Exact computation of the EAF in 2D or 3D

This function computes the EAF given a set of 2D or 3D points and a vector set that indicates to which set each point belongs.

Usage

eaf(x, sets, percentiles = NULL, maximise = FALSE, groups = NULL)

Arguments

x: matrix()|data.frame()
Matrix or data frame of numerical values, where each row gives the coordinates of a point. If sets is missing, the last column of x gives the sets.
sets: integer()
A vector that indicates the set of each point in x. If missing, the last column of x is used instead.
percentiles: numeric()
Vector indicating which percentiles are computed. NULL computes all.
maximise: logical()
Whether the objectives must be maximised instead of minimised. Either a single logical value that applies to all objectives or a vector of logical values, with one value per objective.
groups: factor()
Indicates that the EAF must be computed separately for data belonging to different groups.

Value

data.frame()
A data frame containing the exact representation of EAF. The last column gives the percentile that corresponds to each point. If groups is not NULL, then an additional column indicates to which group the point belongs.

Note

There are several examples of data sets in system.file(package="moocore","extdata"). The current implementation only supports two and three dimensional points.

References

Viviane Grunert da Fonseca, Carlos M. Fonseca, Andreia O. Hall (2001). “Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function.” In Eckart Zitzler, Kalyanmoy Deb, Lothar Thiele, Carlos A. Coello Coello, David Corne (eds.), Evolutionary Multi-criterion Optimization, EMO 2001, volume 1993 of Lecture Notes in Computer Science, 213–225. Springer, Berlin~/ Heidelberg. doi:10.1007/3-540-44719-9_15 .

Carlos M. Fonseca, Andreia P. Guerreiro, Manuel López-Ibáñez, Luís Paquete (2011). “On the Computation of the Empirical Attainment Function.” In R H C Takahashi, Kalyanmoy Deb, Elizabeth F. Wanner, Salvatore Greco (eds.), Evolutionary Multi-criterion Optimization, EMO 2011, volume 6576 of Lecture Notes in Computer Science, 106–120. Springer, Berlin~/ Heidelberg. doi:10.1007/978-3-642-19893-9_8 .

Manuel López-Ibáñez, Diederick Vermetten, Johann Dreo, Carola Doerr (2025). “Using the Empirical Attainment Function for Analyzing Single-objective Black-box Optimization Algorithms.” IEEE Transactions on Evolutionary Computation. doi:10.1109/TEVC.2024.3462758 .

Author

Manuel López-Ibáñez

Examples

extdata_path <- system.file(package="moocore", "extdata")

x <- read_datasets(file.path(extdata_path, "example1_dat"))
# Compute full EAF (sets is the last column)
str(eaf(x))
#>  num [1:215, 1:3] 5128176 5134240 5142568 5144532 5155408 ...

# Compute only best, median and worst
str(eaf(x[,1:2], sets = x[,3], percentiles = c(0, 50, 100)))
#>  num [1:50, 1:3] 5128176 5134240 5142568 5144532 5155408 ...

x <- read_datasets(file.path(extdata_path, "spherical-250-10-3d.txt"))
y <- read_datasets(file.path(extdata_path, "uniform-250-10-3d.txt"))
x <- rbind(data.frame(x, groups = "spherical"),
           data.frame(y, groups = "uniform"))
# Compute only median separately for each group
z <- eaf(x[,1:3], sets = x[,4], groups = x[,5], percentiles = 50)
str(z)
#> 'data.frame':	12650 obs. of  5 variables:
#>  $ X1    : num  0.865 0.787 0.682 0.739 0.865 ...
#>  $ X2    : num  0.966 0.966 0.997 0.966 0.926 ...
#>  $ X3    : num  0.00264 0.00421 0.00483 0.00449 0.00421 ...
#>  $ X4    : num  50 50 50 50 50 50 50 50 50 50 ...
#>  $ groups: chr  "spherical" "spherical" "spherical" "spherical" ...