# An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
## 5 Results and Discussion
### GPS Optimal Satellites
The GA took only 2 s, while ACO took 4.37 s to complete one selection. Furthermore, in [29], the GA was as fast as ABC and PSO in selecting GPS satellites, completing approximately the same number of search iterations within 1, 1.5, and 2 s. The main reason for this unexpected delay in the speed of GA selection is the algorithm modification. GA finds the optimal solution by iteratively generating better new solutions. However, it may create solutions with a duplicate value, which is unacceptable in satellite selection. Thus, solutions with a duplicate value were rejected and new solutions were generated until no duplicates appeared. Clearly, this is time-consuming. Although the same modification was applied to ABC, PSO, and SA, these algorithms took much less time than the GA. This is because a GA creates new solutions by swapping the variables of two good solutions. As GA solutions converge, two nearly identical solutions are selected to create a new solution, which subsequently leads to more duplication. Based on Equation (4), the number of possible satellite constellations changes due to the number of available satellites (8 and 13; Figure 10) and the constellation sizes (four, five, six, and seven; Figure 10). Compared to others, the subset of six GPS satellites had the highest number of possible combinations, with a total of 1744. As a result, the TM, which checks all possible satellite combinations, took slightly longer to find the optimal GPS subset of six satellites than the others, as shown in Figure 11. In contrast to the TM, the five optimization algorithms were unaffected by the number of possible satellite combinations as their number of searching iterations is predetermined. Although the five optimization algorithms were executed with the same number of iterations (100) at all satellite constellation sizes (four, five, six, and seven), the selection time for each algorithm varied from one satellite constellation size to another, as shown in Figure 11, due to the adjustment of duplication in the four algorithms (ABC, GA, PSO, and SA). However, the difference in ACO processing time could be due to the number of possible GPS satellite subsets. In ACO, the pheromone rate on the paths influences the ants' path choice, which is stored in a pheromone matrix containing the pheromone rates of all possible paths. Since the size/burden of the pheromone matrix depends on the number of possible paths, which is equal to the number of possible satellite combinations, the ACO selection time changed with different satellite constellation sizes (four, five, six, seven) as they have different possible satellite constellations. Among the five optimization algorithms, the most suitable one for satellite selection can be determined based on their satellite selection accuracy and speed. SA and GA are not suitable for satellite selection because of their low selection quality and speed, respectively. On the other hand, ABC, ACO, and PSO showed equivalent levels of selection quality and speed. However, the ABC algorithm was considered to be the most suitable algorithm for satellite selection, as only three parameters have to be determined.