## 4 Simulation and Results
### Simulation Results and Discussion
In Scenario 2 (Figure 6b), where the BS is centrally located at (100 m, 100 m), all protocols exhibit improved performance due to reduced communication distances. IK-MACHES still outperforms the other protocols, maintaining stability beyond 1800 rounds. LEACH-GK and PSO-based clustering follow closely, indicating their efficiency in optimizing cluster formation in static environments. Notably, the proximity of the BS reduces the performance gap between IK-MACHES and other protocols, as shorter distances inherently lower energy consumption. LEACH-K and Improved-LEACH maintain moderate performance, while classical LEACH and LEACH-B again exhibit rapid depletion of energy, emphasizing their inefficiency even in favorable conditions. Figure 7 depicts the network lifetime performance of various clustering under a maximum mobility range of 10 m/round. In Scenario 1 (Figure 7a), IK-MACHES demonstrates the best performance, maintaining a higher number of alive nodes throughout the simulation, particularly beyond 500 rounds. The mobility-aware scoring mechanism of IK-MACHES ensures stable CH selection by accounting for residual energy, mobility stability, and distance, which minimizes cluster reconfiguration costs caused by node movement. PSO-based clustering follows as the second-best performer, leveraging its optimization capabilities to adapt to dynamic node movements. However, the computational overhead and reduced stability in high mobility environments lead to earlier energy depletion compared to IK-MACHES. LEACH-GK performs better than other protocols by integrating  
Figure 4: Clustering and alive sensor nodes’ map for a BS located at (100 m, 300 m) scenario; showing the decline to 80, 50, and 20 active nodes at rounds 262, 569, and 1003, respectively. Figure 5: Clustering and alive sensor nodes’ map for a BS located at (100 m, 100 m) scenario; showing the decline to 80, 50, and 20 active nodes at rounds 1443, 1621, and 1702, respectively. grid-based clustering, which localizes mobility effects and improves clustering efficiency. LEACH-K and Improved-LEACH show moderate performance but are less effective in handling mobility due to limited adaptability in their CH selection criteria. Finally, classical LEACH and LEACH-B experience rapid energy depletion, with most nodes dying within the first 600 rounds, highlighting their inability to address mobility challenges effectively. In the centralized BS placement scenario (Figure 7b), all protocols benefit from reduced communication distances, leading to an improved network lifetime compared to Scenario 1. IK-MACHES achieves the longest network lifetime, retaining more alive nodes across all rounds. Its mobility-aware design makes it particularly effective in dynamic environments, ensuring balanced energy consumption and stable clustering. PSO-based clustering and LEACH-GK perform comparably, with both protocols benefiting from their ability to adapt to node movements while optimizing energy usage. However, LEACH-K and Improved-LEACH exhibit limitations in handling mobility, as their CH selection mechanisms do not explicitly account for node stability. Classical LEACH and LEACH-B again show poor performance, with significant energy depletion within the first 400 rounds, emphasizing their unsuitability for high-mobility scenarios. The proposed improved K-means with CHES protocol significantly extends network lifespan by delaying node failures and maintaining a higher percentage of active nodes longer than conventional LEACH and LEACH with K-means protocols as listed in Table 3. The proposed protocol significantly delays the first node death (FND) to rounds 243, 435, and 621 while drastically extending the network's operational life, allowing 80% of the nodes to remain functional up to rounds 262, 697, and 1443, respectively.