Compute (total) weighted hypervolume given a set of rectangles

Calculates the hypervolume weighted by a set of rectangles (with zero weight outside the rectangles). The function total_whv_rect() calculates the total weighted hypervolume as hypervolume() + scalefactor * abs(prod(reference - ideal)) * whv_rect(). The details of the computation are given by DiaLop2020ejor.

Usage

whv_rect(x, rectangles, reference, maximise = FALSE)

total_whv_rect(
  x,
  rectangles,
  reference,
  maximise = FALSE,
  ideal = NULL,
  scalefactor = 0.1
)

Arguments

x

matrix()|data.frame()
Matrix or data frame of numerical values, where each row gives the coordinates of a point.

rectangles

matrix()
Weighted rectangles that will bias the computation of the hypervolume. Maybe generated by eafdiff() with rectangles=TRUE or by choose_eafdiff().

reference

numeric()
Reference point as a vector of numerical values.

maximise

logical()
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.

ideal

numeric()
Ideal point as a vector of numerical values. If NULL, it is calculated as minimum (or maximum if maximising that objective) of each objective in the input data.

scalefactor

numeric(1)
Real value within \((0,1]\) that scales the overall weight of the differences. This is parameter psi (\(\psi\)) in DiaLop2020ejor.

Value

numeric(1)
A single numerical value.

Details

TODO

References

See also

read_datasets(), eafdiff(), choose_eafdiff(), whv_hype()

Examples

rectangles <- as.matrix(read.table(header=FALSE, text='
 1.0  3.0  2.0  Inf    1
 2.0  3.5  2.5  Inf    2
 2.0  3.0  3.0  3.5    3
'))
whv_rect (matrix(2, ncol=2), rectangles, reference = 6)
#> [1] 4
whv_rect (matrix(c(2, 1), ncol=2), rectangles, reference = 6)
#> [1] 4
whv_rect (matrix(c(1, 2), ncol=2), rectangles, reference = 6)
#> [1] 7

total_whv_rect (matrix(2, ncol=2), rectangles, reference = 6, ideal = c(1,1))
#> [1] 26
total_whv_rect (matrix(c(2, 1), ncol=2), rectangles, reference = 6, ideal = c(1,1))
#> [1] 30
total_whv_rect (matrix(c(1, 2), ncol=2), rectangles, reference = 6, ideal = c(1,1))
#> [1] 37.5