## 4 Simulation and Experimental Results
### Network Lifetime  
Figures 1 and 2 show the obtained results of the simulations in terms of the network lifetime. The history of alive nodes is reported in Figure 1, while the number of dead sensor nodes is illustrated in Figure 2. From these figures, it is evident that the proposed clustering routing protocol performs better than the protocols in comparison. Besides, nodes start to die after 230 rounds in the proposed protocol, while nodes begin to die after 180 rounds in DEEC. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Sensing area & 100 m\({}^{2}\) \\ Number of sensor nodes \(N\) & 100 \\ Packet size \(l\) & 4000 bits \\ Energy for 1 bit of data aggregation \(E_{DA}\) & 5 nJ/bit \\ The energy dissipation for transmitting or receiving 1 bit of data \(E_{elc}\) & 50 nJ/bit \\ The coefficient of energy dissipation in the free space \(\varepsilon_{f_{8}}\) & 10 pJ/bit/m\({}^{2}\) \\ (transmission coefficient amplifier) & \\ The coefficient of energy dissipation in the multi-path attenuation & 0.0013 pJ/bit/m\({}^{4}\) \\ model \(\varepsilon_{mp}\) (transmission coefficient amplifier) & 0.07 J \\ Initial energy of sensor nodes \(E_{o}\) & 0.07 J \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Population size & 20 \\ Maximum number of iterations & 50 \\ \(w_{1},w_{2},\)\(w_{3},w_{4}\) & 1 \\ \(\alpha\) & 1 \\ \(b\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Setting parameters of the proposed method. \begin{table}
\begin{tabular}{l l l} \hline \hline  & **Parameter** & **Value** \\ \hline DEED & Probability of CHs \(p_{opt}\) & 0.1 \\ LEACH & Percentage of CHs \(p\) & 0.05 \\ SEP & Probability of CHs \(p\) & 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Setting parameters of compared methods. The proposed method and DEEC might seem similar in their resulting patterns since both schemes are based on similar performing principles. Under such conditions, both techniques could generate similar rates of energy consumption in every round. However, the proposed strategy includes additional factors that influence the selection of CHs, which leads to an optimal cluster configuration that extends the lifetime of the network. In contrast, the DEEC method obtains suboptimal cluster topologies that produce higher consumption. Moreover, selected CHs do not always have the maximum remaining energy, which leads to inefficient energy expenditure. Furthermore, cluster formation also stops quickly in DEEC, which forces normal nodes to communicate directly to the base station, causing faster exhaustion of nodes, and consequently, reducing the network lifetime. Considering the achieved results, our method manages to prolong the lifetime of the network more rounds than the other techniques. These results were obtained because our strategy is able to automatically change the number of clusters in every round to balance the energy load. Besides, the selection of sensor nodes to become CHs is also dynamic. Therefore, the roles of sensor nodes can change in each round to obtain the network configuration that reduces the energy consumption and increases the lifetime of the nodes. Additionally, the clustering evolution of the network is presented in Figure 3, where the clustering formation is visualized in different rounds. This figure shows how clusters are changing as different cluster heads are selected over time. Furthermore, it reveals the distribution of dead nodes and how they are ignored in the clustering process. Figure 1: Network lifetime: alive nodes history. Figure 2: Network lifetime: dead nodes history. In the simulation, sensor nodes are represented as circles, while communication links are symbolized as connection lines. From Figure 3, the base station can be observed at the center of the sensing area, represented as a blue circle.