## 5 Results and Discussion
### Scattered Filtering of the Search Space  
This step means that the search space is sampled. Therefore, we randomly generate solutions and then analyze them. In the tests, we created 100 solutions at random. We chose a relatively low value, even though the task is complicated one, but the number of nodes to be visited is not very large. The following analysis methods were considered: distance of solutions, the distance of the best solution, the distance of the best solution and solutions, cost density. The following distances were analyzed: fitness, hamming, basic swap sequence. For average distances for the search space points were calculated by calculating the average distance to all other search space points. Therefore, each solution is assigned to a point-level average distance. Figure 5(a) shows fitness values and average fitness distances. Fitness values range from \(\approx\)120,000 to \(\approx\)160,000 (fitness unit), while average fitness distances range from \(\approx\)5000 to \(\approx\)19,000 (fitness unit). These values also show a parabolic function because small and large fitness values are paired with a large average distance, while medium fitness values are associated with a medium average distance. Figure 5(b) shows fitness values and average hamming distances. The average hamming distances in each case range from about 35 to 36 (hamming distance unit). Figure 7 shows fitness values and average basic swap sequence distances. The average basic swap sequence distances in each case range from about 28 to 29 (basic swap sequence distance unit). The fitness values and fitness distances from the best solution (the best of the generated solutions) show a linear function, the higher the fitness value of the solution, the greater the distance from the best solution (the best of the generated solutions). According to Figure 5(b), the average hamming distances are around 35 (hamming distance unit), while according to Figure 7, the average basic swap sequence distances are around 29 (basic swap sequence distance unit). Fitness values range from \(\approx\)120,000 to \(\approx\)160,000 (fitness unit), and fitness distances range from \(\approx\)4,000 to \(\approx\)36,000 (fitness unit). In case of fitness values and hamming distance from the best solution (the best of the generated solutions), the Hamming distances range from 30 to 40 (hamming distance unit). The basic swap sequence distance from the best solution (the best of the generated solutions) range from 24 to 35 (basic swap sequence distance unit). The fitness distance from the best solution (the best of the generated solutions) and the average of the fitness distances from the other solutions are described by a parabolic function, thus, low and high distances mean high average distances from the best (best of generated solutions) solution, while medium distances mean low average distances from the best (best of generated solutions) solution. The cost density value shows that almost every solution has a different fitness value. Table 1 presents the meaning of evaluation and Table 2 illustrates the test results. Figure 6: The fitness distance (**a**) and the hamming distance (**b**) of solutions.