nondominated: Identify and remove dominated points according to Pareto...

In moocore: Core Mathematical Functions for Multi-Objective Optimization

Identify and remove dominated points according to Pareto optimality

Description

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

any_dominated() quickly detects if a set contains any dominated point.

Usage

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

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

any_dominated(x, maximise = FALSE, keep_weakly = 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	logical(1) If FALSE, return FALSE for any duplicates of nondominated points, except the last one.

Details

Given n points of dimension m, the current implementation always uses the best-known O(n \log n) dimension-sweep algorithm \citepKunLucPre1975jacm for m \leq 3. For m \geq 4, functions is_nondominated() and filter_dominated() use the best-known O(n \log^{m-2} n) algorithm \citepKunLucPre1975jacm when n > 16, and the naive O(m n^2) algorithm otherwise. Function any_dominated() always uses the naive algorithm for m \geq 4.

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.

any_dominated() returns TRUE if x contains any (weakly-)dominated points, FALSE otherwise.

Author(s)

Manuel López-Ibáñez

References

\insertAllCited

See Also

pareto_rank()

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)
any_dominated(S)
any_dominated(S, keep_weakly = TRUE)
any_dominated(filter_dominated(S))
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)
}

moocore documentation built on July 12, 2026, 5:06 p.m.