hypervolume


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hypervolume

[′hī·pər‚väl·yəm]
(mathematics)
The hypervolume of the direct product of open or closed intervals in each of the coordinates of a Euclidean n-space (where n is a positive integer) is the product of the lengths of the intervals.
The Jordan content of any set in Euclidean n-space whose exterior Jordan content equals its interior Jordan content.
References in periodicals archive ?
Two set hypervolume difference, proposed in [13], represents an "extension" of the hypervolume indicator.
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 Improvement," C.
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 [20].