# whv_hype: Approximation of the (weighted) hypervolume by Monte-Carlo... In eaf: Plots of the Empirical Attainment Function

## 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

 1 2 3 4 5 6 7 8 whv_hype( data, reference, ideal, maximise = FALSE, dist = list(type = "uniform"), nsamples = 100000L ) 

## Arguments

 data (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() | logical(1)) 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 (list()) weight distribution. See Details. nsamples (integer(1)) number of samples for Monte-Carlo sampling.

## Details

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

• type="point" describes a goal in the objective space, where mu gives the coordinates of the goal. The resulting weight distribution is a multivariate normal distribution centred at the goal.

• type="exponential" describes an exponential distribution with rate parameter 1/mu, i.e., λ = \frac{1}{μ}.

## Value

A single numerical value.

## References

\insertAllCited

read_datasets(), eafdiff(), whv_rect()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 whv_hype (matrix(2, ncol=2), reference = 4, ideal = 1) whv_hype (matrix(c(3,1), ncol=2), reference = 4, ideal = 1) whv_hype (matrix(2, ncol=2), reference = 4, ideal = 1, dist = list(type="exponential", mu=0.2)) whv_hype (matrix(c(3,1), ncol=2), reference = 4, ideal = 1, dist = list(type="exponential", mu=0.2)) whv_hype (matrix(2, ncol=2), reference = 4, ideal = 1, dist = list(type="point", mu=c(1,1))) whv_hype (matrix(c(3,1), ncol=2), reference = 4, ideal = 1, dist = list(type="point", mu=c(1,1)))