is_nondominated {moocore}

Identify, remove and rank dominated points according to Pareto optimality

Description

Identify nondominated points with is_nondominated() and remove dominated ones with filter_dominated().

pareto_rank() ranks points according to Pareto-optimality, which is also called nondominated sorting (Deb et al. 2002).

Usage

is_nondominated(x, maximise = FALSE, keep_weakly = FALSE)

filter_dominated(x, maximise = FALSE, keep_weakly = FALSE)

pareto_rank(x, maximise = FALSE)

Arguments

x

matrix()|data.frame()
Matrix or data frame of numerical values, where each row gives the coordinates of a point.

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.

keep_weakly

If FALSE, return FALSE for any duplicates of nondominated points.

Details

pareto_rank() is meant to be used like rank(), but it assigns ranks according to Pareto dominance. Duplicated points are kept on the same front. When ncol(data) == 2, the code uses the O(n \log n) algorithm by Jensen (2003).

Value

is_nondominated() returns a logical vector of the same length as the number of rows of data, where TRUE means that the point is not dominated by any other point.

filter_dominated returns a matrix or data.frame with only mutually nondominated points.

pareto_rank() returns an integer vector of the same length as the number of rows of data, where each value gives the rank of each point.

Author(s)

Manuel López-Ibáñez

References

Kalyanmoy Deb, A Pratap, S Agarwal, T Meyarivan (2002). “A fast and elitist multi-objective genetic algorithm: NSGA-II.” IEEE Transactions on Evolutionary Computation, 6(2), 182–197. doi: 10.1109/4235.996017.

M T Jensen (2003). “Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms.” IEEE Transactions on Evolutionary Computation, 7(5), 503–515.

Examples

S = matrix(c(1,1,0,1,1,0,1,0), ncol = 2, byrow = TRUE)
is_nondominated(S)

is_nondominated(S, maximise = TRUE)

filter_dominated(S)

filter_dominated(S, keep_weakly = TRUE)

path_A1 <- file.path(system.file(package="moocore"),"extdata","ALG_1_dat.xz")
set <- read_datasets(path_A1)[,1:2]
is_nondom <- is_nondominated(set)
cat("There are ", sum(is_nondom), " nondominated points\n")

if (requireNamespace("graphics", quietly = TRUE)) {
   plot(set, col = "blue", type = "p", pch = 20)
   ndset <- filter_dominated(set)
   points(ndset[order(ndset[,1]),], col = "red", pch = 21)
}

ranks <- pareto_rank(set)
str(ranks)
if (requireNamespace("graphics", quietly = TRUE)) {
   colors <- colorRampPalette(c("red","yellow","springgreen","royalblue"))(max(ranks))
   plot(set, col = colors[ranks], type = "p", pch = 20)
}