# A Novel RPL Algorithm Based on Chaotic Genetic Algorithm
## 4 Performance Evaluation
### Results and Discuss  
(1) Success rate  
Figure 3 illustrates the success rate of RPL-CGA, ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4 \(\times\) RER under several different node number circumstances. It can be seen that under low node number circumstances, the success rate is high. In contrast, the average success rate is low. Furthermore, in the case of various node densities, the average success rates of RPL-CGA are all much higher than that of ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4 \(\times\) RER, because ETXOF merely evaluates ETX during network topology construction and the preferred parent selection period. In that way, the selected preferred parent may encounter higher QL, HC, or EED, or lower RER. 0.8 \(\times\) ETX + 0.2 \(\times\) RER and 0.6 \(\times\) HC + 0.4 \(\times\) RER do not consider QL and EED during network topology construction and the preferred parent selection period. So, the selected preferred parent may encounter higher QL or EED. Meanwhile, it is too subjective that every weighting factor is determined by expert personal experience. Moreover, the weighting factors cannot dynamically adjust according to network changes. However, RPL-CGA can consider QL, EED, NE, HC, and ETX at the same time, determine respective weighting factors according to on chaotic genetic algorithm, and select the node with the lowest value of Equation (19) as the next hop (preferred parent). In this way, RPL-CGA can improve the success rate remarkably. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Network scenario (m\({}^{2}\)) & 500 \(\times\) 500 \\ Dead node & Residual energy less than 5\% of its initial energy \\ Maximum number of iteration \(k\) & 100 \\ Cross probability \(P_{c}\) & 0.75 \\ Mutation probability \(P_{m}\) & 0.001 \\ Population size \(w\) & 100 \\ Simulation time (s) & 3000 \\ Maximum queue length (packet number) & 16 \\ Minimum queue length (packet number) & 0 \\ Communication radius (m) & 150 \\ Node number & 50, 100, 150, 200, 250, 300, 350, 400 \\ Packet size (kbits) & 0.1 \\ Energy loss for relaying \(y\) bit message & \(E(y,d)\) \\ \hline \end{tabular}
\end{table} 
Table 2: Experiment parameters. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline \(E_{elec}\) & 50 nJ/bit \\ \(\varepsilon_{amp}\) & 10 pJ/bit/m\({}^{2}\) \\ \(\varepsilon_{fs}\) & 0.0013 pJ/bit/m\({}^{4}\) \\ \(d_{0}\) & 87 m \\ \(d\) & communication distance \\ \hline \end{tabular}
\end{table} 
Table 3: The value of each parameter in \(E(y,d)\). 2. Average end-to-end delay Figure 4 shows the average end-to-end delays of RPL-CGA, ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4 \(\times\) RER under several different node number circumstances. It can be seen that with low node numbers, the average end-to-end delay is small. But the average end-to-end delay increases as the number of nodes in the network increases. Meanwhile, the average end-to-end delay of ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4 \(\times\) RER are all much higher than that of RPL-CGA at different node numbers. It is clear that RPL-CGA can effectively enhance the real-time performance of LLNs. 3. Network lifetime The average residual energy of nodes or average number of dead nodes in the network can clearly estimate the length of the network lifetime. Figures 5 and 6 show RPL-CGA, ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4 \(\times\) RER of these two statistical experimental indicators under several different node number circumstances. It can be seen that the statistical experimental indicators of ETXOF, 0.8 \(\times\) ETX + 0.2 \(\times\) RER, and 0.6 \(\times\) HC + 0.4\(\times\) RER are much lower than that of RPL-CGA at different node density circumstances. Therefore, by employing the chaotic genetic algorithm to determine the weighting factors of QL, EED, RER, HC, and ETX, RPL-CGA can prolong network lifetime significantly.