# Diversity Maintenance for Efficient Robot Path Planning
## 3 Results  
Matlab environment is used to run the simulations. In order to compare different versions of the algorithm, each algorithm was simulated 1000 times. Testing results are presented using histograms and convergence diagrams and shown in Figures 3 and 4, both for the 2D and 3D cases, respectively. Figure 3: 2D case: (**a**) basic algorithm; (**b**) novelty search; (**c**) fitness sharing; (**d**) crowding. Figure 4: 3D case: (**a**) basic algorithm; (**b**) novelty search; (**c**) fitness sharing; (**d**) crowding. Each histogram represents how many times an algorithm found a trajectory in a particular length range. Convergence diagrams show the convergence of average lengths from the discovered trajectories in a specific generation that does not collide with the obstacles. Better performance is for those histograms with the bars grouped in the left region--meaning shorter, and thus fitter, individuals are found with increased frequency compared to those histograms whose values are grouped on the right side. The average length itself is not of crucial importance since a number of poor performers might influence the quality of the whole population. At the same time, the algorithm might find a very fit, even the best individual, while the average quality is low. The average length is included in the figures in order to illustrate the overall performance of the algorithm. In the table presented above, the bold fields denote the best performancefor the given algorithm and fitness sharing method. By simple summation of bold fields, the novelty outperforms other approaches. It is important to note though, that not all fields have the same importance. For instance, column 5 shows the least fit individual from the population which is definitely less important compared to the best solution found by a certain method. Simple counting of bold fields is thus not the ultimate measure of the quality of a certain method, but has to be rather us as an indication of the quality and interpreted carefully based on additional analysis of the data provided in Table 1.  
Comparing the test results of the novelty and the fitness sharing 2D algorithms, we can see that they are similarly effective. Both algorithms found a trajectory without collision in every simulation, lengths of discovered trajectories are placed in a narrow span, and the convergence diagrams are similar. Unlike the previous two algorithms crowding 2D algorithm performed less consistent in terms of quality of results. It failed to find trajectories without a collision in 1% of simulations, lengths of discovered trajectories are approximately 13% longer on average, and convergence to the optimal solution is significantly slower. Regarding the 3D versions of the algorithms, the novelty algorithm gave the best results with very fast convergence. Testing results of the fitness sharing algorithm are also comparably good as in the 2D example. In 7.4% of simulations, the algorithm got trapped in suboptimal regions of the search space, with the consequence of the dissipated quality of solutions. Lengths of the trajectories, not shown in the histogram, are in the range \(\langle 4,\ 30\rangle\). If those simulations were declared unsuccessful and were omitted from the calculation of the average length, the average length would be 1.5659, which is close to the novelty version of the algorithm.