## 3 Proposed Methodology
### Feature Selection Using Hybrid Genetic Fire Hawker Optimizer (FHO)  
Feature selection helps reduce false alarms, simplify data, improve ML and DL approach detection rates, remove redundant data, and simplify computations. This section uses a Hybrid Genetic Fire Hawker Optimizer to select the relevant features. By considering starting and spreading fires and obtaining prey, the FHO algorithm resembles the hunting methods of fire hawks [25]. Several potential solutions \((Y)\) were attained depending on the position of fire hawks and their prey. A random initialization mechanism was utilized to create the starting locations of each vector in the search space. The mathematical representation of the random initialization mechanism is illustrated in Equations (3) and (4):  
\[Y=\left[ \begin{array}{c}Y_{1}\\ Y_{2}\\ \vdots\\ Y_{p}\\ \vdots\\ Y_{M}\end{array} \right]=\left[ \begin{array}{c}y_{1}^{1}y_{1}^{2}\cdots y_{1}^ {q}\cdots y_{1}^{c}\\ y_{2}^{1}y_{2}^{2}\cdots y_{2}^{q}\cdots y_{2}^{c}\\ \vdots\vdots\ddots\vdots\\ y_{M}^{1}y_{M}^{2}\cdots y_{M}^{j}\cdots y_{M}^{c}\\ \end{array} \right],\left\{ \begin{array}{c}p=1,2,3,\ldots,M.\\ q=1,2,3,\ldots,c.\\ \end{array} \right. \tag{3}\]  
\[y_{p}^{q}(0)=y_{p,min}\]  
Here, the number of solution candidates is denoted as \(N\). The candidate solution of the \(i\)-th search space is represented as \(Y_{i}\). Here, \(d\) and \(y_{i}^{j}(0)\) denote the dimension of the problem under consideration and the initial place of the solution candidate. For the \(p\)-th solution candidate, the maximum and minimum values of \(q\)-th decision variables are \(y_{i}^{l}\), \(y_{i,min}^{l}\) and \(y_{i,max}^{j}\), respectively. The fire hawks initially disperse flames throughout the search area, which is also seen as the most efficient global solution. The mathematical representations for these features are illustrated in Equations (5) and (6):  
\[PR=\left[ \begin{array}{c}PR_{1}\\ \vdots\\ p_{R_{1}}\\ \vdots\\ \vdots\\ p_{R_{n}}\end{array} \right],l=1,2,\ldots, \tag{5}\]  
\[FH=\left[ \begin{array}{c}FH_{1}\\ FH_{2}\\ \vdots\\ FH_{c}\\ \vdots\\ FH_{m}\end{array} \right],c=1,2,\ldots, \tag{6}\]  
Here, \(FH_{c}\) denotes the \(c\)-th fire hawk in a complete search space. The \(l\)-th prey in the search space is indicated as \(PR_{l}\). The prey is denoted as \(PR\). The distance between fire hawks and their prey was calculated in Equation (7):  
\[D_{l}^{c}=\sqrt{\left(z_{2}-z_{1}\right)^{2}+\left(x_{2}-x_{1}\right)^{2}}, \left\{ \begin{array}{c}c=1,2,3,\ldots,p\\ l=1,2,3,\ldots,q\end{array} \right.. \tag{7}\]  
Here, the total number of fire hawks and preys is represented as \(p\) and \(q\). The total distance calculated between prey and fire hawk is denoted as \(D_{l}^{c}\). Both of its positions in the search space are presented as \((z_{2},x_{2})\) and \((z_{1},x_{1})\). The group of fire hawks was identified by utilizing the nearby prey in the surroundings. Then, fire hawks gather hot coals to initiate the fire in a particular space. Both actions might be applied in the FHO primary search loop, because some birds use a flaming stick that belongs to a different fire hawk's territory. This is illustrated in Equation (8):  
\[FH_{c}^{new}=FH_{c}+(r_{1}\times GB-r_{2}\times FH_{Near}),c=1,2,\ldots,n \tag{8}\]  
Here, the global solution is denoted as \(GB\). The position vector of \(c\)-th fire hawks is represented as \(FH_{c}^{new}\). The random, uniformly distributed numbers are represented as \(r_{1}\) and \(r_{2}\). In the search area, among many fire hawks, \(FH_{Near}\) represents one. The movement of prey during each fire provides the information for the algorithm's subsequent step. A key aspect of animal behavior is assumed to be the hawk's areas. The mathematical representation of updating a position is expressed in Equation (9):  
\[PR_{w}^{new}=PR_{w}+(r_{3}\times FH_{c}-r_{4}\times SP_{c}),\left\{ \begin{array} []{c}c=1,2,\ldots,n.\\ w=1,2,\ldots,r.\end{array} \right. \tag{9}\]  
where \(PR_{w}^{new}\) is denoted as the actual position vector of the \(w\)-th prey.