1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
|
% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/hv.R
\name{hypervolume}
\alias{hypervolume}
\title{Hypervolume metric}
\usage{
hypervolume(data, reference, maximise = FALSE)
}
\arguments{
\item{data}{(\code{matrix} | \code{data.frame}) \cr Matrix or data frame of numerical
values, where each row gives the coordinates of a point.}
\item{reference}{(\code{numeric()}) \cr Reference point as a vector of numerical values.}
\item{maximise}{(\code{logical()} | \code{logical(1)}) \cr Whether the objectives must be
maximised instead of minimised. Either a single logical value that applies
to all objectives or a vector of logical values, with one value per
objective.}
}
\value{
A single numerical value.
}
\description{
Computes the hypervolume metric with respect to a given reference point
assuming minimization of all objectives.
}
\details{
The algorithm has \eqn{O(n^{d-2} \log n)} time and linear space
complexity in the worst-case, but experimental results show that the
pruning techniques used may reduce the time complexity even further.
}
\examples{
data(SPEA2minstoptimeRichmond)
# The second objective must be maximized
# We calculate the hypervolume of the union of all sets.
hypervolume(SPEA2minstoptimeRichmond[, 1:2], reference = c(250, 0),
maximise = c(FALSE, TRUE))
}
\references{
\insertRef{FonPaqLop06:hypervolume}{eaf}
\insertRef{BeuFonLopPaqVah09:tec}{eaf}
}
\author{
Manuel \enc{López-Ibáñez}{Lopez-Ibanez}
}
\concept{metrics}
|
