# An Approach to Multi-Objective Path Planning Optimization for Underwater Gliders
## 5 Discussion  
From the analysis of the HV evolution (Figures 5 and 6), the trend is to reach a steady state. This means that the resulting trajectories cannot be much more improved without prejudice of the global solutions. In practical terms, obtained trajectories will not have significant improvements regarding the distance to the target point versus the distance to the obstacles even if the optimization process kept being executed.  
Considering all the configurations of both cases, configuration 16 (PS 100, NG 200, CP 1, MP 0.15) provided the best global results, closely followed by 13 (PS 100, NG 200, CP 1.0, MP 0.10) and 17 (PS 100, NG 200, CP 0.9, MP 0.15) (Figure 22). The population size of 100 is a good balance for  
Figure 21: Mult-compare (Tukey–Kramer) results for favourable currents scenarios 1, 4, 5, and 8 (**left**) and against scenarios 2, 3, 6, and 7 (**right**).  
Figure 22: Comparison of all scenarios.  
exploration-exploitation equilibrium of the search in these 10 variable tested scenarios. It provides a faster convergence than the 160 population size case, while a highly elitist algorithm as NSGA-II favours a high crossover rate (1.0) and slightly higher mutation rate (0.15) than the general rule 1/n (0.1), enhancing the population diversity by those operators. Second and third configurations also keep either the crossover rate of 1.0 with mutation rate of 0.1 or a slightly lower crossover rate (0.9) with mutation rate of (0.15), confirming the appropriateness of the operators.  
As for the parameter values, when keeping PS and MP, results worsen with the decrease of CP, meaning that resulting trajectories, overall will present worse results for the fitness functions, either by ending far from the target point and passing too close to the obstacles, two undesirable situations.  
If CP is kept constant, results get better with the increasing of MP, except for PS 160, CP 0.8, and MP 0.15, meaning better balanced distances both to target and to the obstacles. Also, increasing the MP and decreasing CP for each PS results in less dispersion of the results except for PS 50 and MP 0.1.  
Considering the cases of separated versus overlapping obstacles, results show a bigger dispersion on the overlapping cases. Also, although configuration 16 (PS 100) presented the best results on both cases, on overlapping cases some configurations with PS 160 presented closer results to 16 than on the separated case, on which is evident that cases with PS 100 (except 22) are the best ones.  
Another aspect that impacts the results is the direction of ocean currents. In scenarios with favourable currents, cases with PS 160 presented results closer to configuration 16, opposite to unfavourable currents, on which cases with PS 100 are closer to configuration 16.  
Specific scenario analysis--e.g., scenarios 1 and 8 in this paper--could be performed to select the most convenient configuration depending on the particular environmental characteristics, instead of applying the global solution. The results of the post-hoc procedures indicate that there is evidence of statistically significant advantages among the different configurations. Particularly, compared to [PERSON]'s the more powerful Bergmann-Hommel procedure is able to identify a higher number of cases surpassed by the best performing combination; 9 more cases in scenario 1 (Tables 6 and 7) and 12 in scenario 8 (Tables 9 and 10).  
Apart from pure numerical evaluation, the algorithm configuration selection could also depend on additional factors such as available computational resources or time restrictions.