{r}\
i r_{i}\sim\mathcal{L}(1.5)\) & \(\alpha\in[0,1]\) \\  & Genetic Crossover (GC) & _Pairing scheme_, \({}^{\ddagger}\) & \(m_{p}\in[0,1]\) \\  & _Crossover mechanism_\({}^{\lx@sectionsign}\) & \\  & Genetic Mutation (GM) & \(\vec{r}\
i r_{i}\sim\mathcal{U}(-1,1)\) & \(\alpha\in[0,1]\), \(p_{e}\in[0,1]\), \(p_{m}\in[0,1]\) \\  & Differential Mutation (DM) & _Mutation scheme_ & \(M\in\{1,2,3\}\), \(\alpha_{m}\in[0,3]\)\(\forall\)\(m\in\{0,M\}\) \\  & Particle Swarm Dynamic (PS) & Velocity approach, & \(\alpha_{0}\in[0,1]\), \(\phi_{1},\phi_{2}\in[0,4]\), \(\kappa\in[0,1]\) \\  & & \(\vec{r}_{i}\
i r_{i,j}\sim\mathcal{U}(0,1)\)\(\forall i\in\{1,2\}\) \\  & Firefly Dynamic (FD) & \(\vec{r}\
i r_{i}\sim\mathcal{U}(-0.5,0.5)\) & \(\alpha_{0},\alpha_{1}\in[0,1]\), \(\alpha_{2}\in[0,1000]\) \\  & Spiral Dynamic (SD) & – & \(r_{0}\in[0,1]\), \(\theta\in[0^{\circ},360^{\circ}]\), \(\sigma_{r}\in[0,1]\) \\  & Central Force (CF) & – & \(\alpha_{0},\alpha_{1}\in[0,0.01]\), \(\alpha_{2}\in[1,2]\) \\  & Gravitational Search (GS) & – & \(\alpha_{0}\in[0,1]\), \(\alpha_{1}\in[0,0.1]\) \\ \hline \multirow{6}{*}{_N_} & Direct & – & – \\  & Greedy & – & – \\  & Probabilistic & – & \(p_{s}\in[0,1]\) \\  & Metropolis & – & \(k_{B}\in\mathbb{R}_{+}\), \(\Theta(t):Z_{+}\mapsto\mathbb{R}_{+}\) \\ \hline \hline \end{tabular}  
* An alternative distribution function can be implemented instead of the default one, for example, the uniform \(\mathcal{U}(0,1)\), normal standard \(\mathcal{N}(0,1)\), and symmetric Lévy stable \(\mathcal{L}(1.5)\) ones. \({}^{\ddagger}\) This simple heuristic is also used as initialiser. \({}^{\ddagger}\) Available schema: random, rank weighting, roulette wheel, and tournament pairing. Tournament pairing requires two additional parameters such as \(M_{T}\in\{1,2,3\}\) and \(p_{T}\in[0,1]\), \({}^{\lx@sectionsign}\) Possible mechanisms: single-point, two-points, uniform, blend, and linear crossover. Linear crossover requires two additional parameters such as \(\beta_{1},\beta_{2}\in\mathbb{R}\).  
\end{table} 
Table 2: Ten widespread metaheuristics segregated into their search operators. Parameter data are selected based on customary values from the literature.