# An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
## 3 Methodology of Selecting Tracked GNSS Satellites Based on Optimization Algorithms  
To evaluate the performance of the five optimization algorithms (ABC, ACO, GA, PSO, and SA) in the optimization of the satellite subset, the algorithms were modified accordingly to fit the satellite selection problem, while their common parameter values  
Figure 4: Representation of PSO travelling technique for the solution optimization. Figure 5: Schematic representation of SA algorithm procedure. were adjusted and defined uniformly. They were applied in several scenarios of satellite selection for various number of satellites and conditions. In all the cases, the cost function of the five optimization algorithms was the CNR-WGDOP parameter, of which the minimum value would indicate the corresponding optimal GNSS satellite subset. The evaluation of the optimization algorithms was based on comparing the CNR-WGDOP value of their optimal satellite subset with that of the actual optimal satellite subset derived from the TM. The optimization algorithm with the best results in terms of satellite selection accuracy and speed was considered the appropriate algorithm for satellite selection. Even though GNSS satellite selection is a discrete problem [26], not all of the five optimization algorithms are designed for this type of problem. The five optimization algorithms follow an iterative search process to find the optimal satellite subset. At the end of each iteration, new solution(s) are generated. The ABC and PSO algorithms generate solution(s) with a fractional value as they were designed for continuous problems. However, only an integer is accepted in the satellite selection problem. This issue can be overcome by changing the algorithm design for a discrete problem [26; 55; 56] or simply rounding solution values [55; 57]. To reduce complexity, the generated solutions from ABC and PSO were rounded to the nearest integer in each iteration. In addition, the four optimization algorithms (apart from ACO) can provide results with duplicate values. In the case of the GNSS satellite problem, this would mean that the same satellite could be chosen twice in the solution of the optimized satellite constellation. To address this problem with less interference in the algorithm design, the algorithm solution was checked at the end of each iteration. If the solution contained a duplicated value, it was rejected, and a new solution was generated without consuming the number of searching iterations. In this study, the optimal satellite subsets were chosen based on the criterion of minimising the CNR-WGDOP, which indicates the best potential GNSS satellite combination for the given available GNSS satellites. This can be performed without adjustment by all algorithms, except for ACO. ACO was originally designed to simulate the foraging behavior of ants, where ants search for the shortest path to a food source. Due to this, ACO finds the optimal solution based on two criteria: (i) the solution quality and (ii) the distance between solution members [40]. The weight of the two criteria (the solution quality and distance between solution members) on finding the optimal solution can be determined through the values of alpha (\(\alpha\)) and beta (\(\beta\)) parameters, respectively. In this problem, the quality of the CNR-WGDOP and the distance between the satellites in a constellation represent the solution quality and the distance between solution members. To select the optimal satellites based on CNR-WGDOP only  
mance to the other four optimization algorithms, as defined by the number of iterations and population size. To evaluate the five optimization algorithms, they should be applied to a long period of GNSS observation, where (i) the GNSS satellite systems (i.e., GPS, GLONASS, Galileo, etc. ), (ii) the number of corresponding GNSS satellites, and (iii) the position of the GNSS satellites (azimuth, elevation) vary with time. Therefore, we used a 24 h period of GNSS observations.