emoa (version 0.5-0)

hypervolume_indicator: Binary quality indicators

Description

Calculates the quality indicator value of the set of points given in x with respect to the set given in o. As with all functions in emoa that deal with sets of objective values these are stored by column.

Usage

hypervolume_indicator(points, o, ref)
  epsilon_indicator(points, o)
  r1_indicator(points, o, ideal, nadir, lambda, utility = "Tchebycheff")
  r2_indicator(points, o, ideal, nadir, lambda, utility = "Tchebycheff")
  r3_indicator(points, o, ideal, nadir, lambda, utility = "Tchebycheff")

Arguments

points

Matrix of points for which to calculate the indicator value stored one per column.

o

Matrix of points of the reference set.

ref

Reference point, if omitted, the nadir of the point sets is used.

ideal

Ideal point of true Pareto front. If omited the ideal of both point sets is used.

nadir

Nadir of the true Pareto front. If ommited the nadir of both point sets is used.

lambda

Number of weight vectors to use in estimating the utility.

utility

Name of utility function.

Value

Value of the quality indicator.

References

Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., and Grunert da Fonseca, V (2003): Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation, 7(2), 117-132.