# Robust Estimators in Geodetic Networks Based on a New Metaheuristic: Independent Vortices Search
## 5 Results and Discussion
### Performance and Discussion of IVS  
We conducted several tests to compare the solutions obtained with IVS to solutions obtained by other MHs. For a better analysis, we generated four scenarios of errors in a GNSS network. Each scenario contained three simultaneous outliers, ranging from \([3\sigma,6\sigma)\), in 39 observations (about 7.8% contamination). Using the LMS estimator, the MHs executed the scenarios twenty-five times. This allowed for analyzing the stability and quality of the results. More details of the network can be found in the next section. Figure 4: Flowchart of the network adjustment based on Independent Vortices Search and a robust estimator function. The search space is evaluated from the error contribution. Besides the MHs already presented, we also tested the Hybrid Vortex Search algorithm (HVS). The HVS works with the combination of ABC and VS, trying to take advantage of the best characteristics of each strategy. The reader can find more details in [49]. Thus, the algorithms tested were:  
* Artificial Bee Colony (ABC) [23; 24];
* Vortex Search algorithm (VS) [32];
* Modified Vortex Search algorithm (MVS) [33];
* Hybrid Vortex Search algorithm (HVS) [49]; and,
* Independent Vortices Search (IVS). The configurations of the MHs obeyed the following parameters: 5,000,000 FE as processing limit, 50 candidates per center for vortex algorithms, and 50 bees in ABC (25 food sources). In addition, we tested the MVS and IVS with five vortices, as presented in [33], and 40 vortices. Preliminary tests showed better results from 20 to 60 vortices, so we adopted an intermediate value of 40. It is important to note that cycle counting was not used as a configuration parameter or as a limit for the MH executions. For more objective comparisons between MHs, we should not use the cycle count as a stopping criterion. As each MH has different strategies in its execution, it can use a different quantity of FE in each cycle. Using a fixed number of cycles as a parameter to limit the execution can cause a large variation in the total amount of FE for each MH. This would favor MHs that make more FE per cycle, since they have more opportunities to test their solutions [50]. We adapted the algorithms to use the number of FE as the limit for suspension. This allowed for a more adequate performance comparison. To better situate the reader, executing 5,000,000 FE was equal to 100,000 cycles in ABC with 50 bees (25 food sources); 100,000 cycles in VS with 50 candidates; and 20,000 cycles in IVS with five vortices and 50 candidates per center. The MVS experiments performed in [33] divided the quantity of candidates by the number of vortices. Thus, in executions with 50 candidates and five vortices, MVS generated only 10 candidates per vortex every cycle. As this work uses the number of FE as the execution limit of the MHs, each vortex generated a number of candidates established by the number of candidates parameter. For a run with 50 candidates and five vortices, the algorithm generated 50 candidates per vortex each cycle. This characteristic is standard in IVS. For better representation of results, we present them in box plots. Each point represents the result of one run. The number after \"c\" in brackets (e.g., \"c[5]\" and \"c[40]\") is the amount of vortices, where applicable. Figures 5-8 show the results for Scenarios 01, 02, 03, and 04, respectively. Figure 5: Results of 20 runs in error scenario 01 for each metaheuristic (MH). c[X] indicates the number of vortices, where applicable. Figure 8: Results of 20 runs in error scenario 04 for each MH. c[X] indicates the number of vortices, where applicable. Figure 6: Results of 20 runs in error scenario 02 for each MH. c[X] indicates the number of vortices, where applicable. Figure 7: Results of 20 runs in error scenario 03 for each MH. c[X] indicates the number of vortices, where applicable. By analyzing the charts, we see that IVS performed better than other MHs.