Table 2 assesses the confidence that can be given when comparing those mean results, by applying the Kruskal-Wallis nonparametric test to the hypervolume
Two set hypervolume
difference, proposed in , represents an "extension" of the hypervolume
In this respect, the results acquired are analyzed via two MO quality metrics: hypervolume
and coverage of two sets [12, 13].
Illustration of hypervolume
indicator for a set of points formed by the union of open circles and filled diamonds: the gray area is the hypervolume
indicator of the Pareto Front (set of filled diamond points) with respect to the filled square reference point.
Secondly, there is no correlation between the number of individuals, generations, or iterations and the hypervolume
. For example, the hypervolume
of 140 individuals is much higher than the one of 160 individuals.
Similarly, if k [member of] (1, 2, ..., m}, then the hypervolume
of [[intersection].sup.k.sub.j=1] [B.sub.j](t) is
The current metrics available to Hypervolume
is probably the most popular one that is employed for multiobjective search.
For the hypervolume
value of the nondominated solutions of datasets Ute92, Sta83, Lse91, Kfu93, Hec92, and Ear83, the application of the two local search settings shows better results than other three settings.
The morphological variability of the wild population was higher than that of the hatchery population, because the wild fish presented higher dispersion in morphological space (ANOVA log(DC+1): F(1; 131) = 11.9207, p = 0.0007) and thus occupied a larger morphological hypervolume
(Kruskal-wallis' test CDN: KW(1; 133) = 18.7552; p = 0.0001).
where the sum runs over all faces, volumes or hypervolumes
for p = 2, 3, 4 respectively, comprising the lattice.
Other conceptions about niche are more appropriate for these educational goals, such as Hutchinson's conception of the niche as a n-dimensional hypervolume
delimited by the environmental conditions and resources defining the requirements of a species to survive and exhibit its mode of living 14].
To validate the performance of the proposed algorithm, three performance metrics, namely, generational distance (GD) , minimal spacing (MSP) , and hypervolume
(HV) , are used to compare the performance of the proposed HMOPSO with MOPSO, NSGA-II, MOEA/D, and other methods recently reported in the literature.