eaf (version 2.5.2)

hypervolume: Hypervolume metric

Description

Computes the hypervolume metric with respect to a given reference point assuming minimization of all objectives.

Usage

hypervolume(data, reference, maximise = FALSE)

Value

A single numerical value.

Arguments

data

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

reference

(numeric())
Reference point as a vector of numerical values.

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.

Author

Manuel López-Ibáñez

Details

The algorithm has \(O(n^{d-2} \log n)\) time and linear space complexity in the worst-case, but experimental results show that the pruning techniques used may reduce the time complexity even further.

References

FonPaqLop06:hypervolumeeaf

BeuFonLopPaqVah09:teceaf

Examples

data(SPEA2minstoptimeRichmond)
# The second objective must be maximized
# We calculate the hypervolume of the union of all sets.
hypervolume(SPEA2minstoptimeRichmond[, 1:2], reference = c(250, 0),
            maximise = c(FALSE, TRUE))