## 4 Simulation and Results
### Simulation Results and Discussion  
Figure 3 presents the clustering outcomes following an initial K-means clustering simulation, depicting the distribution of sensor nodes, CHs, and the BS for three scenarios. Each scenario is defined to set different BS locations: Scenario 1 positions the BS at (100 m, 300 m) and Scenario 2 at (100 m, 100 m). This visualization shows how the initial clustering phase constructs sensor nodes and identifies CHs relative to the BS location. Figures 4 and 5 illustrate the status of alive nodes for various simulation rounds under two distinct scenarios. For Scenario 1, with the BS positioned at (100 m, 300 m), nodes remained active until round 262 with 80 nodes and round 569 with 50 nodes, and by round 1003, only 20 nodes were active. Conversely, Scenario 3, with the BS at (100 m, 100 m), showed slightly prolonged node activity, where 80 nodes remained active until round 276, 50 nodes until round 579, and 20 nodes until round 1010. This variation highlights the impact of BS placement on the network lifetime span. Additionally, the CHES algorithm applied in the simulation aimed to balance the energy consumption between clusters, potentially enhancing the operational efficiency and prolonging the lifespan of CHs. The effectiveness of this method can be confirmed by tracking the remaining energy of cluster heads each round, providing a tangible metric for assessing the impact of energy redistribution on the sustainability of cluster energy resources. Figure 6 illustrates the network lifetime comparison between the number of rounds and the number of alive nodes in a simulation under no-mobility conditions, conducted in over 2000 rounds with 100 deployed sensor nodes and for two scenarios. In Scenario 1 (Figure 6a, BS located at (100 m, 300 m)), the results show that IK-MACHES outper \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Protocol**} & \multirow{2}{*}{**Clustering**} & \multirow{2}{*}{**Key Metrics**} & \multicolumn{2}{c}{**Feature**} \\ \cline{3-5}  & & & **Strength** & **Weakness** \\ \hline Improved-LEACH [10] & Randomness with & Residual Energy & Balanced CH selection & No optimization for proximity \\  & Residual Energy & & & or mobility \\ LEACH-K [15] & K-Means Clustering + & Distance, Residual Energy & Balanced clustering, & High computational cost in \\  & Residual Energy & & scalable & dense networks \\ LEACH-GK [17] & Grid-Based K-Means & Distance, Residual Energy & Scalability, clustering & Limited adaptation to mobility \\  & Clustering & & accuracy & \\ PSO [22] & Particle Swarm & Distance, Residual Energy & Optimized energy and & High computational cost, \\  & Optimization & & proximity & requires tuning \\  & Improved K-Means + & Distance, Residual Energy, & Stability, energy & Moderate computational \\ IK-MACHES (Proposed) & Mobility-Aware CH & Mobility & mobility-aware & complexity \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 3: Clustering results with distributed sensor nodes, CHs, and BS, after initial K-means clustering simulation for each scenario; BS location at (100 m, 300 m) for Scenario 1 and at (100 m, 100 m) for Scenario 2, respectively. forms other protocols, maintaining a higher number of alive nodes for a longer duration, especially after 1000 rounds. This is due to its effective integration of residual energy, proximity, and clustering stability through its mobility-aware scoring despite the absence of node mobility. PSO-based clustering also exhibits strong performance, leveraging its optimization-based approach to balance energy consumption. LEACH-GK performs better than other K-means-based protocols (LEACH-K and Improved-LEACH), demonstrating its scalability and clustering accuracy. Classical LEACH and LEACH-B, while simple, show the poorest performance due to their lack of optimization, with the majority of nodes depleting energy before 750 rounds.