GetHypervolume function

Compute hypervolume

Compute the hypervolume formed by the points w.r.t. a reference point. If no reference is supplied, use the nadir point*(1.1,...,1.1).

GetHypervolume(
  objective,
  reference = NULL,
  method = "exact",
  ref_multiplier = 1.1
)

Arguments

• objective: The set of points in the objective space (The objective values). A single column should contain one point, so the size would be numberOfObjective x nPoint, e.g. in 5 objective problem, it is 5 x n.
• reference: The reference point for HV computation. A column vector.
• method: Exact using WFG method or approximate HV using the method by Bringmann and Friedrich. Default to "exact".
• ref_multiplier: Multiplier to the nadir point for dynamic reference point location

Returns

Hypervolume size, a scalar value.

Examples

nObjective <- 5 # the number of objectives
nPoint <- 10 # the number of points that will form the hypervolume
objective <- matrix(stats::runif(nObjective*nPoint), nrow = nObjective, ncol = nPoint)
numpyready <- reticulate::py_module_available('numpy')
pygmoready <- reticulate::py_module_available('pygmo')
py_module_ready <- numpyready && pygmoready
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,,"exact") # no reference supplied

reference <- rep(2,nObjective) # create a reference point at (2,2,2,2,2)
if(py_module_ready) # prevent error on testing the example
GetHypervolume(objective,reference,"exact") # using reference point