## 5 Experimental Study
### Route Constructure in Consideration of a Trade-off between Energy Consumption and Lifetime  
In this simulation, we further consider nodal remaining energy. We fix \(r_{c}\) to 50 m, and set \(k\) to be 7 and \(q\) to be 20 nJ/bit and 80 nJ/bit respectively. As previously mentioned, problem (10) is a multi-objective optimization problem and its Pareto optimal solutions are multiple. Figure 8 presents all Pareto optimal solutions in a certain stage where each node is left with different energy, with \(\varepsilon\) to be 1.5 and \(q\) to be 20 nJ/bit and 80 nJ/bit, respectively. Figure 8: Pareto Front when \(\varepsilon=1.5\). Figure 7: Impact of \(r_{c}\) to energy consumption when \(k=15\). Then, in order to achieve better Pareto optimal solutions, we further conduct experiments under four different penalty functions proposed in this paper. The experimental results are shown in Table 2 as follows. The table shows the number of the feasible solution we can get under the iteration in the case of 100, 300 and 500, when using different penalty functions and the value of \(\varepsilon\) changing from 1.1 to 1.8. According to the experimental results shown in Table 2, we can see that in different iterations, the four different penalty functions exhibit different effects. After a relatively small number of iterations, for example, 100 times, the use of penalty function P1 can give more feasible solutions. As the number of iterations increases, P3 and P4 begin to gradually show better results. After 300 and 500 iterations, respectively, P3 and P4 achieve the most feasible solutions. The results illustrate well that in a relatively small number of iterations, in order to converge as soon as possible, we maximize the degree of punishment for the particles' constraint violations. With the increase of the number of iterations, we should also take into account the optimal information carried by these particles, so the more the number of iteration increases, the smaller the intensity of the punishment is. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline  & \multicolumn{3}{c}{\(\varepsilon\) = 1.1} & \multicolumn{3}{c}{\(\varepsilon\) = 1.2} & \multicolumn{3}{c}{\(\varepsilon\) = 1.3} & \multicolumn{3}{c}{\(\varepsilon\) = 1.4} \\ \cline{2-13}  & **100** & **300** & **500** & **100** & **300** & **500** & **100** & **300** & **500** & **100** & **300** & **500** \\ \hline
**P1** & 5.61 & 5.65 & 5.87 & 5.82 & 5.82 & 5.95 & 5.38 & 5.61 & 5.88 & 5.61 & 5.78 & 6.10 \\
**P2** & 4.17 & 4.88 & 4.89 & 4.32 & 4.56 & 5.00 & 4.16 & 4.61 & 5.03 & 4.41 & 4.51 & 5.23 \\
**P3** & 5.23 & 5.73 & 5.82 & 5.54 & 5.86 & 5.88 & 5.43 & 5.71 & 5.95 & 5.36 & 6.02 & 6.11 \\
**P4** & 5.16 & 5.49 & 6.65 & 5.64 & 5.80 & 5.96 & 5.31 & 6.21 & 6.22 & 5.58 & 5.75 & 6.26 \\ \hline  & \multicolumn{3}{c}{\(\varepsilon\) = 1.5} & \multicolumn{3}{c}{\(\varepsilon\) = 1.6} & \multicolumn{3}{c}{\(\varepsilon\) = 1.7} & \multicolumn{3}{c}{\(\varepsilon\) = 1.8} \\ \cline{2-13}  & **100** & **300** & **500** & **100** & **300** & **500** & **100** & **300** & **500** & **100** & **300** & **500** \\ \hline
**P1** & 5.83 & 5.90 & 6.11 & 5.65 & 5.80 & 6.01 & 5.71 & 5.85 & 5.96 & 5.66 & 5.72 & 5.95 \\
**P2** & 4.43 & 4.66 & 5.40 & 4.48 & 4.74 & 4.86 & 4.33 & 4.55 & 4.80 & 4.37 & 4.68 & 4.69 \\
**P3** & 5.73 & 6.09 & 6.13 & 5.64 & 5.85 & 6.03 & 5.77 & 5.86 & 5.90 & 5.64 & 5.81 & 5.86 \\
**P4** & 5.50 & 5.63 & 6.35 & 5.62 & 5.68 & 5.78 & 5.54 & 5.80 & 5.99 & 5.63 & 5.77 & 5.97 \\ \hline \end{tabular}
\end{table} 
Table 2: The number of Pareto optimal solutions obtained by four different penalty functions. Figure 9: Impact of \(\varepsilon\) on network lifetime. We can also see that when the value of \(\varepsilon\) is 1.5, the number of the feasible solutions is the greatest. This occurs because as the \(\varepsilon\) value is too big, the energy consumption constraint relaxes, and the lifetime becomes smaller. The Pareto solution requires minimal energy consumption and maximized lifetime.