## 3 The Proposed Model
### PTA-Based Route Selection in Group Communication
 \tag{11}\]  
where \(e\) denotes the constant to prevent supervision by 0. The flower is modified to the \([X_{\text{min}},X_{\text{max}}]\) interval so that when \(F_{i,j}^{iter}<X_{\text{min}}\), the \(F_{i,j}^{iter}=X_{\text{min}}\), and if \(F_{i,j}^{iter}>x_{\text{max}}\), then \(F_{i,j}^{iter}=X_{\text{max}}\), where \(j=1,D\). Every plum location can be upgraded using the following equation:  
\[P_{i}^{iter}= \begin{cases}\begin{array}{c}F_{i}^{iter},if\;OF\big{(}F_{i}^{ iter}\big{)}<OF\Big{(}P_{i}^{iter-1}\Big{)}\\ P_{i}^{iter-1},otherwise.\end{array}\end{cases} , \tag{12}\]  
The value of global better plum \(p_{gbest}\) is upgraded to the plum location that has the better fitness value based on the objective function OF. Lastly, return the \(p_{gbest}\) value. In this work, the PTA is applied for the identification of the routes in the IoT network. The latency and power consumption of the method was determined in the subsequent equations [25]. The latency of the IoT has been contained in 3 portions. \[T_{\text{all}}=T_{1}+T_{2}+T_{3} \tag{13}\]  
where \(T_{1}\) refers to the data communication latency between IoT devices and the data center. \(T_{3}\) simulates the delay of IoT in the data center to the last node. The \(T_{2}\) comprises 2 portions. \[T_{2}=T_{21}+T_{\bar{\text{j}}} \tag{14}\]  
in which \(T_{\bar{\text{j}}}\) represents the latency in node \(i\) to node j, and \(T_{21}\) stands for the latency of residence time for IoT (time of reception and data transmission, and time of establishing the transmission connection amongst IoT and node). At this point, \(R_{\text{i}}\) implies the broadcast range of node \(i\). \(H\) signifies the height of IoT overground. \(L_{\text{c}}\) showcases the connection to make a transmission among \(i\) and IoT. \(T_{\text{c}}\) denotes the latency of the evolving transmission link in i-th node to the IoT. Because of the length of data transferred \((f_{\text{d}})\) and bit per second \((V_{\text{c}})\), the kind of transmission chip remains similar, and \(T_{\text{c}}\) is signified as follows:  
\[T_{\text{c}=l_{\text{d}}}V_{\text{c}} \tag{15}\]  
In addition, the speed \((V_{\text{U}})\) of the IoT has to meet the provided condition in the subsequent:  
\[V_{\text{U}}<=L_{\text{C}}/T_{\text{C}} \tag{16}\]  
\[T_{21}=T_{\text{C}}+T_{\text{S}} \tag{17}\]  
in which \(T_{\text{s}}\) represents the latency of data forwarded amongst nodes as well as the IoT. If the visited nodes are \(n\) that is dependent on Equations (14)-(17), \(T_{\text{all}}\) is written as  
\[T_{all},=T_{1}+\sum_{1}^{n}\bigl{(}T_{\text{C}}+T_{\text{S}}+T_{\bar{\text{j }}}\bigr{)}+T_{3} \tag{18}\]  
where \(T_{\bar{\text{j}}}\) demonstrates the time in \(i\)-\(th\) to jth nodes. The energy utilization of the IoT is contained in three portions. \[P_{\text{all}}=P_{1}+P_{2}+P_{3} \tag{19}\]  
in which \(P_{1}\) illustrates the power consumption in CHs to the data center. \(T_{3}\) signifies the power application in the resultant node to the data center. The \(P_{2}\) has 2 portions. \[P_{2}=P_{21}+P_{\bar{\text{j}}} \tag{20}\]  
where \(P_{21}\) implies the power consumption of the IoT, and \(P_{\bar{\text{j}}}\) showcases the energy consumption of IoT devices from \(i\) to j nodes. \[P_{oll}=P_{1}+\sum_{1}^{n}\bigl{(}P_{\text{C}}+P_{\text{S}}+P_{\bar{\text{j }}}\bigr{)}+P_{3} \tag{21}\]  
Consider that the speed \(V_{\text{U}}\) was considerable; therefore, the \(T_{1}\), \(T_{3}\), \(P_{1}\), and \(P_{3}\) were also considerable. \(T_{\text{C}}\), \(T_{\text{S}}\), \(P_{\text{C}}\), _and_\(P_{\text{S}}\) are maximum because of the data length of data maximum. The objective function of the PTA technique is to decrease power utilization along with delay. The power consumption or delay are selected by a frequent visit to the IoT device, and it is represented as follows:  
\[\text{min}f(L)=\sum_{l=1}^{n-1}d_{L_{l}L_{l+1}} \tag{22}\]where L denotes the sequence of nodes. The NP-hard problem can be resolved by using the PTA technique. The overall process involved in PTA is shown in Algorithm 1.