The fast non-dominated sorting algorithm was proposed by Deb et al. [1]. Non-dominated sorting expects a set of points and returns a set of non-dominated fronts. In short words, this is done as follows: the non-dominated points of the entire set are determined and assigned rank 1. Afterwards all points with the current rank are removed, the rank is increased by one and the procedure starts again. This is done until the set is empty, i.e., each point is assigned to a rank/level.
nds(x)
| x | [ |
|---|
List with the following components
Integer vector of ranks of length ncol(x). The higher
the rank, the higher the domination front the corresponding point is
located on.
Integer vector of length ncol(x). The \(i\)th element
is the domination number of the \(i\)th point.
This procedure is the key survival selection of the famous NSGA-II multi-objective evolutionary algorithm [1].
Keep in mind that this function assumes all objectives to be minimized. In case at least one objective is to be maximized, the data needs to be transformed accordingly in advance.
[1] Deb, K., Pratap, A., and Agarwal, S. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6 (8) (2002), 182-197.