The AUC of the EAF and the AOC (Hypervolume)
The Area-Over-the-Curve (i.e., the hypervolume) of a set of nondominated sets is exactly the the Area-Under-the-Curve (AUC) of their corresponding EAF, as this example shows.
library(reshape2)
library(ggplot2)
extdata_dir <- system.file(package="moocore", "extdata")
A <- read_datasets(file.path(extdata_dir, "ALG_1_dat.xz"))
A[,1:2] <- normalise(A[,1:2], to_range = c(0,1))
aoc <- mean(sapply(split.data.frame(A[,1:2], A[,3]), hypervolume, reference = 1))
eafA <- eaf(A[,1:2], A[,3])
eafA[,3] <- eafA[,3]/100
auc <- hypervolume(eafA, reference = c(1,1,0), maximise = c(FALSE,FALSE,TRUE))
cat("Runs = ", length(unique(A[,3])),
"\nAUC of EAF = ", auc,
"\nMean AOC = ", aoc, "\n")
#> Runs = 90
#> AUC of EAF = 0.7452171
#> Mean AOC = 0.7452171
runs <- 5:length(unique(A[,3]))
aocs <- c()
aucs <- c()
for (r in runs) {
a <- A[A[,3] <= r, ]
aoc <- mean(sapply(split.data.frame(a[,1:2], a[,3]), hypervolume, reference = 1))
eafa <- eaf(a[,1:2], a[,3])
eafa[,3] <- eafa[,3]/100
auc <- hypervolume(eafa, reference = c(1,1,0), maximise = c(FALSE,FALSE,TRUE))
aocs <- c(aocs, aoc)
aucs <- c(aucs, auc)
}
x <- melt(data.frame(r = runs, AOC = aocs, AUC=aucs), id.vars="r")
ggplot(x, aes(r, value, color=variable, linetype=variable)) +
geom_line(linewidth=1.5) +
labs(x = "Number of sets", y = "Value", color = "", linetype="")