## 3 Results  
In this section, we provide numerical results for various configurations for a number of nodes, communication ranges, network area, and load balancing factors. The developed cluster optimization method for route optimization in vehicular networks, namely (p-WOA), was evaluated in comparison to two state-of-the-art methods: the Ant Lion Optimizer (ALO) [38] and the Grey Wolf Optimizer (GWO) [22]. A. Cluster Density and Optimal Transmission Range  
A variety of experiments were carried out with varying parameters, such as increasing the number of nodes to 100, reducing the communication range to 100-600 m, and extending the grid size from 1 km \(\times\) 1 km to 4 km \(\times\) 4 km, to identify the boundaries of the developed p-WOA. In Figure 4, we see the wide variety of clusters that form when the number of nodes is fixed at 100 but the communication distance between them is changed (from 100 m to 600 m). Taking a transmission range of 100 to 600 m and a total of 100 nodes, a 1 km \(\times\) 1 km grid is depicted in the Figure 4a. When compared to other state-of-the-art approaches such as ALO [38] and GWO [22], it is clear that the suggested p-WOA had the lowest overall cost. Using the same constraints as in (a), but with a grid size of 2 km \(\times\) 2 km, we obtained (b) in Figure 4. As the range of the transmission grew, the number of clusters reduced, and vice versa. The smaller the clusters that were generated, the less effort was expended by the network. Although the other settings in Figure 4c remain the same, the grid size was fixed at 3 km \(\times\) 3 km. Compared to the other two approaches, the number of clusters created using the developed p-WOA was much smaller. An enhanced packet delivery ratio and reduced hop count will result from using these findings. To see how p-WOA performs in comparison to the previously described techniques, see Figure 4d, which depicts the final scene with a grid size of 4 km \(\times\) 4 km. More clusters are needed to accommodate vehicles that are geographically separated in a larger grid size, which is evident when the grid size is raised. The result is an increase in routing costs and a deterioration in the lifespan of the network. It can be observed from Figure 4 that, as the transmission range increased, the number of clusters decreased. However, it is observed that the developed p-WOA produced a relevantly lesser number of clusters compared to other bio-inspired algorithms (ALO and GWO). \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Number of vehicles (Particles) & 100 \\ Epoch & 350 \\ Vehicle Speed & 22–30 m/s \\ Grid size (Area of Network) & 1 km \(\times\) 1 km to 4 km \(\times\) 4 km \\ Communication Range & 100–600 m \\ Mobility Model & Freeway Mobility Model \\ Number of Simulations & 10 \\ Weights & 0.5 \\ Convergence Factor & 0.001 \\ Processor & AMD RadeonTM RX 5700 XT \\ Memory & 8 GB \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation Parameters. B. Grid Size vs. Number of Clusters  
Next, to confirm the advantage of utilizing p-WOA over other bio-inspired algorithms, a new angle was tested by creating multiple clusters to compare with varying grid sizes and transmission distances. Figure 5 shows the results of maintaining a fixed number of nodes (30) while increasing the transmission range from 200 m to 500 m. The y-axis shows the number of clusters, and the x-axis represents the dynamic grid sizes. It was found that there was a clear correlation between the grid size and the number of clusters, which in turn directly affected the routing cost, packet delay, and, ultimately, the network's lifetime. Figure 4: Transmission range vs. CHs for Nodes 100 and Grid Size 1 km \(\times\) 1 km, 2 km \(\times\) 2 km, 3 km \(\times\) 3 km, and 4 km \(\times\) 4 km. (**a**) Nodes = 100, Grid-Size = 1 km \(\times\) 1 km; (**b**) Nodes = 100, Grid-Size = 2 km \(\times\) 2 km; (**c**) Nodes = 100, Grid-Size = 3 km \(\times\) 3 km; (**d**) Nodes = 100, Grid-Size = 4 km \(\times\) 4 km.