## 5 Energy Optimization Approach Based on MAC/Routing Cross-Layer (EOAMRCL)
### Clusters Formation Phase (Network Layer)
The EEUC protocol demonstrates better performance than DWEHC, with a delayed FND and a more gradual progression to HND and LND. This indicates that EEUC has more effective clustering and energy management strategies, which help in prolonging the network's operational period. However, by the time half the nodes are dead, the network starts to decline rapidly, showing that while EEUC is better than DWEHC, it still falls short in maintaining node energy levels uniformly over extended periods. The CGA-GWO protocol further improves the EEUC performance, with the FND occurring later and a slower progression to HND and LND. This improvement can be attributed to the integration of the GWO algorithm, which enhances the selection of cluster heads and routing paths, leading to more balanced energy consumption among nodes. The prolonged periods before reaching HND and LND indicate that CGA-GWO manages

Figure 9: Comparison of FND, HND, and LND. to maintain network stability and efficiency for a longer duration compared to DWEHC and EEUC. EOAMRCL exhibits the best performance among all the protocols, with the FND occurring much later and a very gradual progression to HND and LND. This is due to the effective cross-layer optimization approach, which integrates the MAC and network layers to enhance energy efficiency. By leveraging GWO, EOAMRCL optimally selects cluster heads and routes, minimizing energy consumption during data transmission. Additionally, the duty-cycle scheduling at the MAC layer allows nodes to switch between active and sleep modes, further conserving energy. The result is a significantly extended network lifetime, with nodes remaining functional for longer periods, thus delaying the FND, HND, and LND milestones. Figure 10 compares the percentage of live nodes over 500 iterations. The DWEHC protocol shows a rapid decline in the percentage of live nodes, with a significant drop occurring early in the iterations. By around 150 iterations, less than half of the nodes remain alive, indicating inefficient energy management. The steep decline continues, and by 400 iterations, almost all nodes are dead. This pattern suggests that DWEHC's approach to clustering and routing is not effective in conserving node energy, leading to a shorter network lifespan. In contrast, the EEUC protocol performs better than DWEHC but still shows a steady decline in the percentage of live nodes. The drop is less steep initially, with around 60% of nodes remaining alive by 150 iterations. However, the decline accelerates after this point, and by around 400 iterations, the network is nearly depleted. This indicates that while EEUC improves energy efficiency compared with DWEHC, it is still not sufficient to sustain long-term network operations. The CGA-GWO protocol demonstrates a more gradual decline in the percentage of live nodes. By leveraging the GWO algorithm, CGA-GWO achieves better clustering and routing decisions, which help in distributing the energy consumption more evenly across nodes. As a result, the percentage of live nodes remains higher for a longer duration, with around 50% of nodes still alive at 250 iterations. This indicates that CGA-GWO is more effective in managing energy consumption and extending network life compared with DWEHC and EEUC. EOAMRCL shows the best performance among all protocols, maintaining the highest percentage of live nodes throughout the 500 iterations. The decline in live nodes is the most gradual, with over 60% of nodes still alive at 250 iterations. This superior performance can

Figure 10: Comparison of live node percentage. be attributed to the cross-layer optimization approach of EOAMRCL, which integrates the MAC and network layers for enhanced energy efficiency. By using GWO to optimally select cluster heads and routes and incorporating duty-cycle scheduling at the MAC layer to alternate nodes between active and sleep modes, EOAMRCL effectively conserves energy. As a result, the network maintains a higher percentage of live nodes for a significantly extended period.