## 3 Results and Discussion  
We conducted experiments across six scenarios using the parameters listed in Table 2. The initial experiment aimed to demonstrate that the simplistic method (transmission power of \(-10\) dBm or \(0.0001\) Watt, as suggested by [15]) can be optimized using swarm algorithms. As shown in Figure 4, applying a standard swarm optimization method such as PSO results in lower power requirements compared to the simplistic method for all nodes. Building on these findings, we then focus on comparing the performance of various swarm optimization algorithms. \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & **Value [Unit]** \\ \hline Number of Sensor Nodes & 20 \\ Area for Random Sensors & \\ Distribution (L \(\times\) L) & 20 [m] \(\times\) 20 [m] \\ Sensor Transmission Frequency (f) & 915 [MHz] \\ Sensor Transmission Power Range & \\ (xMin; xMax) & (\(-30\), 0) [dBm] \\ Sensor Sensitivity (\(\rho_{\text{th}}\)) & \(-60\) [dBm] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of parameters with units. Figure 3: The topology utilized in the experiments. (**a**) Scenario 1, (**b**) Scenario 2, (**c**) Scenario 3, (**d**) Scenario 4, (**e**) Scenario 5, and (**f**) Scenario 6. Figure 5 presents the average minimum fitness values achieved by all swarm algorithms across all scenarios. Notably, some algorithms, such as Simulated Annealing (SA) [21] and the Tuna Swarm Algorithm (TSA) [22], do not exhibit any fitness values, indicating that these algorithms failed to converge to any solution. Other algorithms, including the Chicken Swarm Optimization (CSO) [23], Salp Swarm Algorithm (SSA) [24], Whale Optimization Algorithm (WOA) [25], and BESO, display positive fitness values, signifying convergence to suboptimal solutions. In contrast, algorithms like Particle Swarm Optimization (PSO), Genetic Algorithm (GA) [6; 26], and Grey Wolf Optimization (GWO) achieve negative fitness values, indicating that these methods are very close to optimal solutions. Consequently, we focus exclusively on these three swarm algorithms for the remaining experiments. If infinite values are observed in the Best Fitness test (Figure 5) or NaN values appear in the Execution Time test (Table 3), only algorithms with finite values are included in the analysis. Based on the filtered results in Table 4, only EGWO, GWO, BESO, and PSO are  
Figure 4: Power transmission: simplistic vs. PSO. Figure 5: Fitness by algorithm. considered for both Execution Time and Best Fitness metrics. Asymptotically, the four algorithms have the same main complexity:  
\[O(T\times n\times N^{3}) \tag{34}\]  
where  
\[T=\text{number of iterations},\quad n=\text{population size},\quad N=\text{number of nodes}.\]  
This is because the fitness evaluation function dominates the computation with an operation of  
\[O(N^{3}) \tag{35}\]  
(primarily due to the eigenvalue calculation on the Laplacian matrix). Among these, GWO achieves the smallest Best Fitness value (\(-9.274447\)) with an Execution Time of 13.291528 s.  
Table 4 summarizes the swarm comparison in terms of fitness values. These statistics represent the results of the experimental comparison across all scenarios, where each scenario is repeated 10 times. GWO achieves the lowest minimum fitness value of \(-9.274447\), followed by EGWO with 9.006406. However, for other statistics, the maximum fitness value is achieved by PSO (\(-2.605\)) and the mean fitness value by EGWO (\(-4.150733\)). Further details can be observed in Figure 6, which illustrates the power transmission to each node for Scenario 1. From Figure 6, it is evident that the three algorithms--GWO, PSO, and BESO--produce different power transmission values for each node, ranging from approximately \(-5\) dBm to \(-30\) dBm. For most nodes, the Grey Wolf Optimizer (GWO) achieves the lowest power transmission values (represented by the orange bars), indicating that it frequently finds more optimal (lower) power solutions compared to PSO and BESO. BESO and PSO also