compute_R2HV {MaOEA}

Modified powered tchebyscheff R2-indicator designed to approximate HV

Description

Compute the R2-HV from Shang et al.

Usage

compute_R2HV(dataPoints, reference, weights = NULL, nPoints = 100)

Arguments

dataPoints

The Points coordinate. Each column contains a single point (column major).

reference

The reference point for computing R2-mtch (similar as reference for HV)

weights

The weights/direction to be used to compute the achievement scalarization. Each column contains a single weight vector. If no weight is supplied, weights are generated using Sobol sequences.

nPoints

Used only when no weights are supplied. An input for the weight generator (sobol sequences). This defines how many points are created.

Value

The function return the powered R2-indicator of the set.

References

Ke Shang, Hisao Ishibuchi, Min-Ling Zhang, and Yiping Liu. 2018. A new R2 indicator for better hypervolume approximation. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '18), Hernan Aguirre (Ed.). ACM, New York, NY, USA, 745-752. DOI: https://doi.org/10.1145/3205455.3205543

Examples

nPointToSample <- 100
nObjective <- 3
points <- matrix(runif(nPointToSample*nObjective), nrow = nObjective) # sample the points
ranks <- nsga2R::fastNonDominatedSorting(t(points)) # non-dominated sorting
points <- points[,ranks[[1]],drop=FALSE] # take only the non-dominated front
nPoints <- ncol(points) # check how many points are on the non-dominated front
reference <- rep(2,nObjective)

compute_R2HV(points,reference)