computeIndicators {ecr}

Computation of EMOA performance indicators.

Description

Given a data.frame of Pareto-front approximations for different sets of problems, algorithms and replications, the function computes sets of unary and binary EMOA performance indicators. This function makes use of parallelMap to parallelize the computation of indicators.

Usage

computeIndicators(
  df,
  obj.cols = c("f1", "f2"),
  unary.inds = NULL,
  binary.inds = NULL,
  normalize = FALSE,
  offset = 0,
  ref.points = NULL,
  ref.sets = NULL
)

Arguments

df

[data.frame]
Data frame with columns obj.cols, “prob”, “algorithm” and “repl”.

obj.cols

[character(>= 2)]
Column names of the objective functions. Default is c("f1", "f2"), i.e., the bi-objective case is assumed.

unary.inds

[list]
Named list of unary indicators which shall be calculated. Each component must be another list with mandatory argument fun (the function which calculates the indicator) and optional argument pars (a named list of parameters for fun). Function fun must have the signiture “function(points, arg1, ..., argk, ...)”. The arguments “points” and “...” are mandatory, the remaining are optional. The names of the components on the first level are used for the column names of the output data.frame. Default is list(HV = list(fun = computeHV)), i.e., the dominated Hypervolume indicator.

binary.inds

[list]
Named list of binary indicators which shall be applied for each algorithm combination. Parameter binary.inds needs the same structure as unary.inds. However, the function signature of fun is slighly different: “function(points1, points2, arg1, ..., argk, ...)”. See function emoaIndEps for an example. Default is list(EPS = list(fun = emoaIndEps)).

normalize

[logical(1)]
Normalize approximation sets to [0, 1]^p where p is the number of objectives? Normalization is done on the union of all approximation sets for each problem. Default is FALSE.

offset

[numeric(1)]
Offset added to reference point estimations. Default is 0.

ref.points

[list]
Named list of numeric vectors (the reference points). The names must be the unique problem names in df$prob or a subset of these. If NULL (the default), reference points are estimated from the approximation sets for each problem.

ref.sets

[list]
Named list matrizes (the reference sets). The names must be the unique problem names in df$prob or a subset of these. If NULL (the default), reference points are estimated from the approximation sets for each problem.

Value

[list] List with components “unary” (data frame of unary indicators), “binary” (list of matrizes of binary indicators), “ref.points” (list of reference points used) and “ref.sets” (reference sets used).

References

[1] Knowles, J., Thiele, L., & Zitzler, E. (2006). A Tutorial on the Performance Assessment of Stochastic Multiobjective Optimizers. Retrieved from https://sop.tik.ee.ethz.ch/KTZ2005a.pdf [2] Knowles, J., & Corne, D. (2002). On Metrics for Comparing Non-Dominated Sets. In Proceedings of the 2002 Congress on Evolutionary Computation Conference (CEC02) (pp. 711–716). Honolulu, HI, USA: Institute of Electrical and Electronics Engineers. [3] Okabe, T., Yaochu, Y., & Sendhoff, B. (2003). A Critical Survey of Performance Indices for Multi-Objective Optimisation. In Proceedings of the 2003 Congress on Evolutionary Computation Conference (CEC03) (pp. 878–885). Canberra, ACT, Australia: IEEE.