# Red Fox Optimizer with Data-Science-Enabled Microarray Gene Expression Classification Model
## 3 The Proposed Model
### Design of RFO-Based Feature Selection Approach  
During the process of feature selection, the RFO-FS model was executed and the optimum set of features was chosen. A new metaheuristic approach was determined, which was named the RFO approach, and was based on the hunting processes of red foxes. Initially, the red foxes seek food in territories [18]. This can be modelled as an exploration term for global search. Next, they move over the territory to get close to their prey before attacking. This stage can be modelled as an exploitation term for local search. The process was initiated by a constant value of random candidates; each one determines a point, where \(\overline{x}=(x_{0},x_{1},\ \ldots,x_{n-1})\) and \(n\) defines a coordinate. For discriminating every fox \(\overline{x}^{i}\) in iteration \(t\), where \(i\) indicates the fox number in the population, we introduce the notation \(\left(\overline{x}_{j}^{i}\right)^{t}\), in which \(i\) describes the coordinate as the solution space dimension. Based on \(\ f\in\mathbb{R}^{n}\), the criterion function of the \(n\) variable depends on the dimension of the searching space, and the notation \(\left(\overline{x}\right)^{(i)}=\left[\left(\overline{x}_{0}\right)^{(i)}, \ \left(\overline{x}_{1}\right)^{(i)},\ \left(\overline{x}_{n-1}\right)^{(i)}\right]\) indicates the point in the space \(\left[a,\ b\right]^{n}\) in which \(a,b\in\mathbb{R}\). Then, \(\left(\overline{x}\right)^{(i)}\) is the optimum solution when the value of function \(f(\left(\overline{x}\right)^{(i)})\) represents a global optimal on \(\left[a,b\right]\). The outcomes of the estimated function by the candidate are sorted initially according to fitness condition, and for \(\left(\overline{x}^{best}\right)^{t}\), the square of Euclidean distance is estimated for the candidate in the following:  
\[D(\left(\left(\overline{x}\right)^{(i)}\right)^{t},\left(\left(\overline{x} \right)^{best}\right)^{t})=\sqrt{\left\|\left(\left(\overline{x}\right)^{(i) }\right)^{t}-\left(\left(\overline{x}\right)^{best}\right)^{t}\right\|} \tag{2}\]  
and the candidate moves towards the optimal population as:  
\[\left(\left(\overline{x}\right)^{(i)}\right)^{t}=\left(\left(\overline{x} \right)^{(i)}\right)^{t}+\alpha\times sgn\left(\left(\left(\left(\overline{x} \right)^{best}\right)^{t}-\left(\overline{x}\right)^{(i)}\right)^{t}\right) \tag{3}\]  
where \(\alpha\) defines an arbitrary number in which \(\in\left(0,\ D(\left(\overline{x}\right)^{best}\right)^{\epsilon},\left( \left(\overline{x}\right)^{best}\right)^{t}\right)\). In the RFO approach, movements and observations delude prey when hunting in a local searching phase. For simulating the probability of a fox approaching the prey, an arbitrary number \(\gamma\in\left[0,\ 1\right]\) set in the iteration for each candidate can be used. \[\left\{ \begin{array}{ll}\mbox{\it move\;oser\;if}&\gamma>3/4\\ \mbox{\it stay\;and\;hile\;if}&\gamma\leq 3/4\end{array} \right. \tag{4}\]  
Figure 2 depicts the steps involved in RFO. The radius comprises \(a\) as an arbitrary number within 0 and 0.2, and \(\varphi_{0}\) denotes an arbitrary number within 0 and 2\(\pi\) which defines the fox observation angle:  
\[r=\left\{ \begin{array}{ll}a\times\ \sin\left(\varphi_{0}\right)/\varphi_{0}& \mbox{\it if}\ \varphi_{0}\
eq 0\\ \beta&\mbox{\it if}\ \varphi_{0}=0\end{array} \right. \tag{5}\]  
\(\beta\) represents an arbitrary number within 0 and 1. The approaching method of the fox was modelled as follows:\[\left\{