## 3 The Proposed Model
### Process Involved in HBO-RVFL Technique  
At this stage, the chosen features are passed into the RVFL model to classify data. The basic framework of RVFL is generally the same as the artificial neural network that comprises hidden, output, and input layers [23]. However, the major difference between RVFL and ANN is that RVFL directly connects the output and input layers. This connection supports RVFL by an appropriate mechanism to prevent the over-fitting problems that take place in ANN. The training RVFL begins with the employment of the input data that comprise target \(y_{i}\) and sample \(x_{i}\), to the input state. Next, the output of the hidden node is computed by the subsequent formula:  
\[O_{j}\big{(}\alpha_{j}x_{i}+\beta_{j}\big{)}=\frac{1}{1+e^{-(\alpha_{j}x_{i}+ \beta_{j})}},\ \beta_{j}\in[0,\ S],\ \alpha_{j}\in[-S,\ S] \tag{9}\]  
From the above equation, \(\alpha_{j}\) represents the value of weight, which connects the hidden and input nodes. \(S\) and \(\beta_{j}\) denote the scale bias and factor, correspondingly. Then, last output is calculated by the Equation (11):  
\[Z=Fw,\ w\in R^{n+P},\ F=[F_{1},\ F_{2}] \tag{10}\]  
\[F_{1}=\left[ \begin{array}{cc}x_{11}&x_{1n}\\ \vdots&\vdots\\ x_{N1}&x_{Nn}\end{array} \right]F_{2}=\left[ \begin{array}{ccc}G_{1}\big{(} \alpha_{1}x_{1}+\beta_{1}\big{)}&\cdots&G_{P}\big{(}\alpha_{P}x_{1}+\beta_{P} \big{)}\\ \vdots&\ddots&\vdots\\ G_{1}\big{(}\alpha_{1}x_{N}+\beta_{1}\big{)}&\cdots&G_{P}\big{(}\alpha_{P}x_{N} +\beta_{P}\big{)}\end{array} \right] \tag{11}\]  
Here, \(w\) is upgraded by the subsequent equation:  
\[w=F^{\dagger}Z \tag{12}\]  
In Equation (12), \(\dagger\) indicates the Moore-Penrose pseudo-inverse. Figure 2 demonstrates the structure of RVFL technique. To optimally adjust the parameters related to the RVFL method, the HBO algorithm has been utilized. The presented algorithm is stimulated by the corporate rank hierarchy (CRH), which declares that a team could arrange in a hierarchal manner to fulfill organization goals [24]. The HBO algorithm is categorized as interaction between colleagues, interaction between subordinates, self-contribution of employees, and the immediate supervisor. In the CRH approach, the population is established as a CRH, while the heap node is established as a searching agent. The agent location of every search is upgraded by:  
\[x_{i}^{k}(t+1)=B^{k}+\gamma(2r-1)\Big{|}B^{k}-x_{i}^{k}(t)\Big{|} \tag{13}\]  
The \(k\)-th components of \(\lambda\) vector \(\overrightarrow{\lambda}\) is signified as:  
\[\lambda^{k}=2r-1 \tag{14}\]  
\(\gamma\) is evaluated by using Equation (15):  
\[\gamma=\left|2-\frac{\left(tmod\frac{t}{c}\right)}{\frac{1}{4C}}\right| \tag{15}\]  
The (C) parameter in Equation (16) controls the variation. However, this will complete in \(T\) iteration as in the following:  
\[C=T^{max}/25 \tag{16}\]  
Additionally, the interaction between colleagues is modeled. As expressed in Equation (17), the location of every agent \(\left(\overrightarrow{x_{i}}\right)\) is upgraded by randomly designated colleague \(\overrightarrow{S_{r}}\):  
\[x_{i}^{k}(t+1)= \begin{cases}S_{r}^{k}+\gamma\lambda^{k}\Big{|}S_{r}^{k}-x_{i }^{k}(t)\Big{|},&f\left(\overrightarrow{S_{r}}<f\left(\overrightarrow{x_{i} }(t)\right)\right.\\ x_{i}^{k}+\gamma\lambda^{k}\Big{|}S_{r}^{k}-x_{i}^{k}(t)\Big{|},&f\left( \overrightarrow{S_{r}}\geq f\left(\overrightarrow{x_{i}}(t)\right)\end{cases}  \tag{17}\]  
In Equation (17), the fitness of the searching agent is denoted as \(f\). Figure 2: Structure of RVFL. Further modeled is the self-contribution of all the employees, whereby the location of every agent is upgraded based on the following equation:  
\[x_{i}^{k}(t+1)=x_{i}^{k}(t) \tag{18}\]  
At last, the updating position equation has been taking place. The roulette wheel probability, \(p_{1}\), \(p_{2}\), and \(p_{3}\), are designated to balance the exploitation and exploration stages. The searching agent upgrades the location by utilizing Equation (18).