## 5 Energy Optimization Approach Based on MAC/Routing Cross-Layer (EOAMRCL)
### Clusters Formation Phase (Network Layer)
The network zone is set to 100 \(\times\) 100 m\({}^{2}\), balancing sufficient coverage and computational feasibility, while the number of sensors ranges from 50 to 250 to test the protocol's scalability under different network densities. The base station (BS) is located at coordinates (90,90) to simulate real-world scenarios where the BS is positioned at the network's edge, challenging the protocol's datarouting efficiency. A clusterhead percentage (P\({}_{\text{opt}}\)) of 5% ensures the effectiveness of selecting optimal CHs for energy efficiency and load balancing. Incorporating 20% advanced nodes with an additional energy factor (\(\theta\)) of 1 tests the protocol's ability to leverage these nodes for prolonged network operation. The initial energy (E\({}_{0}\)) of 3 J/node provides a reasonable starting point for observing energy consumption patterns and the protocol's impact on network lifetime. Transmission energy (E\({}_{\text{elec}}\)) of 50 nJ/bit and packet size (L) of 4000 bits reflect typical WSN energy consumption, which is crucial for assessing data transmission efficiency. Propagation energy values (\(\epsilon_{\text{fs}}\) = 15 pJ/bit/m2 and \(\epsilon_{\text{mp}}\) = 0.0015 pJ/bit/m4) account for energy loss during data transmission over varying distances, essential for realistic wireless communication simulation. Data aggregation energy (E\({}_{\text{DA}}\)) of 5 nJ/bit/signal evaluates the protocol's effectiveness in reducing energy consumption through data aggregation. Limiting the node pairing distance to less than 2 m ensures close proximity for efficient sleep/active mode coordination. Fitness function weights (w\({}_{1}\),w\({}_{2}\),w\({}_{3}\)) of 0.45, 0.45, and 0.1 balance the importance of intra-cluster distances, inter-cluster distances, and residual energy, ensuring a comprehensive performance evaluation. These parameters collectively create a realistic and challenging simulation environment, enabling a thorough assessment of the EOAMRCL protocol's ability to enhance energy efficiency, extend network lifetime, and improve overall network performance in WSNs. ### Evaluation Metrics

The evaluation metrics used in the experimentations are described as follows:

* Network Residual Energy:
* Measures the remaining energy in the network over time;
* Indicates the efficiency of energy management by each protocol;
* Higher residual energy implies better energy conservation and a longer network lifespan. * Clustering Iteration Performance:
* Assessed using First Node Dead (FND), Half of Nodes Dead (HND), and Last Node Dead (LND);
* FND: Iteration count when the first node dies;
* HND: Iteration count when half of the nodes are dead;
* LND: Iteration count when the last node dies;
* Higher values indicate better energy distribution and prolonged network operation. * Percentage of Live Nodes:
* Represents the percentage of nodes remaining active over time;
* Higher percentages indicate better energy management and network sustainability; \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Network Zone & 100 \(\times\) 100 m2 \\ Number of Sensors (\(n\)) & 50–250 \\ BS Coordinates & (90,90) \\ Clusterhead Percentage (P\({}_{\text{opt}}\)) & 5\% \\ Advanced Node Percentage (\(m\)) & 20\% \\ Initial Energy (E\({}_{0}\)) & 3 J/node \\ Additional Energy Factor (\(\theta\)) & 1 \\ Transmission Energy (E\({}_{\text{elec}}\)) & 50 nJ/bit \\ Packet Size (L) & 4000 bits \\ Propagation Energy (fading space \(\epsilon_{\text{fs}}\)) & 15 pJ/bit/m2 \\ Propagation Energy (multi – – path \(\epsilon_{\text{mp}}\)) & 0.0015 pJ/bit/m4 \\ Data Aggregation Energy (E\({}_{\text{DA}}\)) & 5 nJ/bit/signal \\ Node Pairing Distance & \textless{}2 m \\ Fitness Function Weights (w\({}_{1}\),w\({}_{2}\),w\({}_{3}\)) & 0.45, 0.45, 0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Simulation settings for network simulations. * Critical for assessing the protocol's ability to maintain network functionality.