## 5 Simulation Results
### Performance Evaluation
\[E_{e}=\frac{\sum\textit{The number of packets send to the BS}}{\sum\textit{Total energy consumption}}\] (17)
* Packet loss rate (\(\textit{PLR}\)): The goal of using this metric, calculated by a formula given in Equation (18), is informing the rate of packet losses due to the functionality of the implemented protocol. We have tested the worked algorithms in terms of packet loss rate versus the number of nodes. \[\textit{PLR}=1-\frac{\sum\textit{The number of packets received by the BS}}{\sum\textit{The number of packets send to the BS}}\] (18) As seen in Figure 18b, our proposed algorithm produces the least packet loss rate among the algorithms. As the number of nodes increases in the network, the packet loss rate also increases due to the events of packet collisions and uncorrect packet deliverations. * Number of selected CHs and advanced energy usage rate (%): We also evaluate the advanced energy usage rate as the percentage in the network. We formulate this ratio with the abbreviated name \(AEUR\), as given in Equation (19). Normally, CHs are selected from normal nodes because there is no heterogeneity in other algorithms. However, we used the other algorithms for the comparison terms to be equal. Thus, we distributed the same number of advanced nodes to  
Figure 18: Comparison of the proposed scheme with existing algorithms versus energy efficiency and packet loss rate results: (**a**) Energy efficiency; and, (**b**) Packet loss rate. the network area as our algorithm. We have calculated the number of selected CHs using the algorithms varying from 40 to 200 advanced nodes for scenario 1 (see Figure 19a) and scenario 2 (see Figure 19b). The higher this score, the more performance on behalf of the energy of the advanced nodes is proportionally used in the network. If more CH is selected than the existing advanced nodes, the energy of the advanced nodes is not wasted. As seen in Figure 19a,b, when using our proposed algorithm, the number of selected CHs is higher for both scenarios when compared to other algorithms. However, in scenario 2, the number of selected CHs decreases because of the distance factor and the uncontrolable effect of selecting CHs (see Figure 19b). Tables 7 and 8 present the advanced energy usage results for scenario 1 and scenario 2, respectively. According to the results, it can be said that our proposal combined scheme has achieved 88.1 and 72.8 \(AEUR\) for scenario 1 and scenario 2, respectively. \[ \begin{array}{c}\textit{dvanced energy usage rate}(\%)=AEUR\\ =\sum\frac{\textit{The number of selected CHs}}{\textit{The total number of advanced nodes}}\times 100\end{array}  \tag{19}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**The Number of Total**} & \multicolumn{6}{c}{**The Number of Selected CHs**} \\ \cline{2-7}  & **Proposed** & **Starfish** & **BI-DFAMDT** & **nCRO-UCRA** & **EPMS-PSO** & **IACO** \\ \hline
40 & 29 & 23 & 19 & 19 & 17 & 16 \\
80 & 62 & 58 & 55 & 51 & 47 & 45 \\
120 & 102 & 95 & 90 & 78 & 71 & 65 \\
160 & 148 & 138 & 129 & 120 & 114 & 99 \\
200 & 188 & 176 & 168 & 155 & 147 & 130 \\ Total & 529 & 490 & 461 & 423 & 396 & 355 \\ \(AEUR(\%)\) & 88.1 & 81.6 & 76.8 & 70.5 & 66.0 & 59.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Advanced energy usage results for scenario 1. Figure 19: Comparison of the proposed scheme with existing algorithms versus number of selected CHs: (**a**) Simulation graph for scenario 1; and, (**b**) Simulation graph for scenario 2.