Plot the Empirical Attainment Function for two objectives

Computes and plots the Empirical Attainment Function, either as attainment surfaces for certain percentiles or as points.

Usage

eafplot(x, ...)

# Default S3 method
eafplot(
  x,
  sets,
  groups = NULL,
  percentiles = c(0, 50, 100),
  attsurfs = NULL,
  maximise = c(FALSE, FALSE),
  type = "point",
  xlab = NULL,
  ylab = NULL,
  xlim = NULL,
  ylim = NULL,
  log = "",
  col = NULL,
  lty = c("dashed", "solid", "solid", "solid", "dashed"),
  lwd = 1.75,
  pch = NA,
  cex.pch = par("cex"),
  las = par("las"),
  legend.pos = paste0(ifelse(maximise[1L], "bottom", "top"), ifelse(rep_len(maximise,
    2L)[2L], "left", "right")),
  legend.txt = NULL,
  extra.points = NULL,
  extra.legend = NULL,
  extra.pch = 4:25,
  extra.lwd = 0.5,
  extra.lty = NA,
  extra.col = "black",
  xaxis.side = "below",
  yaxis.side = "left",
  axes = TRUE,
  sci.notation = FALSE,
  ...
)

# S3 method for class 'list'
eafplot(x, ...)

Arguments

x: Either a matrix of data values, or a data frame, or a list of data frames of exactly three columns.
...: Other graphical parameters to plot.default().
sets: (numeric())
Vector indicating which set each point belongs to.
groups: This may be used to plot profiles of different algorithms on the same plot.
percentiles: (numeric()) Vector indicating which percentile should be plot. The default is to plot only the median attainment curve.
attsurfs: TODO
maximise: (logical() | logical(1))
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.
type: (character(1))
string giving the type of plot desired. The following values are possible, points and area.
xlab, ylab, xlim, ylim, log, col, lty, lwd, pch, cex.pch, las: Graphical parameters, see plot.default().
legend.pos: the position of the legend, see legend(). A value of "none" hides the legend.
legend.txt: a character or expression vector to appear in the legend. If NULL, appropriate labels will be generated.
extra.points: A list of matrices or data.frames with two-columns. Each element of the list defines a set of points, or lines if one of the columns is NA.
extra.legend: A character vector providing labels for the groups of points.
extra.pch, extra.lwd, extra.lty, extra.col: Control the graphical aspect of the points. See points() and lines().
xaxis.side: On which side that xaxis is drawn. Valid values are "below" and "above". See axis().
yaxis.side: On which side that yaxis is drawn. Valid values are "left" and "right". See axis().
axes: A logical value indicating whether both axes should be drawn on the plot.
sci.notation: Generate prettier labels

Value

the attainment surfaces computed (invisibly).

Details

This function can be used to plot random sets of points like those obtained by different runs of biobjective stochastic optimisation algorithms. An EAF curve represents the boundary separating points that are known to be attainable (that is, dominated in Pareto sense) in at least a fraction (quantile) of the runs from those that are not. The median EAF represents the curve where the fraction of attainable points is 50%. In single objective optimisation the function can be used to plot the profile of solution quality over time of a collection of runs of a stochastic optimizer.

Methods (by class)

eafplot(default): Main function
eafplot(list): List interface for lists of data.frames or matrices

References

Manuel López-Ibáñez, Luís Paquete, Thomas Stützle (2010). “Exploratory Analysis of Stochastic Local Search Algorithms in Biobjective Optimization.” In Thomas Bartz-Beielstein, Marco Chiarandini, Luís Paquete, Mike Preuss (eds.), Experimental Methods for the Analysis of Optimization Algorithms, 209–222. Springer, Berlin, Germany. doi:10.1007/978-3-642-02538-9_9 .

Examples

# \donttest{
extdata_path <- system.file(package = "moocore", "extdata")
A1 <- read_datasets(file.path(extdata_path, "ALG_1_dat.xz"))
A2 <- read_datasets(file.path(extdata_path, "ALG_2_dat.xz"))
eafplot(A1, percentiles = 50, sci.notation = TRUE, cex.axis=0.6)

# The attainment surfaces are returned invisibly.
attsurfs <- eafplot(list(A1 = A1, A2 = A2), percentiles = 50)

str(attsurfs)
#> List of 2
#>  $ 50-A1:'data.frame':	1183 obs. of  2 variables:
#>   ..$ X1: num [1:1183] 4.95e+09 4.95e+09 4.95e+09 4.95e+09 4.96e+09 ...
#>   ..$ X2: num [1:1183] 8.59e+09 8.57e+09 8.52e+09 8.49e+09 8.40e+09 ...
#>  $ 50-A2:'data.frame':	1422 obs. of  2 variables:
#>   ..$ X1: num [1:1422] 5.16e+09 5.17e+09 5.18e+09 5.21e+09 5.21e+09 ...
#>   ..$ X2: num [1:1422] 8.22e+09 8.19e+09 8.12e+09 8.09e+09 8.02e+09 ...

## Save as a PDF file.
# dev.copy2pdf(file = "eaf.pdf", onefile = TRUE, width = 5, height = 4)
# }

## Using extra.points
# \donttest{
data(HybridGA, package="moocore")
data(SPEA2relativeVanzyl, package="moocore")
eafplot(SPEA2relativeVanzyl, percentiles = c(25, 50, 75),
        xlab = expression(C[E]), ylab = "Total switches", xlim = c(320, 400),
        extra.points = HybridGA$vanzyl, extra.legend = "Hybrid GA")


data(SPEA2relativeRichmond, package="moocore")
eafplot (SPEA2relativeRichmond, percentiles = c(25, 50, 75),
         xlab = expression(C[E]), ylab = "Total switches",
         xlim = c(90, 140), ylim = c(0, 25),
         extra.points = HybridGA$richmond, extra.lty = "dashed",
         extra.legend = "Hybrid GA")


eafplot (SPEA2relativeRichmond, percentiles = c(25, 50, 75),
         xlab = expression(C[E]), ylab = "Total switches",
         xlim = c(90, 140), ylim = c(0, 25), type = "area",
         extra.points = HybridGA$richmond, extra.lty = "dashed",
         extra.legend = "Hybrid GA", legend.pos = "bottomright")


data(SPEA2minstoptimeRichmond, package="moocore")
SPEA2minstoptimeRichmond[,2] <- SPEA2minstoptimeRichmond[,2] / 60
eafplot (SPEA2minstoptimeRichmond, xlab = expression(C[E]),
         ylab = "Minimum idle time (minutes)", maximise = c(FALSE, TRUE),
         las = 1, log = "y", main = "SPEA2 (Richmond)",
         legend.pos = "bottomright")

# }