# Diversity Maintenance for Efficient Robot Path Planning
## 5 Conclusions  
The results show that diversity maintenance methods have an impact on the overall fitness of the end solution found, what is expected. The basic version of the algorithm performed less successfully compared to all the three other versions with diversity maintenance included.  
Both for the two-dimensional and three-dimensional environment, the novelty algorithm gave solutions that are consistent and converge fast towards the optimal solution.  
The fitness sharing algorithm gave comparably good results for the two-dimensional environment but had certain problems with the three-dimensional. The algorithm got trapped in the local optimum in 7.4% of the simulations.  
Even though it found trajectories without collisions, the length of those trajectories was such that those simulations could be considered unsuccessful. With the dismissal of those outlying solutions, fitness sharing algorithm has results that are getting close to those of the novelty algorithm. Crowding algorithm gave evidently the least quality results out of the tested algorithms, for both problem domains.  
Looking at the results, of this and the past research, the reason for the difference in the performance is not straightforward to explain. It originates from the diversity maintenance methods, which include parent selection models. The novelty and fitness sharing algorithms use a lot more stochastic models when choosing the parent population, which results in greater freedom in the exploration of the environment.  
Crowding algorithm is based on the random pairing of parents from the population, and then offspring is compared to parents and fitter individuals are preserved. In the case where the population is sparsely distributed in the large search space, this can become a limitation, since good parents might not be selected to create offspring, and thus their genetic material disappears in the evolutionary process.  
Diversity maintenance is not straightforward to implement and requires a significant amount of experimental work to tune the parameters for the algorithm to work efficiently.  
It is then a question if this additional work is justified if the increase of the end solution quality is not significant.  
Figure 6: Robot motion along the trajectory found by the novelty algorithm. Top left start configuration, bottom right end configuration.  
The main conclusions regarding the application of different diversity maintenance methods to the problem of path planning drawn from this study are that novelty search equals fitness sharing for simpler scenarios of path planning. The strength of the novelty search arises with the complexity of the environment and path to be found. Also, diversity maintenance methods generally positively influence the quality of solutions to the problem of path planning, when compared to the basic algorithm.  
Conceptualization, P.C.; investigation, L.C.; methodology, P.C.; software, L.C.; supervision, P.C.; validation, L.C.; writing--original draft, L.C.; writing--review and editing, P.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by grant no 4192 by the Croatian Ministry of Sciences, Education, and Sports.  
[PERSON] would kindly acknowledge the hospitality of professor [PERSON] from Columbia University, NYC, and the Fulbright postdoctoral research grant during which the main idea for this paper emerged.  
The authors declare no conflict of interest.