## 4 Simulation and Results Discussion  
The performance of the GA-based MSTs is first established for convergence using simulation. Secondly, the performance analysis of the proposed routing protocol is achieved with simulations using the performance metrics of network lifetime, number of alive sensor nodes (NAN), energy consumption, and computation time. These performance metrics of the CRPLEOGALSPI are compared with that of the recent CRPLOGARL [13] as a way of validation. The lifetime of the network is calculated as the time taken for the sink not to be reachable by the alive sensor node(s). The NAN is the number of alive sensor nodes at the lifetime of the network. The CRPLEOGALSPI and CRPLOGARL are coded with python 3.8 under the \"PyCharm\" development environment. The graphical layout of the WSN is implemented with the python NetworkX module [52]. The python codes are executed on the SLURM (Simple Linux Utility for Resource Management) cluster on the IRIT's OSIRIM platform. The Computer nodes of the OSIRIM platform adopted are the 4 AMD EPYC 7402 bi-processor computing nodes at 2.8 GHz, with 48 processors and 512 GB of RAM each. These nodes enable more than 24 threads and/or 192 GB of RAM for the same process. The simulation parameters used to carry out the performance analysis and the network graph of the deployed WSN are shown in Table 2 and Figure 4, respectively. Figure 4: Network Graph of the deployed WSN. The performance of the GA-based MSTs for the deployed network graph of the WSN given in Figure 4 is shown in Figure 5.  
As seen in Figure 5, the GA-based MSTs is able to find 376 MSTs of the network graph for 1000 generations. This also implies the convergence of the solution of the GA-based MSTs in a reasonable number of generations. The GA-based MSTs can work for all MSTs problems in polynomial time. The number of alive sensor nodes of the WSN at each round of data transmission of the proposed routing protocol, CRPLEOGALSPI, as compared with CRPLOGARL when the initial sensor nodes energies and the packet generation rate of the sensor nodes are set arbitrarily at 10 J and 1/s, respectively, as shown in Figure 6. As seen in Figure 6, the number of alive sensor nodes of both protocols remains constant for certain rounds of \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Number of sink & 1 \\ Number of sensors & 100 \\ Deployment Area of WSN & 1000 m \(\times\) 1000 m \\ Deployment of Sensor nodes & Random \\ \(x-y\) coordinate of sink & \((500,500)\) \\ Maximum transmission range & 150 m \\ Bandwidth of links & 1 kbps \\ Size of data packet & 1024 bits \\ Sensors initial residual energy & 1 J to 10 J \\ Rate of packet generation & 1/s to 10/s \\ \(e_{mp}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \(e_{fs}\) & 10 pJ/bit/m\({}^{2}\) \\ \(E_{elec}\) & 50 nJ/bit \\ Discount factor & 0.9 \\ Epsilon & 0.1 \\ Sample size & 100 \\ Maximum generations & 1000 \\ Rate of crossover & 0.1 \\ Rate of Mutation & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Simulation Parameters. Figure 5: Number of MSTs with Number of Generations. data transmission and decreases subsequently. This behavior continues for both protocols until the network graph is disconnected. When the network graph is disconnected, there is no path to reach the sink located at the \(x-y\) coordinates of \((500,500)\), as shown in Figure 4. The deaths of the sensor nodes are because of the depletion of the energy of the sensor nodes as the round of data transmission increases. Consequently, on average, it took CRPLEOGALSPI more rounds of data transmission for the sink not to be reachable by alive sensor nodes. This is because CRPLEOGALSPI converges faster to the RT, which maximizes the network lifetime while minimizing the network energy consumption when compared to CRPLOGARL. This shows that the LSPI used in implementing CRPLEOGALSPI utilizes data effectively and efficiently when compared to the baseline Q-learning used to implement the CRPLOGARL.