## 6 Conclusions  
In this study, two schemes of GS deployment for the tracking of LEO constellations are presented, namely global deployment and regional deployment. Firstly, for global deployment, GS number and placement are optimized based on evolutionary algorithms. For triple-heavy observing coverage (3-HC), the optimization process includes two objectives (i.e., the observing rate and the number of GSs used for deployment) in addition to another sub-objective (the minimum distance between the two nearest GSs) in order to avoid the concentration of GSs in the same place. Subsequently, 95 ground stations formed the optimal deployment to reach 3-HC. The 95 GSs for 3-HC reached a 97.63% observing rate and 92.01% was obtained for quadruple coverage. The distribution of SPDOP, when only the GSs are considered, is discussed. Secondly, for regional deployment and using three scenarios according to the number of GSs used, SPDOP decreases with the increasing number of GSs. A regional area in East Asia is chosen as the local area for deployment under three scenarios with 15, 20 and 25 ground stations used. The optimal SPDOP values are 2.05, 1.40 and 1.33, respectively. The results were enhanced with ISLs, where the SPDOP mean value was reduced from 2.06 to 0.44 for 15 GSs, from 1.40 to 0.42 for 20 GSs, and from 1.33 to 0.41 for 25 GSs. The complexity of GS deployment for LEO satellite constellations is due to the majority of the globe being occupied by oceans and seas. The choice of the best method to determine the optimal deployment in addressing this problem is not clear. As seen from the results obtained in this study, evolutionary algorithms present a suitable solution. These algorithms can be applied to solve real problems in the field of navigation with LEO satellites. In terms of future work, it is recommended that the developed algorithm be reused for other scenarios such as 4-heavy observing coverage or for regional deployment in other regions, even without a fixed number of GSs. Furthermore, the hybrid method of the evolutionary algorithms used presents the advantage of fast convergence compared to other evolutionary algorithms such as NSGA, MOSPO and SPEA, when each is used in isolation. Each evolutionary algorithm (such as NSGA, MOSPO, etc.) could be used instead of the hybrid method, but convergence may take too long. The hybrid method is used due to its fast convergence, as many tests have confirmed. Conceptualization, M.K. and F.W. ; methodology, M.K. ; software, M.K. and A.O. ; validation, A.T. and X.S. ; investigation, M.K., F.W. and A.O. ; writing--original draft preparation, M.K. ; writing--review and editing, F.W. and A.T.; visualization, A.O. ; supervision, F.W. ; funding acquisition, F.W. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The APC was funded by Beihang University. Data Availability Statement: Data are contained within the article. **Acknowledgments:** We are very grateful for the contributions and comments of peer reviewers. **Conflicts of Interest:** The authors declare no conflicts of interest. Appendix A Hybrid Method with Integration of Non-Dominated Sorting Genetic Algorithm-III (NSGA-III), Strength Pareto Evolutionary Algorithm-II (SPEA-II), and Multi-Objective Particle Swarm Optimization (MOPSO)  
Figure 11 shows the flow chart for the hybrid method of the evolutionary algorithms (HMEAs) used for ground station deployment. It should be noted that for this method based on NSGA-III [35], SPEA-II [36] and MOPSO [37], the codes are available online in the public file exchange of MathWorks. A 2: Overall procedure of the hybrid method of evolutionary algorithms (HMEAs). The overall procedure is outlined as follows:In the NGSA-III process:
* Apply the operator of the crossover to a random number of crossover individuals \(N_{Crossover}\), which is calculated by the probability of crossover \(P_{Crossover}\) of the NSGA-III parameter as \(N_{Crossover}=0.5*[2P_{Crossover}.N_{pop}/3]\).