## 4 Results and Discussion  
The proposed MFA-AOA optimized protocol, as well as the existing Hybrid Red Deer-Simulated Annealing (RDSA) [34], Genetic Algorithm-PSO (GAPSO) [35], Clan Separator Elephant Herding Optimization operator (CSEHO) [36], and Meth Flame-GA (MFGA) [37]techniques, are tested using MATLAB 2019b. The simulation setup consists of 500 SNs distributed randomly in a network area of 1500 \(\times\) 1500 square meters, with one sink node at 500 m. Three thousand five hundred rounds were employed in the implementation process. In addition, Table 1 shows the simulation setup used to implement the proposed MFA-AOA optimized protocol. The proposed MFA-AOA optimized protocol and the existing RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques are first examined in terms of network lifetime, energy usage, throughput, and packet delay with SN density. Figures 3 and 4 show the comparison of the proposed MFA-AOA optimized routing protocol with existing protocols in terms of network lifespan, energy usage, and density of SN. Since it included the advantages of MFA into the AOA for determining the superior nodes of the network as CH, the network lifespan of the proposed MFA-AOA optimized protocol and the existing methods demonstrate a better life with a systematic increment of SNs. Furthermore, this dominance of the proposed MFA-AOA optimized protocol is achieved by replacing MFA's searching phase with AOA's hunting phase throughout the search space to preserve the trade-off between exploitation and exploration. The proposed MFA-AOA optimized protocol and the existing schemes' energy consumptions are shown to grow consistently as SN density increases. However, because it comprises different techniques that combine candidate solutions into prospective offspring solutions, the proposed MFA-AOA optimized protocol can sustain energy consumption. This analysis of future offspring focused on identifying and eliminating the worst solutions that avoid the least critical SNs from being chosen as CFs. The proposed MFA-AOA optimized protocol enhances network lifespan by 9.78%, 11.24%, and 14.25% with varied density of SNs, compared to the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques. With different densities of SNs, the proposed MFA-AOA optimized routing protocol reduces energy consumption by 10.22%, 11.26%, and 14.28%, which is better than the existing systems. Figures 5 and 6 compare proposed MFA-AOA optimized protocols with existing protocols in terms of throughput and packet delaying of SN densities. The proposed MFA-AOA optimized protocol's throughput is verified to be superior to the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques with scaling increases in the density of SNs. Furthermore, this capacity of the proposed protocol is improved proportionally because of the benefits of hunting, which assisted in better CH selection and prevented packet drop to an expected level. Figure 4: Density of sensor nodes vs. Energy consumption [34; 35; 36; 37]. Figure 5: Density of sensor nodes vs. throughput [34; 35; 36; 37]. Similarly, the proposed MFA-AOA optimized protocol achieves significantly lower packet latency. The selection of prospective CH in the network was always ensured by categorizing solutions and creating important offspring solutions. As a result, the proposed MFA-AOA optimized protocol enhances throughput by 11.36%, 12.79%, and 14.45%, respectively, when compared to the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques. Furthermore, with variable densities of SNs, the proposed MFA-AOA optimized protocol reduces packet latency by 9.27%, 10.34%, and 12.78%, which is better than the existing systems. The proposed MFA-AOA optimized protocol, as well as the RDSA [34], GAPSO [35], CSEHO [36], and MFOGA [37] techniques, are compared in terms of the number of living and dead SNs, throughput, and mean residual energy over several rounds.