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

Source: R/whv.R
whv_hype.Rd

Return an estimation of the hypervolume of the space dominated by the input data following the procedure described by AugBadBroZit2009gecco. A weight distribution describing user preferences may be specified.

Usage

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

dist

character(1)
weight distribution type. See Details.

nsamples

integer(1)
number of samples for Monte-Carlo sampling.

seed

integer(1)
random seed.

mu

numeric()
parameter of the weight distribution. See Details.

Value

A single numerical value.

Details

The current implementation only supports 2 objectives.

A weight distribution AugBadBroZit2009gecco 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., \(\lambda = \frac{1}{\mu}\).

References

See also

read_datasets(), eafdiff(), whv_rect()

Examples

whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42)
#> [1] 3.99807
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42)
#> [1] 3.00555
whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "exponential", mu=0.2)
#> [1] 1.14624
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "exponential", mu=0.2)
#> [1] 1.66815
whv_hype(matrix(2, ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "point", mu=c(2.9,0.9))
#> [1] 0.64485
whv_hype(matrix(c(3,1), ncol=2), reference = 4, ideal = 1, seed = 42,
         dist = "point", mu=c(2.9,0.9))
#> [1] 4.03632