## 3 The Proposed Model
### Parameter Tuning Using the MFO Algorithm  
For the hyperparameter tuning process, the MFO algorithm was used in this study. The major idea of this method is based on the flight and mating behaviors of the mayfly (MF) [24]. It integrates the benefits of the firefly algorithm (FA), particle swarm optimization (PSO), and the genetic algorithm (GA). Initially, the MFO algorithm generates an MF population encompassing males and females. The existing velocity and location of _i-th_ MFs are two \(n\)-dimensional vectors; they are correspondingly represented as \(v_{i}=(v_{i1},v_{i2}\dots,v_{in})\) and \(x_{i}=(x_{i1},x_{i2}\dots,x_{in})\). Every MF adapts its location based on its individual best \((pbest)\) location and the optimal \((gbest)\) location originated by the entire MF swarm. Male MFs cluster together, which recommends that the position is upgraded on the basis of social and personal experience. \(x_{i}^{t}\) denotes the current location of _i-th_ male MFs at \(t\) iteration. Assume that \(x_{i}^{t}\) denotes the existing location of _i-th_ MFs at \(t\) iteration; the location is upgraded by adding velocity \(v_{i}^{t}\), and it is shown below:  
\[x_{i}^{t+1}=x_{i}^{t}+v_{i}^{t}. \tag{16}\]  
Assume that male MFs often implement their mating dance not distant from the water, and it is updated in the following equation:  
\[v_{i\bar{j}}^{t+1}=gv_{i\bar{j}}^{t}+a_{1}e^{-\beta r_{p}^{2}}\left(pbest_{i \bar{j}}-x_{i\bar{j}}^{t}\right)+a_{2}e^{-\beta r_{\bar{j}}^{2}}\left(gbest_{ j}-x_{i\bar{j}}^{t}\right), \tag{17}\]  
In Equation (17), \(\beta\) refers to the visibility coefficient, \(a_{1}\) and \(a_{2}\), determined by the positive constant that represents the attraction. \(pbest_{i\bar{j}}\) indicates the optimal location attained using the _i-th_ male MFs in \(j\) dimension. \(r_{p}\) and \(r_{\bar{g}}\) indicate the Euclidean distance between \(\chi_{j}\) and \(pbest_{j}\), and between \(\chi_{j}\) and \(gbest\), respectively. The gravity coefficient is denoted as \(g\), which is a fixed number among [0, 1], or it is steadily lowered over the iteration, as follows:  
\[g=g_{\text{ max }}-\frac{g_{\text{ max }}-g_{\text{ min }}}{iter_{\text{ max }}}\times iter, \tag{18}\]  
In Equation (18), \(g_{\text{ max }}\) and \(g_{\text{ min }}\) correspondingly embody the minimum and maximum weights. The current and the overall number of iterations are represented as \(iter\) and \(ter_{\text{ max }}\)/. The personal optimal location \(pbest_{i}\) at iteration \(t+1\) is defined as follows:  
\[pbest_{i}=\left\{ \begin{array}{l}x_{i}^{t+1},iff\left(x_{i}^{t+1}\right)<f (pbest_{i})\\ same\text{ as }before,\text{ }otherwise.\end{array} \right. \tag{19}\]  
The finest male MF continues implementing up and down movements at distinct velocities, and this equation is shown below:  
\[v_{ij}^{t+1}=v_{ij}^{t}+d\times r, \tag{20}\]  
In Equation (20), the mating dance coefficient can be represented as \(d\), and \(r\) denotes an arbitrary number within [\(-\)1, 1]. Female MFs do not cluster together, but they move to male MFs. \(y_{i}^{t}\) denotes the current location of the \(i\)-\(th\) female MF at \(t\) iteration. The change of \(i\)-\(th\) female MF in location is evaluated by Equation (21):  
\[y_{i}^{t+1}=y_{i}^{t}+v_{i}^{t}. \tag{21}\]  
In the MFO algorithm, female and male MFs with similar individual fitness rankings attract one another, and the female MF's location changes in terms of the position of the male MF with a similar ranking, as follows:  
\[v_{ij}^{t+1}=\left\{ \begin{array}{l}gv_{ij}^{t}+a_{2}e^{-\beta v_{mf}^{2}} \left(x_{ij}^{t}-y_{ij}^{t}\right),\text{ }if\text{ }f(y_{i})>f(X_{i})\\ gv_{ij}^{t}+fl\times r,\text{ }if\text{ }f(y_{i})\leq f(xi)\text{ },\end{array} \right. \tag{22}\]  
where \(v_{ij}^{t}\) and \(y_{ij}^{t}\) denote the \(i\)-\(th\) female MF's velocity and location in \(j\) dimension at \(t\) iteration. \(a_{2}\) and \(\beta\) indicate the attraction constant and visibility coefficient, correspondingly.