# An Evaluation of Optimization Algorithms for the Optimal Selection of GNSS Satellite Subsets
## 1 Introduction
The closed-form solution reduces the TM's computational complexity [16; 24]. However, it cannot reduce the number of calculations, so it becomes time-consuming when the number of satellites increases [25]. The maximum volume method is based on maximizing the volume of the tetrahedron or orthogonal projection created between the satellites [22; 26]. The WGDOP value decreases (improves) as the tetrahedron volume and maximum orthogonal projection increase. However, the positioning quality obtained with the selected satellites via this method is not guaranteed [25; 27], as the method focuses on maximizing the volume of the tetrahedron/orthogonal projection and not on the WGDOP value [22; 27], and it is also a time-consuming technique [27]. On the other hand, ANN and optimization algorithms, which are broadly applied in artificial intelligence (AI) problems, can both provide good results in satellite selection [22; 28; 29]. However, optimization algorithms, contrarily to ANNs and generally to any AI or machine-learning algorithms, do not require any training or, consequently, any large dataset for training [30; 31; 32], which makes optimization algorithms faster than ANNs. In addition, an ANN-trained model could be difficult to apply due to the varying geometry of tracked satellites due to the different revolution periods of GNSS systems [30; 31]. Thus, optimization algorithms are potentially more suitable for the selection of satellites than ANNs and similar AI techniques. In the current study, we investigated five well-known optimization algorithms, the Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Simulated Annealing (SA), and evaluated which optimization algorithm was the most suitable and reliable for selecting optimal GNSS satellites in a subset from available tracked GNSS satellites. The evaluation of the five optimization algorithms was based on two criteria: (i) the validity of the selected GNSS satellites of each optimization algorithm in terms of high signal quality and optimal geometry (WGDOP) of the satellite subset and (ii) the required computation time of each optimization algorithm for satellite optimization. For the first criterion, we considered the selection of the GNSS satellite subset derived from the TM with the lowest value of WGDOP as the actual truth for the most optimal GNSS satellite subset (for a given number of GNSS satellites in the subset). We compared the WGDOP value of the optimal satellite subset from each optimization algorithm with that of the optimal GNSS satellite subset derived from the TM. We consider an optimization algorithm to be accurate when the WGDOP value of its selected optimal satellite subset exactly matches the WGDOP value of the TM optimal satellite subset, and consequently, the accuracy expresses how closely the WGDOP value of the selected GNSS satellite subset of each optimization algorithm matches that of the TM optimal GNSS satellite subset. The optimization algorithm with the highest accuracy in the selection of the optimal GNSS satellite subset and the shortest required computation time was considered as the most suitable and reliable. The current study was based on 24 h data of GNSS permanent data, where the optimization algorithms selected the GNSS satellite subset for each epoch and compared against the optimal subset derived for the corresponding epoch from the TM. This study is the first attempt at an overall evaluation of the five optimization algorithms in the problem of selecting an optimal GNSS satellite subset, by (i) examining the accuracy required from each optimization algorithm against the TM based on real GNSS data and (ii) evaluating the impact of functional principles, settings, and parameters on the performance of the optimization algorithms regarding the problem of the optimization of tracked GNSS satellite subsets.