## 5 Energy Optimization Approach Based on MAC/Routing Cross-Layer (EOAMRCL)
### Clusters Formation Phase (Network Layer)
This superior performance can be attributed to EOAMRCL's effective cross-layer optimization approach, which integrates the MAC and network layers for enhanced energy efficiency and data transmission. By leveraging GWO for optimal cluster head selection and routing and incorporating duty-cycle scheduling to alternate nodes between active and sleep modes, EOAMRCL minimizes packet loss and maximizes successful data delivery. This efficient management of data transmission ensures that the protocol can handle increasing network sizes without compromising performance. Figure 13 presents the energy consumption of four different protocols that implement four different optimization algorithms:

* Fuzzy logic (FL), implemented by FQA [23];
* Distance Vector (DV), implemented by M2 TLSC [31];

Figure 12: Comparison of network throughput. Starting with the FQA, it is evident that this method incurs the highest energy consumption across all iterations. At the 50 th iteration, the FQA algorithm's energy consumption stands at approximately 10 joules and escalates to around 90 joules by the 500 th iteration. This increase suggests that while FQA might be effective in certain aspects, it is not optimal for energy conservation in WSNs, which is a critical consideration given the limited power resources of sensor nodes. The M2 TLSC protocol exhibits a moderate energy consumption pattern. Initially, at the 50 th iteration, it consumes roughly 5 joules, doubling to about 40 joules by the 500 th iteration. Although it performs better than FQA in terms of energy efficiency, its energy consumption trajectory indicates a steady increase, making it less suitable for applications requiring long-term deployment of sensor nodes. The PSO-C protocol demonstrates a more promising energy efficiency profile. At the 50 th iteration, its energy consumption is just below 5 joules, and even at the 500 th iteration, it consumes around 10 joules. This relatively flat curve suggests that PSO-C is effective in minimizing energy usage over time, making it a viable option for prolonging the lifespan of WSNs. The low energy consumption can be attributed to the algorithm's ability to find optimal solutions with minimal energy expenditure, balancing exploration and exploitation efficiently. The EOAMRCL protocol shows the lowest energy consumption among the four algorithms. At the 50 th iteration, its energy consumption is around 3 joules, and by the 500 th iteration, it reaches just under 10 joules. The gentle slope of the EOAMRCL curve highlights its superior energy efficiency, making it the most effective in conserving energy and thereby extending the operational life of the WSN. Figure 14 illustrates the number of live nodes for four different optimization techniques. Starting with FL implemented by FQA protocol, we observe a rapid decline in the number of live nodes beginning at around 150 iterations. By approximately 350 iterations, the number of live nodes drops to zero. This indicates that while FQA may initially maintain a high number of active nodes, its efficiency diminishes rapidly, leading to a complete node depletion relatively early in the network's operation. Figure 13: Comparison of energy consumption of different optimization techniques. The M2 TLSC protocol that implements DV shows a more gradual decline in live nodes compared with FQA. The number of live nodes begins to decrease noticeably after 200 iterations, but it maintains a higher number of live nodes than FQA for a longer duration. By around 450 iterations, however, the number of live nodes also drops to zero. This suggests that M2 TLSC performs better in maintaining node survivability than FQA, but it still faces challenges in extending the overall network lifespan significantly. Next, the PSO-C protocol demonstrates a steady decline in the number of live nodes starting at around 250 iterations. Although the decline is slower than FQA, by 400 iterations, the number of live nodes reduces to zero.