hv_contributions {eaf} | R Documentation |
Computes the hypervolume contribution of each point given a set of points with respect to a given reference point assuming minimization of all objectives. Dominated points have zero contribution. Duplicated points have zero contribution even if not dominated, because removing one of them does not change the hypervolume dominated by the remaining set.
hv_contributions(data, reference, maximise = FALSE)
data |
( |
reference |
( |
maximise |
( |
(numeric) A numerical vector
Manuel López-Ibáñez
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.
data(SPEA2minstoptimeRichmond)
# The second objective must be maximized
# We calculate the hypervolume contribution of each point of the union of all sets.
hv_contributions(SPEA2minstoptimeRichmond[, 1:2], reference = c(250, 0),
maximise = c(FALSE, TRUE))
# Duplicated points show zero contribution above, even if not
# dominated. However, filter_dominated removes all duplicates except
# one. Hence, there are more points below with nonzero contribution.
hv_contributions(filter_dominated(SPEA2minstoptimeRichmond[, 1:2], maximise = c(FALSE, TRUE)),
reference = c(250, 0), maximise = c(FALSE, TRUE))