hypervolume {eaf} | R Documentation |
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)
Arguments
data |
( |
reference |
( |
maximise |
( |
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.
Value
A single numerical value.
Author(s)
Manuel López-Ibáñez
References
Carlos M. Fonseca, Luís Paquete, Manuel López-Ibáñez (2006). “An improved dimension-sweep algorithm for the hypervolume indicator.” In Proceedings of the 2006 Congress on Evolutionary Computation (CEC 2006), 1157–1163. IEEE Press, Piscataway, NJ. doi: 10.1109/CEC.2006.1688440.
Nicola Beume, Carlos M. Fonseca, Manuel López-Ibáñez, Luís Paquete, Jan Vahrenhold (2009). “On the complexity of computing the hypervolume indicator.” IEEE Transactions on Evolutionary Computation, 13(5), 1075–1082. doi: 10.1109/TEVC.2009.2015575.
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))