# Seeking Optimal GNSS Radio Occultation Constellations Using Evolutionary Algorithms
## 4 Discussion  
As introduced in Section 2.3, the fitness function used in the evolutionary algorithms is based on the concept of a spatio-temporal point pattern. In Equation (6), \(N_{total}\) represents the total number of \(10^{\circ}\times 10^{\circ}\times 3\) h spatio-temporal grids over the globe for one day, hence, the degree of the optimization both in the spatial and temporal ROEs distribution is taken into consideration by this fitness function. Searching for the optimal 12 satellite walker constellation for GNSS RO observation with a GA algorithm, [PERSON] et al. (2014) used a fitness function similar to Equation (6), while the spatio-temporal grids of \(4.5^{\circ}\times 4.5^{\circ}\times 24\) h were used and there was no evaluation of the temporal distribution of ROEs during one day. Furthermore, here in Equation (6), \(Y_{0}\), the expected mean number of ROEs of each spatio-temporal grid, was calculated based on the total number of simulated 24 h ROEs over the globe and the number of spatio-temporal grids, while this parameter was just simplified to be equal to 4 in the study by [PERSON] et al. (2014).  
Both [PERSON] et al. (2014) and [PERSON] et al. (2016) used a GA to search for the optimal LEO constellation configuration for GNSS RO performance over the target region. Considering that the optimized constellation configuration sought depends on the optimization algorithm used, it stands to reason to use more than one evolutionary algorithm in the optimization process only if the comparison between the algorithms is fair ([PERSON] et al., 2016). Hence, both a GA and PSO were applied in our study. To ensure the fairness of the comparison between the two algorithms, the evolutionary processes were iterated the same number of times (100 generations) in each algorithm. It was found that regardless of the constellation pattern, the PSO algorithm generally (although not necessary) performed better than a GA, which means that the spatial and temporal distributions of ROEs, observed by the optimal constellations obtained by the PSO algorithm, are generally better compared to those derived by GA.  
As to the comparison between the two constellation patterns, [PERSON] et al. (2016) found that for a LEO constellation composed of six satellites, the daily number of GPS ROEs, which occur over the Asia and Pacific region observed by the optimized 2D-LFC, is larger than those observed by the optimized 3D-LFC. Our study further confirms that for a LEO constellation composed of \(n(n=6,7,8,\ldots\ldots\cdot 12)\) satellites, the optimized 2D-LFCs generally could observe more GNSS ROEs over the globe compared with the optimized 3D-LFCs. In Reference ([PERSON] et al., 2016), the altitudes of the circular orbits in the optimized 2D-LFC are lower than those of the elliptical orbits in the optimized 3D-LFC. In our study, the comparison between Tables 4 and 5 also revealed that, for a LEO constellation composed of \(n(n=6,7,8,\ldots\ldots\cdot 12)\) satellites, with the whole globe as the target region of GNSS RO observation, all the circular orbits in the optimized 2D-LFC were lower in height than the elliptical orbits of the optimized 3D-LFC. [PERSON] et al. (2014) found that high inclinations of LEO satellites are beneficial for a sufficient global coverage of the ROEs. All the optimal 2D-LFCs and 3D-LFCs were of high inclinations in our study, which are shown by Tables 4 and 5.  
The comparisons of the COV mean values and its standard deviation between the two different constellation patterns show that, as the number of LEO satellites varies between 6 and 12, the GNSS ROEs observed by the optimized 2D-LFCs were generally more homogeneous in space and time compared to the optimized 3D-LFCs. The comparison of the optimized 6 satellite 2D-LFC and 3D-LFC with COSMIC further approved the superiority of the optimized 2D-LFC performance.