## 4 Discussion  
Keeping the number of nodes at 100 and the transmission range at 100-600 m, the findings in Figure 4 demonstrate that p-WOA generated 45 clusters for a grid size of 1 km \(\times\) 1 km and 53 clusters for a grid size of 4 km \(\times\) 4 km. According to the comprehensive evaluation, the created method outperformed the state-of-the-art alternatives. It also demonstrates that an increase in grid size results in a corresponding rise in clusters. There was a correlation between transmission range and cluster output in p-WOA, with more optimal clusters being generated as the range expanded. Figures 5 and 6 show the results of the experiments in which the grid size was varied while the number of nodes was held constant at 30 and 40. Moreover, PDR, latency, and throughput were calculated and compared with other bio-inspired methods (ALO and GWO), exhibiting the superiority of the developed method. It was observed that by incorporating probability-based functions into the whale optimization algorithm, the randomness of vehicles at the time of initialization was significantly improved, and the convergence factor was increased.  
The load balance factor was used to verify the results by comparing them to those obtained using a standard procedure. As shown in Figures 10 and 11, p-WOA achieved superior results when compared to other benchmark algorithms by distributing the burden of overall cluster leaders. The LBF was utilized to evaluate the proposed method with other methods in terms of the ability of vehicles to stay in a cluster for a maximum length of time. Moreover, the LBF assures that each cluster has been assigned an equal number of nodes.  
The typical range for the number of nodes in a published work is between twenty and one hundred and twenty [37; 38]. In this analysis, we only evaluated clusters with up to 100 nodes because increasing the number of nodes affects the longevity of the cluster and the network, and thus, it raises the cost of the network. Because the nature-inspired algorithms were random, overlaps occurred during the experiments [39; 40; 41; 42; 43; 44]. In the current study, we integrated self-adaptive weights via fitness function optimization to overcome this issue using a probabilistic intelligence technique. The developed technology has a wide range of possible uses, including enhancing the accuracy of maps generated using  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Dependent Variables** & **Variable** & **Coefficient** & **Prob.** & **R-Squared** & **Adjusted R-Squared** & **ANOVA** \\ \hline \multirow{2}{*}{NO OF CLUSTERS ALO [38]} & TR & 0.042088 & 0.0097 & \multirow{2}{*}{0.715376} & \multirow{2}{*}{0.679798} & \multirow{2}{*}{F(1 9) = 20.73 ***} \\  & C & 27.73294 & 0.0005 & & & \\ \hline \multirow{2}{*}{NO OF CLUSTERS GWO [22]} & TR & 0.040038 & 0.0124 & \multirow{2}{*}{0.706213} & \multirow{2}{*}{0.669490} & \multirow{2}{*}{F(1 9) = 22.81 ***} \\  & C & 27.15528 & 0.0006 & & & \\ \hline \multirow{2}{*}{NO OF CLUSTERS p-WOA} & TR & 0.039256 & 0.0092 & \multirow{2}{*}{0.779748} & \multirow{2}{*}{0.752216} & \multirow{2}{*}{F(1 9) = 25.55 ***} \\  & C & 27.00485 & 0.0004 & & & \\ \hline \multicolumn{6}{c}{***\(p<\) 0.01 or 1\%.} \\ \end{tabular}
\end{table}
Table 2: Transmission Regression Coefficients Under Fully Modified Least-Squares (FMOLS) Approaches Vary Depending on the Number of Clusters.  
the global positioning system and employing media services to distribute news and other information via the internet.