# Data Collection for Target Localization in Ocean Monitoring Radar-Communication Networks
## 3 Method
### Update Parent Population Parameter
#### 3.4.2 Case with More than One Nondomination Level  
Since we have to eliminate only one solution from \(\hat{\mathbf{U}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\), the last non-domination level is chosen to process. Specifically, if the last non-domination level contains only one solution of \(\mathbf{l}_{\mathbf{U}}^{a}\) and \(\mathbf{p}^{a}\), the density of the sub-region \(\psi_{l}\) has to be investigated first. In this case, if the associated sub-region \(\psi_{l}\) has more than one solution, \(\hat{\mathbf{U}}_{\mathbf{U}}^{a}\) and \(\mathbf{p}^{a}\) will be eliminated from \(\hat{\mathbf{U}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\). In terms of convergence, better solutions inside of \(\psi_{l}\) will be contained, and the solutions can not provide further useful information. Otherwise, \(\psi_{l}\) might not be fully exploited in the object space, which can be treated as the isolated sub-region. \(\hat{\mathbf{l}}_{\mathbf{U}}^{a}\) and \(\mathbf{p}^{a}\) play an important role in population diversity which will be saved to the next round. Then, the worst solutions \(\{\mathbf{l}_{\mathbf{U}}^{\prime},\mathbf{p}^{\prime}\}\in E\) which are obtained in the most crowded sub-region \(\psi_{h}\) that are included in the current worst non-domination level are eliminated from \(\{\hat{\mathbf{U}}^{hp},\mathbf{p}^{hp}\}\) based on the following  
\[\{\mathbf{l}_{\mathbf{U}}^{\prime},\mathbf{p}^{\prime}\}=\max_{\{\mathbf{l}_{\mathbf{U}},\mathbf{p}\} \in E}d^{pbi}(\mathbf{l}_{\mathbf{U}},\mathbf{p}|(\mathbf{w}^{h},\mathbf{z}^{*})). \tag{19}\]  
If the last non-domination level contains more than one solution. There are also two cases that have to be considered. If more than one solution is related to the most crowded sub-region \(\psi_{h}\), the worst solution \(\{\mathbf{l}_{\mathbf{U}}^{\prime},\mathbf{p}^{\prime}\}\in\psi_{h}\) which has the largest PBI value is eliminated from \(\{\hat{\mathbf{l}}_{\mathbf{U}}^{hp},\mathbf{p}^{hp}\}\) according to (18). Otherwise, if every member is associated with an isolated sub-region, the solutions will be saved for the next round and the worst solution \(\{\mathbf{l}_{\mathbf{U}}^{\prime},\mathbf{p}^{\prime}\}\) is eliminated from \(\{\hat{\mathbf{l}}_{\mathbf{U}}^{hp},\mathbf{p}^{hp}\}\). Once the worst solution is eliminated from \(\hat{\mathbf{l}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\), the non-domination level structure is updated to form the parent population \(\mathbf{l}_{\mathbf{U}}^{(l+1)}\) and \(\mathbf{p}^{(l+1)}\). Furthermore, if every member in the last nomination level is associated with an isolated sub-region, the worst solution \(\{\mathbf{l}_{\mathbf{U}}^{\prime},\mathbf{p}^{\prime}\}\) will be eliminated from \(\{\hat{\mathbf{l}}_{\mathbf{U}}^{hp},\mathbf{p}^{hp}\}\). Considering the infeasible solutions associated with an isolated sub-region is given a second chance to survive in the process. Specifically, the solutions in \(\hat{\mathbf{l}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\) which has the largest \(CV\) is identified first. The solutions will be considered the current worst solutions if they are not associated with an isolated sub-region. Otherwise, they will be preserved for later consideration to guarantee population density. And the solution in \(\hat{\mathbf{l}}_{\mathbf{U}}^{\prime}\) and \(\mathbf{p}^{\prime}\) which has the second largest solution of (16) will be obtained instead. Whether the solutions are treated as \(\mathbf{l}_{\mathbf{U}}^{\prime}\) and \(\mathbf{p}^{\prime}\) depends on whether the solutions are associated with an isolated sub-region. Moreover, if every infeasible solution in \(\hat{\mathbf{l}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\) is associated with an isolated sub-region, the solutions with the largest \(CV\) will be considered as \(\mathbf{l}_{\mathbf{U}}^{\prime}\) and \(\mathbf{p}^{\prime}\) and then be eliminated from \(\hat{\mathbf{l}}_{\mathbf{U}}^{hp}\) and \(\mathbf{p}^{hp}\).