emoaIndEps: Computation of the unary epsilon-indicator.

Description

Functions for the computation of unary and binary measures which are useful for the evaluation of the performace of EMOAs. See the references section for literature on these indicators.

Given a set of points points, emoaIndEps computes the unary epsilon-indicator provided a set of reference points ref.points.

The emoaIndHV function computes the hypervolume indicator Hyp(X, R, r). Given a set of point X (points), another set of reference points R (ref.points) (which maybe the true Pareto front) and a reference point r (ref.point) it is defined as Hyp(X, R, r) = HV(R, r) - HV(X, r).

Usage

emoaIndEps(points, ref.points)
emoaIndHV(points, ref.points, ref.point = NULL)
emoaIndR1(points, ref.points, ideal.point = NULL, nadir.point = NULL,
  lambda = NULL, utility = "tschebycheff")
emoaIndR2(points, ref.points, ideal.point = NULL, nadir.point = NULL,
  lambda = NULL, utility = "tschebycheff")
emoaIndR3(points, ref.points, ideal.point = NULL, nadir.point = NULL,
  lambda = NULL, utility = "tschebycheff")

Value

[numeric(1)] Epsilon indicator.

Arguments

points: [matrix]
Matrix of points.
ref.points: [matrix]
Set of reference points.
ref.point: [numeric]
A single reference point used, e.g., for the computation of the hypervolume indicator via emoaIndHV. If NULL the nadir point of the union of the points and ref.points is used.
ideal.point: [numeric]
The utopia point of the true Pareto front, i.e., each component of the point contains the best value if the other objectives are neglected.
nadir.point: [numeric]
Nadir point of the true Pareto front.
lambda: [integer(1)]
Number of weight vectors to use in estimating the utility function.
utility: [character(1)]
Name of the utility function to use. Must be one of “weightedsum”, “tschebycheff” or “augmented tschbycheff”.