whv_hype: Approximation of the (weighted) hypervolume by Monte-Carlo...
In moocore: Core Mathematical Functions for Multi-Objective Optimization

whv_hype

R Documentation

Approximation of the (weighted) hypervolume by Monte-Carlo sampling (2D only)

Description

Return an estimation of the hypervolume of the space dominated by the input data following the procedure described by \citetAugBadBroZit2009gecco. A weight distribution describing user preferences may be specified.

Usage

whv_hype(
  x,
  reference,
  ideal,
  maximise = FALSE,
  nsamples = 100000L,
  seed = NULL,
  dist = "uniform",
  mu = NULL
)

Arguments

`x`	`matrix()`\|`data.frame()` Matrix or data frame of numerical values, where each row gives the coordinates of a point.
`reference`	`numeric()` Reference point as a vector of numerical values.
`ideal`	`numeric()` Ideal 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.
`nsamples`	`integer(1)` Number of samples for Monte-Carlo sampling. Higher values typically produce more accurate approximations of the true hypervolume, but require more time.
`seed`	`integer(1)` Random seed.
`dist`	`character(1)` Weight distribution type. See Details.
`mu`	`numeric()` Parameter of the weight distribution. See Details.

Details

The current implementation only supports 2 objectives.

A weight distribution \citepAugBadBroZit2009gecco can be provided via the dist argument. The ones currently supported are:

"uniform" corresponds to the default hypervolume (unweighted).
"point" describes a goal in the objective space, where the parameter mu gives the coordinates of the goal. The resulting weight distribution is a multivariate normal distribution centred at the goal.
"exponential" describes an exponential distribution with rate parameter 1/mu, i.e., \lambda = \frac{1}{\mu}.

Value

A single numerical value.

References

\insertAllCited

Examples

whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42)
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42)
whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "exponential", mu=0.2)
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "exponential", mu=0.2)
whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "point", mu=c(2.9,0.9))
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "point", mu=c(2.9,0.9))

moocore documentation built on July 12, 2026, 5:06 p.m.