## 3 Network Model and Problem Formulation
### Energy Estimation for Node Coverage Optimization  
In the proposed system, the Euclidean distance is used to compute the distance between the sensor nodes and the adjacent nodes by using the LEACH routing protocol. Equation (2) gives the Euclidean distance formula used in the proposed system. \[E_{D}\big{(}N_{i},D_{j}\big{)}=\sqrt{\Big{(}\big{(}X_{i},D_{j}\big{)}^{2}- \big{(}Y_{i},Y_{j}\big{)}^{2}\Big{)}} \tag{2}\]  
The distance measurement is computed with the obstruction of values analyzed with probability estimation using the sensor nodes and the adjacent nodes. Euclidean distance (\(E_{D}\)) is calculated using (\(X_{i},D_{j}\)), (\(Y_{i},Y_{j}\)), which are the two different coordinates. The nodes are aligned with the task of predicting the defined modelling using the LEACH protocol, which is shown in Equation (3). \[\Pr_{\text{ch}}\big{(}N_{i},D_{j}\big{)}\!=\! \begin{cases}0&I_{ri}\leq E_{D}~{} \big{(}N_{i},D_{j}\big{)}\\ e^{-\gamma~{}\frac{E_{D}~{}\big{(}N_{i},D_{j}\big{)}-I_{ri}-I_{re}}{I_{ri}-E_{D }~{}\big{(}N_{i},D_{j}\big{)}}}&I_{ri}-I_{re}\leq E_{D}~{}\big{(}N_{i},D_{j} \big{)}<I_{re}\\ 1&I_{ri}-I_{re}\geq E_{D}~{}\big{(}N_{i},D_{j}\big{)}\end{cases}  \tag{3}\]  
The sensing error is identified in the sensor node using the \(I_{re}\), and the radius is determined using the \(I_{ri}\). The \(\gamma\) illustrates the sensing parameter and attenuation coefficient. The target coefficient is obscured with the sensor network using the assumptions in the probability evaluation, defined as \(\text{Porch}\big{(}N_{i},D_{j}\big{)}\), which is shown in Equation (4). \[P_{sn}=1-\prod_{i=1}^{N}\text{Pch}\big{(}N_{i},D_{j}\big{)} \tag{4}\]  
Figure 2 represents the formation of the cluster nodes between the nodes to monitor the energy conservation before the application of Bat implementation. The node coverage of the sensor node is illustrated by using the parameters in the received signal strength in each node of clusters, which is given in Equation (5):  
\[E_{S(i)}=\left(\sum_{i=1}^{Num}\sum_{Src\in CH}E_{Source}\ SN_{ch}+E_{RSSI}+E_{ DA}\right)+\sum_{i=1}^{num}E_{dest}\ SN_{ch}+E_{Final} \tag{5}\]  
Equation (5) shows the assumptions used in the network's sensor node energy prediction using the LEACH protocol. Let \(E_{Source}\) be the source node energy for the sensor nodes in clusters. \(E_{RSSI}\) also predicts the energy of the received signal strength, and \(E_{DA}\) is the data predicting the node in the transmission range. \(E_{dest}\) is the destination node energy. The destination is assumed to be within the mean values, and \(E_{final}\) is the final energy of the nodes that are assumed with the num values of the cluster head selection in the predetermined evaluation. The sensor nodes have been classified according to the metrics given in Table 2 for implementing the \(MB-NO\) algorithm and Q learning parameters. \begin{table}
\begin{tabular}{c c} \hline \hline
**Values** & **Estimations** \\ \hline \(-1\) & The sensor node and the route are assumed to be non-alive \\ \hline \(0\) & The sensor node and the route are assumed to be of static or ideal mode \\ \hline \(1\) & The sensor node and the route are assumed to be in the cluster head assumption \\ \hline \(>\)1 & A node acting as cluster head \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Assumptions in energy monitoring using the cluster for \(MB-NO\) algorithm. The energy consumed in the proposed work can be estimated using the optimum coverage. The parameters for the optimum coverage are given in Equation (6):  
\[E_{\textit{Src},\textit{dest}}=\left\{ \begin{matrix}E_{\textit{consum}}&X&Z+E_{ \textit{disisp}}X&Z&X&E_{D}&\left(N_{i},D_{j}\right)&\textit{if}&E_{D}&\left(N_{ i},D_{j}\right)<E_{D0}\\ E_{\textit{consum}}&X&Z+E_{\textit{utilised}}X&Z&X&E_{D}&\left(N_{i},D_{j}\right)& \textit{if}&E_{D}&\left(N_{i},D_{j}\right)\geq E_{D0}\end{matrix} \right. \tag{6}\]  
Let \(E_{\textit{Src},\textit{dest}}\) be the energy consumption from the source node to the destination nodes in the network.