## 5 Performance Evaluation
### Numerical Results  
In this subsection, we present numerical results to validate the efficacy of our proposed DLSMR protocol. The simulation settings are outlined in Table 7. We use the NS3 simulation, where the algorithm is run for 200 s with 5 s for each session. For the DNN model, the dataset is generated over 1,000,000, 90% of which are used for training while the remaining 10% are allocated for validation. Additionally, we construct 100 distinct datasets to evaluate the performance of the trained DNN model. Our objective is to predict the secure next node through the DNN model accurately. The parameters employed for DNN training are detailed in Table 8.  
To demonstrate the effectiveness of the proposed algorithm (DLSMR with TD-PSO), we compare its performance with the multicast ad hoc on-demand distance vector (MAODV) routing protocol with or without TD-PSO clustering protocol. First, we evaluate the impact of the number of iterations on the maximum cost of the TD-PSO clustering algorithm in Figure 8. As can be observed in Figure 8, the proposed \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Value** \\ \hline Simulator & NS-3 simulator \\ Simulation area & \(1000\times 1000\) m\({}^{2}\) \\ Packet size & \(1024\) bits \\ Mobility model & RPGM and RWP \\ Transmission range & \(250\) m \\ Simulation time & \(200\) s \\ Session length & \(5\) s \\ Number of nodes & \([30,50,100]\) \\ Wormhole pairs & \(1\) (Wormhole nodes 2) \\ Node’s speed range & \([15\):\(15\):\(75]\) (km/h) \\ Receive signal strength indicator (RSSI) threshold & \(-80\) dBm \\ MAC protocol & \(802.11\)a \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters and simulation environments. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Dataset & 1,000,000 \\ Epoch & \(50\) \\ Batch size & \(256\) \\ Optimizer & Adam \\ Initial learning rate & \(0.00001\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: DNN training parameters. Algorithm 1 converges at the fifth iteration with the number of population (nPop) of 100, which shows the proposed TD-PSO for the clustering protocol is efficient to find the optimal value. The reason is that the algorithm has a higher chance of generating a solution close to the global optimum during the initial stages. Moreover, the algorithm with a population of 100 outperforms the algorithm with a population of 50. The reason is that when the population size increases from 50 to 100, the algorithm has a larger set of candidate solutions to find the optimal solution. Figure 9 shows the comparison of the average number of cluster head changes in each session as a function of node speed. As can be seen in Figure 9, when the number of nodes increases from 30 to 100, the average number of cluster head changes increases. Furthermore, when node speed increases from 15 to 75 km/h, the average number of cluster head changes also increases. The reason is that, when the node's speed increases, the node's relative position can change quickly. Therefore, the nodes' arrangement and connections can also be changed rapidly. In the clustering protocol, if nodes are moving quickly, the optimal choice for the cluster head can change frequently as nodes move in and out of range of each other. This might require frequent re-election of the cluster head, increasing the average number of cluster head changes. Additionally, higher speeds might lead to increased link breakages, which would necessitate the formation of new clusters, further increasing the frequency of cluster head changes. Furthermore, when comparing the mobility models, the proposed protocol with the RPGM model outperforms that with the RWP model. In RPGM, nodes in a group follow a predefined reference point, resulting in more stable network topology and less frequent cluster head changes.