whv_rect: Compute (total) weighted hypervolume given a set of...
In moocore: Core Mathematical Functions for Multi-Objective Optimization

whv_rect

R Documentation

Compute (total) weighted hypervolume given a set of rectangles

Description

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 \citetDiaLop2020ejor.

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 \citetDiaLop2020ejor.

Details

TODO

Value

numeric(1) A single numerical value.

References

\insertAllCited

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)
whv_rect (matrix(c(2, 1), ncol=2), rectangles, reference = 6)
whv_rect (matrix(c(1, 2), ncol=2), rectangles, reference = 6)

total_whv_rect (matrix(2, ncol=2), rectangles, reference = 6, ideal = c(1,1))
total_whv_rect (matrix(c(2, 1), ncol=2), rectangles, reference = 6, ideal = c(1,1))
total_whv_rect (matrix(c(1, 2), ncol=2), rectangles, reference = 6, ideal = c(1,1))

moocore documentation built on Aug. 8, 2025, 6:12 p.m.