A special data structure needed by FonsecaHyperVolume.
A special data structure needed by FonsecaHyperVolume.
It consists of several doubly linked lists that share common nodes. So, every node has multiple predecessors and successors, one in every list.
Reference point for the hypervolume computation
Compute the hypervolume that is dominated by a non-dominated front.
Compute the hypervolume that is dominated by a non-dominated front. Before the HV computation, front and reference point are translated, so that the reference point is [0, ..., 0].
the parato front
the hypervolume
Compute the hypervolume contribution for each front
Compute the nadir of a set of points
Compute the nadir of a set of points
the nadir point
Hypervolume computation based on variant 3 of the algorithm in the paper: C. M. Fonseca, L. Paquete, and M. Lopez-Ibanez. An improved dimension-sweep algorithm for the hypervolume indicator. In IEEE Congress on Evolutionary Computation, pages 1157-1163, Vancouver, Canada, July 2006.
FIXE: The implementation is ugly, as the algorithm as directly been translated from python