eaf (version 1.0)

eafplot: Plot the Empirical Attainment Function for two objectives

Description

Computes and plots the Empirical Attainment Function, either as attainment surfaces for certain percentiles or as points. This function can be used to plot random sets of points like those obtained by different runs of biobjective stochastic optimization 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 optimization the function can be used to plot the profile of solution quality over time of a collection of runs of a stochastic optmizer.

Usage

eafplot(x, ...)eafplot.default(x, sets = NULL, groups = NULL,
            percentiles = c(0,50,100),
            attsurfs = NULL, 
            xlab = "objective 1", ylab = "objective 2",
            xlim = NULL, ylim = NULL,
            log = "",
            type = "point",
            col = c("black", "darkgrey", "black", "grey40", "darkgrey"),
            lty = c("dashed", "solid", "solid", "solid", "dashed"),
            lwd = c(1.75),
            pch = NA,
            cex.pch = par("cex"),
            las = par("las"),
            legend.pos = "topright",
            legend.txt = NULL,
            extra.points = NULL, extra.legend = NULL,
            extra.pch = c(4:25),
            extra.lwd = 0.5,
            extra.lty = "dashed",
            extra.col = "black",
            ymaximise = FALSE,
            xaxis.side = 1, yaxis.side = 2,
            ... )eafplot.data.frame(x, y = NULL, ...)eafplot.formula(x, data = data.frame(), groups = NULL, subset = NULL,
            percentiles = NULL, include.extremes = FALSE, ...)eafplot.list(x, ...)

Arguments

x

either a matrix of data values, or a data frame, or a list of data frames of exactly three columns, or a a formula. Formulas of the type: time + cost ~ run | instance will draw time on the x-axis and cost

y

either a matrix of data values, or a data frame.

data

a data frame containing the fields mentioned in the formula and in groups.

groups

this may be used to plot profiles of different algorithms on the same plot.

subset

a vector indicating which rows of the data should be used. If left to default NULL all data in the data frame are used.

include.extremes

whether the plot has to include x and y extremes. These points are weakly dominated and hence they would not be plotted with the default include.extremes=FALSE.

sets

a vector indicating which set each point belongs to.

percentiles

a vector indicating which percentile should be plot. The default is to plot only the median attainment curve.

attsurfs

if different than NULL, a list of attainment surfaces as ????

type

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.

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.pch, extra.lwd, extra.lty, extra.col

control the graphical aspect of the points. See points and lines.

extra.legend

is a character vector providing labels for the groups of points.

ymaximise

whether the y-axis denotes a maximisation problem. The EAF is calculated accordingly, and the y-axis is reversed for plotting.

xaxis.side

controls on which side that xaxis is drawn. See axis.

yaxis.side

controls on which side that yaxis is drawn. See axis.

...

Other graphical parameters to plot.default.

Value

• No value is returned.

See Also

read.data.sets, eafdiffplot

Examples

data(gcp2x2)
tabucol<-subset(gcp2x2, alg!="TSinN1")
tabucol$alg<-tabucol$alg[drop=TRUE]
eafplot(time+best~run,data=tabucol,subset=tabucol$inst=="DSJC500.5")

eafplot(time+best~run|inst,groups=alg,data=gcp2x2)
eafplot(time+best~run|inst,groups=alg,data=gcp2x2,
	percentiles=c(0,50,100),include.extremes=TRUE,
	cex=1.4, lty=c(2,1,2),lwd=c(2,2,2),
        col=c("black","blue","grey50"))

A1 <- read.data.sets(file.path(system.file(package = "eaf"), "extdata", "ALG_1_dat"))
A2 <- read.data.sets(file.path(system.file(package = "eaf"), "extdata", "ALG_2_dat"))
eafplot(A1, A2, percentiles = c(50))
eafplot(list(A1 = A1, A2 = A2), percentiles = c(50))
dev.copy2pdf(file = "eaf.pdf", onefile = TRUE, width = 5, height = 4)

## Using extra.points
data(HybridGA)
data(SPEA2relativeVanzyl)
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)
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")

data(SPEA2minstoptimeRichmond)
SPEA2minstoptimeRichmond[,2] <- SPEA2minstoptimeRichmond[,2] / 60
eafplot (SPEA2minstoptimeRichmond, xlab = expression(C[E]),
         ylab = "Minimum idle time (minutes)",
         las = 1, log = "y", ymaximise = TRUE, main = "SPEA2 (Richmond)")