## 4 Results and Discussion
The comparison of the number of living SNs and the number of dead SNs deployed in the network of the proposed MFA-AOA optimized protocol and the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques are shown in Figures 7 and 8. As the network's energy is saved by choosing only the possible SNs as CH throughout the clustering process, the proposed MOA-AOA optimized routing protocol is superior to the state-of-art schemes in terms of the number of alive nodes maintained. This selection technique eliminates unnecessary clustering because the worse SNs are not picked as CH nodes. It keeps the network's energy at a reasonable level by preventing wasteful energy-training in the SN. As a result, the proposed MFA-AOA protocol maintains the number of living nodes by 12.54%, 13.63%, and 15.28%, respectively, compared to the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques. Furthermore, the proposed MFA-AOA protocol reduces the number of dead nodes by 11.46%, 13.28%, and 14.63% with varied rounds, which is superior to the existing methods. Figures 9 and 10 show the comparison of throughput and mean residual energy of the proposed MFA-AOA optimized protocol as well as the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques with different rounds. Figure 6: Density of sensor nodes vs. Packet Delay [34; 35; 36; 37]. Figure 8: Different Number of Rounds vs. Dead sensor nodes [34; 35; 36; 37]. Figure 7: Different Number of Rounds vs. Alive sensor nodes [34; 35; 36; 37]. Figure 9: Different Number of Rounds vs. Throughput [34; 35; 36; 37]. The proposed MFA-AOA strategy outperforms the other schemes in terms of throughput because the local search ability initiated by MFA into AOA allows for enhanced CH selection. MFA's local search capability is also essential to minimize local points of optimization problem and stagnation to the maximum level, regardless of the number of implementation cycles performed. As a result, the proposed MFA-AOA protocol enhances throughput by 8.52%, 10.98%, and 12.69%, respectively, compared to the existing techniques. In addition, the mean residual energy of the proposed MFA-AOA protocol improves by 9.56%, 11.78%, and 13.76% with a varied number of rounds, which is superior to the benchmarked methods. Figure 11 shows the convergence rate of the proposed MFA-AOA algorithm for 100 nodes. The performance of MFA, AOA, and hybrid MFA-AOA is calculated at the 15 th iteration. Hybrid MFA-AOA provides an optimal path with the minimum time consumption compared to the individual MFA and AOA algorithm performances. Moreover, the number of rounds until the first node death, half of the node death, and the last node death in the network are explored, and the proposed MFA-AOA protocol is compared with the existing state-of-art methods [34; 35; 36; 37]. Figure 11: Number of iterations vs. Fitness. Figure 10: Different Number of Rounds vs. Mean Residual Energy [34; 35; 36; 37]. From Figure 12, the proposed MFA-AOA protocol experiences the first node death at round 3400, whereas the first SN death of the compared techniques occurs between rounds 2695 and 3200. The adaptive technique included by MFA into the basic AOA scheme throughout the exploitation process is primarily responsible for the proposed MFA-AOA protocol's remarkable performance. Figure 13 shows that the proposed MFA-AOA protocol is estimated to be half of the node's death by round 4250, whereas the other techniques have half of the node's death between 3520 and 3892 rounds. The proposed AOA protocol's critical performance is achieved by including a flexible exploitation mechanism that varies based on the potentiality of solutions found during the mating phase. Furthermore, Figure 14 shows that the proposed AOA protocol's last node death occurs at 4450 rounds, whereas the compared schemes occur between 3500 and 4126 rounds. Figure 12: Number of rounds until first node death [34; 35; 36; 37]. Figure 13: Number of rounds until half nodes death [34; 35; 36; 37].