# Node Deployment of Marine Monitoring Networks: A Multiobjective Optimization Scheme
## 5 Simulations and Discussion
### Performance Validation in Small-Scale and Medium-Scale Networks  
We first evaluate the network performance of small-scale network scenarios with a small number of nodes, i.e., Scenario 0 and Scenario 1. Let us take Scenario 0 as an example. The results obtained by [PERSON] in Figure 4 show the deployment solution of Scenario 0. The deployment cost of this solution is 68, which is the minimum cost in Scenario 0. Similarly, the energy consumption is \(8.18\times 10^{-5}\), which is also the lowest one among all deployment plans. In this simple case, the optimization solution obtained by [PERSON] is optimal, compared with the results obtained from the exhaustive search.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scenario Index**} & \multicolumn{6}{c}{**Number of**} \\ \cline{2-7}  & **BS** & **MP** & **CLs of ARN** & **CLs of ECN** & **CLs of SSN** & **CLs of URN** \\ \hline
0 & 1 & 2 & 2 & 3 & 4 & 6 \\
1 & 1 & 2 & 1 & 2 & 10 & 15 \\
2 & 1 & 4 & 1 & 2 & 20 & 25 \\
3 & 1 & 6 & 2 & 8 & 20 & 30 \\
4 & 1 & 8 & 2 & 8 & 25 & 40 \\
5 & 1 & 10 & 3 & 5 & 35 & 50 \\
6 & 1 & 12 & 3 & 10 & 40 & 60 \\
7 & 1 & 15 & 3 & 9 & 50 & 70 \\
8 & 1 & 20 & 4 & 12 & 80 & 100 \\
9 & 1 & 25 & 5 & 16 & 100 & 120 \\
10 & 1 & 35 & 7 & 25 & 125 & 150 \\
11 & 1 & 50 & 7 & 25 & 170 & 200 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The setting of simulated scenarios. CLs—Candidate Locations.  
Figure 3: The impacts of \(\omega\): DC stands for Deployment Cost, and EC stands for Energy Consumption. See. is the abbreviation of Scenario.  
We then compare the solutions of the MO problem (P1) with each of the subproblems of MO, i.e., to minimize the cost (P2) or to minimize the energy consumption (P3) under different scenarios from scenario 1 to 7. The results are compared in Figure 5. As shown in Figure 4(a), the deployment cost of P1 is slightly greater than that of P2, but smaller than that of P3. Figure 4(b) shows that the energy consumption of P1 is similar to that of P3, but much smaller than that of P2. Correspondingly, the network lifetime of P1 is much greater than that of P2, while smaller-than or equal-to that of P3, as shown in Figure 4(c). Thus, using P1, a longer network lifetime can be achieved with a lower deployment cost. Again, Gurobi can achieve the optimal solution.  
Figure 4: The optimal solution of Scenario (\(\mathbb{C}_{net}=68\) gcu, \(\mathbb{E}_{max}=8.18\times 10^{-5}\%\)).  
Figure 5: Comparison of P1, P2, and P3 in terms of the deployment cost, energy consumption, and network lifetime.  
Based on the above process, a series of small-scale network simulation are carried out to verify the performance of the algorithm and compare it with the exhaustive search and Gurobi. As shown in Figure 6, the results of the proposed algorithm in Scenarios 0-2 approaches that of the exhaustive search and Gurobi. For instance, the optimal solution of the AC-ETO in Scenario 0 is 68.818, which equals to that of the exhaustive search. Thus, the solutions of the algorithm in small-scale networks are close to optimal. As the scale of the network increase, it is difficult to obtain the optimal solutions by the exhaustive search. We further compare the solutions of the algorithm with that of the Gurobi in Scenarios 3-4. Figure 6 shows that the results of the algorithm is very close to that of Gurobi. Therefore, the optimization solution of the AC-ETO are close to optimal in small-scale and medium-scale networks.