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.
The results are compared with those obtained by SPEA2 and NSGAII in terms of hypervolume
values, extreme solutions, and CPU time.
The corresponding R-indicator and hypervolume
indicator values (best, worst, mean, and standard deviation) are provided in Table 4.
For an M-dimensional hypervolume
with N known nodes (i.
In defining niche breadth in terms of the Hutchinsonian hypervolume
, it is pertinent to determine whether the mean optimal climate for P.
The latter examines overall multivariate morphometric variance between groups, is roughly proportional to the squared perimeter of the morphospace hypervolume
occupied, and takes into account both total scatter as well as dispersion among points.
In the paper entitled "A Study on Many-Objective Optimization Using the Kriging-Surrogate-Based Evolutionary Algorithm Maximizing Expected Hypervolume
Naujoks, "An EMO algorithm using the hypervolume
measure as selection criterion," Lecture Notes in Computer Science, vol.
The upper-level evolutionary algorithm searches for the best sets of input-parameter values for the lower-level algorithm and maximizes the hypervolume