## 5 Results and Discussion
### Network Lifetime  
By considering various proportions of advanced nodes in the simulation, Figure 3 shows the advantages of the EPOA-CHS algorithm in terms of network lifetime. The EPOA-CHS method significantly extends the network lifespan in Figure 2(a) where the energy multiplier for advanced nodes is \(\alpha=0\) and the proportion of advanced nodes is \(\text{m}=0\). Specifically, it shows a relative increase of 246.4%, 214.2%, 389.0%, and 65.0% compared to the SEP, DEEC, Z-SEP, and PSO-ECSM algorithms, respectively. Moving to Figure 2(b), with \(\text{m}=0.1\) and \(\alpha=2\), the EPOA-CHS algorithm still outperforms the other protocols with an increase of 100.1%, 116.8%, 91.2%, and 22.4% in network lifespan compared to SEP, DEEC, Z-SEP, and PSO-ECSM, respectively. Similarly, in Figure 2(c) (\(\text{m}=0.2\) and \(\alpha=3\)) and Figure 2(d) (\(\text{m}=0.3\) and \(\alpha=1.5\)), the EPOA-CHS algorithm maintains its superiority, exhibiting improvements of 73.7%, 131.4%, 103.3%, and 21.5% in network lifespan over SEP, DEEC, Z-SEP, and PSO-ECSM for \(\text{m}=0.2\), and 70.2%, 120.2%, 91.2%, and 21.2% for \(\text{m}=0.3\), respectively. The results clearly demonstrate that the EPOA-CHS algorithm surpasses the tested protocols in terms of efficacy and network lifespan extension.  
Table 2 and Figure 4 show the simulation results for the network life cycle at various percentages of advanced nodes for the first node to die (FND, First Node Death), 50% of nodes to die (HND, Half Nodes Death), 70% of nodes to die (MND, Most Nodes Death), and all nodes to die (LND, Last Node Death). And as can be seen from these two tables, we perform better on the time of death for other protocols. And the table also clearly shows that the EPOA-CHS algorithm, compared with other protocols, is also dominant in the unstable time of the network. This is because EPA-CHS takes into account the heterogeneity and global optimization ability, which makes the distribution of node energy use more balanced and reduces the unstable period of the network.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{**No. of Rounds**} \\ \hline
**Cases for Heterogeneity** & **Protocol** & **FND** & **HND** & **MND** & **LND** \\ \hline \multirow{8}{*}{\(\text{m}=0\), \(\boldsymbol{\alpha=0}\)} & SEP & 840 & 1158 & 1232 & 1837 \\  & DEEC & 926 & 1216 & 1321 & 1888 \\  & Z-SEP & 595 & 1498 & 1724 & 2266 \\  & PSO-ECSM & 1763 & 2139 & 2285 & 2384 \\  & EPOA-CHS & 2910 & 2417 & 2442 & 2484 \\  & SEP & 1116 & 1302 & 1372 & 5383 \\  & DEEC & 1030 & 1259 & 1361 & 5341 \\ \hline \multirow{8}{*}{\(\text{m}=0.1\), \(\boldsymbol{\alpha=2}\)} & Z-SEP & 1168 & 1923 & 2086 & 6450 \\  & PSO-ECSM & 1825 & 2212 & 2316 & 7055 \\ \cline{1-1}  & EPOA-CHS & 2233 & 2441 & 2452 & 7373 \\ \cline{1-1}  & SEP & 1291 & 1486 & 1676 & 3888 \\ \cline{1-1}  & DEEC & 969 & 1274 & 1699 & 4165 \\ \hline \multirow{8}{*}{\(\text{m}=0.2\), \(\boldsymbol{\alpha=3}\)} & Z-SEP & 1103 & 2055 & 2256 & 5638 \\  & PSO-ECSM & 1846 & 2269 & 2402 & 5989 \\ \cline{1-1}  & EPOA-CHS & 2243 & 2445 & 2482 & 6198 \\ \cline{1-1}  & SEP & 1312 & 1491 & 1652 & 7480 \\ \cline{1-1}  & DEEC & 1014 & 1243 & 1448 & 8088 \\ \hline \multirow{8}{*}{\(\text{m}=0.3\), \(\boldsymbol{\alpha=1.5}\)} & Z-SEP & 1168 & 1951 & 2125 & 8677 \\ \cline{1-1}  & PSO-ECSM & 1842 & 2253 & 2340 & 9436 \\ \cline{1-1}  & EPOA-CHS & 2233 & 2443 & 2458 & 9856 \\ \cline{1-1} \cline{2-5}  & EPOA-CHS & 2243 & 2443 & 2458 & 9856 \\ \cline{1-1} \cline{2-5}  & SEP & 1168 & 1923 & 2086 & 6450 \\ \cline{1-1}  & EPOA-CHS & 1825 & 2212 & 2316 & 7055 \\ \cline{1-1} \cline{2-5}  & EPOA-CHS & 2233 & 2441 & 2452 & 7373 \\ \cline{1-1} \cline{2-5}  & EPOA-CHS & 2243 & 2441 & 2458 & 9856 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Number of rounds and network life cycle.