# An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
## 5 Results and Discussion  
### GPS Optimal Satellites  
The five optimization algorithms were applied for the optimization of GPS-only satellite constellations of four, five, six, and seven GPS satellite constellations for the 24 h GPS data. Optimal GPS satellites were selected every five minutes; hence, the optimization algorithms selected the optimal satellite constellation for 288 epochs (i.e., 1 epoch per 5 min)  
Figure 10: The possible combinations of satellite constellations for **(left)** GPS-only in the cases of 8 and 13 available GPS satellites and **(right)** multi-GNSS satellite constellation in the case of 18 and 31 available GNSS satellites. Figure 9: Sample of the file of the GPS data information, which includes (i) date–time, (ii) satellite PRN, (iii) azimuth, (iv) elevation angle, and (v) CNR (in dB-Hz). in the 24 h period. Figure 11 shows (i) the matching quality of the GPS satellite subsets selected by the algorithms, which was determined by comparing the satellite selection results of the optimization algorithms with those of the TM, and (ii) the selection time that was taken by the algorithms for the GPS satellite selection over 288 epochs. According to Figure 11, all the optimization algorithms effectively selected the optimal GPS satellites, except for the SA algorithm. More specifically, for the cases of a GPS satellite constellation of four, five, six, and seven satellites, the four algorithms ABC, ACO, GA, and PSO achieved a GPS satellite selection accuracy of over 99%, with the algorithms ABC and GA achieving the best GPS satellite selection accuracy as they had a 100% match with the optimal GPS satellite constellation as derived by the TM. In contrast, SA had the lowest accuracy in choosing the optimal GPS satellite constellation, with a match ranging between 83% and 93%. However, the SA proved to perform the fastest in satellite selection among the five optimization algorithms, but it was still slower than the TM. The performance of optimization algorithms, and consequently the quality of their results, can be affected by the value of optimization algorithms' parameters. However, the main reason for SA's lower quality in satellite selection is its design, and specifically, the technique of finding the optimal solution. ABC, ACO, GA, and PSO are population-based algorithms, which mean that they use groups of individuals to find the optimal solution [45]. In this project, the population size of these algorithms was set as 100. In contrast, SA was originally designed to find the optimal solution using a single population size. Since increasing the population size can improve the quality of the algorithms' results [45], the performance of SA was negatively affected by its small population. On the other hand, it can be seen that the four algorithms (ABC, ACO, GA, and PSO) are equally accurate in selecting satellites. These algorithms achieved more than 99% accuracy in selecting the optimal GPS subsets of four, five, six, and seven satellites. ABC and GA constantly selected the optimal satellites with a quality of 100% in all cases, whereas ACO and PSO exhibited less accurate satellite selection (99.3%) in one and two cases, respectively. Since each case included 288 epochs, the satellite selection accuracy of 99.3% means that the optimal GPS satellite subset was mis-selected in two epochs. When reviewing the selection of satellites in each epoch (Figure 12), no significant difference could be found between the ACO and PSO results and the TM results (actual results). This indicates that ACO and PSO fall into a local optimum that was too close to the best solution (i.e., satellite combination) ever found in the two epochs. ACO and PSO mis-selected the  
Figure 11: **(Left)** The quality of match (accuracy) of the selection of the optimal GPS satellite subset by the optimization algorithms with respect to the actual optimal GPS satellite subset derived by the TM. **(Right)** The time required for the TM and the optimization algorithms to perform optimal GPS satellite subset selection.