eaf (version 1.9-1)

is_nondominated: 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(data, maximise = FALSE, keep_weakly = FALSE)
filter_dominated(data, maximise = FALSE, keep_weakly = FALSE)
pareto_rank(data, maximise = FALSE)

Arguments

data

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

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.

keep_weakly

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

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.

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).

References

Deb, K., S. Agrawal, A. Pratap, and T. Meyarivan. A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2): 182-197, 2002.

M. T. Jensen. Reducing the run-time complexity of multiobjective EAs: The NSGA-II and other algorithms. IEEE Transactions on Evolutionary Computation, 7(5):503<U+2013>515, 2003.

Examples

# NOT RUN {
path_A1 <- file.path(system.file(package="eaf"),"extdata","ALG_1_dat")
set <- read_datasets(path_A1)[,1:2]

is_nondom <- is_nondominated(set)
cat("There are ", sum(is_nondom), " nondominated points\n")

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)
colors <- colorRampPalette(c("red","yellow","springgreen","royalblue"))(max(ranks))
plot(set, col = colors[ranks], type = "p", pch = 20)

# }