## 3 Proposed Method
The objective of this optimization problem is to maximize the sum of the weights of the links between the \(\chi_{i}\) and its neighbors. This means each vehicle has a list of neighboring nodes and the node with the highest \(\phi_{i}\) to its neighbors is selected as the \(\chi_{i}\). We consider \(\phi_{i}\) to be the encounter history of node \(i\), representing the number of encounters node \(i\) has had with its neighbors, which can be expressed as follows:  
\[\phi_{i\max}=\max(V_{i},V_{j}),\sum(\phi(V_{i},V_{j})\ for\ all\ V_{j}\in neighbors\ V_{i}) \tag{2}\]  
A higher \(\phi_{i}\) indicates greater efficiency in terms of easily sending and receiving more packets. Therefore, the node with the highest \(\phi_{imax}\) is a good candidate for \(\chi_{i}\) as it helps maintain long-term stability in the cluster and enables communication with nearest neighbors. The encounter rate as used in our study refers specifically to the number of times vehicles come within their communication range of each other, rather than the duration for which they remain in mutual proximity. \(\Psi_{i}\) is employed for gauging the remaining energy of a node, which can be computed using Equation (3), where \(\Psi_{i}^{Current}(t)\) denotes the remaining energy of node \(i\) at time slot \(t\), and \(\Psi_{i}^{Initial}(o)\) represents the initial energy of node \(i\). By utilizing this equation, we are able to identify the node with the highest remaining energy, which has the potential to serve as a cluster head. \[\Psi_{i}=\frac{\Psi_{i}^{Current}(t)}{\Psi_{i}^{Initial}(o)} \tag{3}\]  
To choose cluster heads, we propose a heuristic function. Initially, we need to compare two factors: the highest encounter rate (\(\phi_{i}\)) and the most remaining energy (\(\Psi_{i}\)). To make this comparison fair, we can apply min-max normalization. This process standardizes the data, making sure all features are scaled equally. This prevents any one feature from dominating others due to differences in their sizes. This process involves rescaling the data to a fixed range, usually between 0 and 1. In general, we determine the minimum (\(\sigma_{i(min)}\)) and maximum (\(\sigma_{i(max)}\)) values of the feature we want to normalize. Then, we calculate the range of the feature by subtracting the minimum value from the maximum value: \(\sigma_{i(max)}-\sigma_{i(min)}\). Therefore, for each data point (\(\sigma_{i}\)) in the feature, we apply the min-max normalization formula. The min-max(\(\sigma_{i(normalized)}\)) scale is as follows:  
\[\sigma_{i(normalized)}=\frac{\sigma_{i}-\sigma_{i(min)}}{\sigma_{i(max)}- \sigma_{i(min)}} \tag{4}\]  
By following Equation (4), we guarantee uniform scaling across all nodes, ensuring that each node's data are standardized to the same scale relative to the entire dataset. Normalization not only ensures that both factors are scaled within the range of \([0,1]\), but also ensures equal contribution from both factors in the analysis, facilitating a balanced consideration of encounter rate and remaining energy when selecting cluster heads. Consequently, the normalized expressions for encounter rate (\(\phi_{i}\)) and remaining energy (\(\Psi_{i}\)) for node \(i\), utilizing the min-max scaling technique, can be articulated as follows:  
\[\phi_{i(normalized)}=\frac{\phi_{i}-\phi_{i(min)}}{\phi_{i(max)}-\phi_{i(min)}} \tag{5}\]  
and  
\[\Psi_{i(normalized)}=\frac{\psi_{i}-\psi_{i(min)}}{\psi_{i(max)}-\phi_{i(min)}} \tag{6}\]  
Therefore, utilizing Equations (5) and (6), we introduce a heuristic function for the selection of cluster heads. The heuristic function \(\xi_{i}\) is as follows:  
\[\xi_{i}=\phi_{i(normalized)}+\Psi_{i(normalized)} \tag{7}\]  
The \(\chi_{i}\) is a vehicle selected as the group leader and maintains a routing table for every vehicle in its cluster. Based on the \(\chi_{i}\), clusters are formed (\(C_{i}\)), with each cluster containing some nodes (\(M_{i}\)) that are supported by its respective cluster head \(\chi_{i}\).