## 3 Proposed w-SMNO
### Local Leader Validation  
For the evaluation of the best vehicle node from the population for the local leader, the corresponding function \(F(X_{k})\) is defined to evaluate the node performance equivalent to the fitness function in the spider monkey optimization approach. The identification of the global best relay candidate by the global leader among the selected relays relative to the best monkey position is given in Equation (5), returning the optimized and maximum values among the nodes (monkeys).  
Figure 4: SMNO working steps.  
At \(X_{k}(t+1)\), optimize the condition for the best solution;  
\[candidate\leftarrow\textbf{return}\{max(F(X_{k}(t+1)))\} \tag{5}\]  
The specific details and variations of the approach involve additional strategies or refinements to guide the vehicle (monkey) movements or based on the problem being solved. For the \(k\)th vehicle \(V_{k}\) in the population (\(N\)), the optimized fitness function \(F\) evaluation is based on the considered nodes' parameters, including the range of transmission (\(R_{T}\)), speed (\(S\)), energy consumption (\(Ec\)), throughput (\(Th\)), and neighbor size (\(n\)) to assess their performance, connectivity, or overall efficiency within the network while comparing for the leader. A list of all populations with the mentioned parameter values at any time instant, as shown in Figure 5, is maintained by the global leader. In this case, the source node is the global leader's (\(GL\)) process to select local leaders for subgroups using the parameter value list.  
Leader node selection is crucial for efficient communication and relay functionality. Threshold-based equations are commonly used to determine whether a node should act as a leader based on various parameters. These equations define conditions that must be met for a node to perform a specific action of a subgroup leader. The fitness evaluation to select \(LL\) for cut-off \(C\), having a total dimension weight (\(W\)) for all \(Q\) dimensions, is given in Equations (6)-(8).  
\[F(X)>C; \tag{6}\]  
for;  
\[F(X)=\sum_{k=1}^{N}\frac{w_{k}(R_{T})+w_{k}(S)+w_{k}(Ec)+w_{k}(Th)+w_{k}(n)}{ Total\;\;weight\;\;(parameters)}\cdot W \tag{7}\]  
where;  
\[W=\int_{q=1}^{Q}[w(R_{T})_{q}+w(S)_{q}+w(Ec)_{q}+w(Th)_{q}+w(n)_{q}] \tag{8}\]  
Figure 5: Population parameter record.  
For the selection of local leader nodes considering threshold or cut-off values, an equation that filters nodes according to criteria is based on the scenario where the set of parameters \(P\) is associated with each node, and the approach seeks to select some nodes that meet a specific cut-off value, \(C\), while considering a dynamic maximum limit \(L\) to the number of selected nodes. To achieve this filtering of nodes based on the cut-off and limit including \(P_{A}\) represents the value of parameter \(P\) for node \(A\) (where \(A\) ranges from 1 to \(N\)), \(C\) is the cut-off for parameter \(P\), and \(L\) is the maximum limit of the selected leaders for subgroups. Ensuring that the nodes meeting the threshold value \(C\) are selected until the maximum limit, \(L\), for local leaders is reached is shown in Algorithm 1.  
```
Input: Population Parameter Record {\(P\)}, Threshold {\(C\)}, Range {\(A\)}: \(N\) Output: Local Leader for \(N\) Groups; \(LL_{Monkey}\) [\(N\)] functionLL_Identification (n[\(D\)]) Initialization Monkey (Nodes) Arrangement forall\(monkeys\in N\)do  Sorting of the nodes based on their parameter value (\(P\))  Population parameter record  sort(\(P_{A}[N]\))  update \(P_{A}[]\) forallLocal monkeysdo  Counter initialization  count = 0;  Iterate through the sorted list of monkeys: forall\(N\)do if\(P_{A}[N]>=C\)andcount < \(L\)then  Increase the counter  count = count + 1 else if\(count>=L\)then  Reached to Maximum limit  Break the iteration \(LL_{Monkey}[N]\leftarrow\)max(\(P_{A}[N]\))  Disseminate \(LL\) return\(LL_{Monkey}[N]\)
```  
**Algorithm 1**LL Validation