Description Usage Arguments Details Value Author(s) References See Also

`dominated_hypervolume`

calculates the dominated
hypervolume of the points in `points`

.

1 2 3 | ```
dominated_hypervolume(points, ref)
hypervolume_contribution(points, ref)
``` |

`points` |
Matrix containing the points one per column. |

`ref` |
Optional reference point. If not provided the maximum in each dimension is used. |

`hypervolume_contribution`

calculates the
hypervolume contribution of each point.

If no reference point `ref`

is given, one is
automatically calculated by determening the maximum in
each coordinate.

Currently only one general algorithm is implemented due to Fonseca et.al. but work is underway to include others such as the Beume & Rudolph approach as well as the approach by Bradstreet et.al.

The 1D and 2D cases are handle seperately by efficient
algorithms. Calculates the exact dominated hypervolume of
the points given in `x`

subject to the reference
point `ref`

.

For `dominated_hypervolume`

the dominated
hypervolume by the points in `points`

with respect
to the reference point `ref`

. For
`hypervolume_contribution`

a vector giving the
hypervolume soley dominated by that point.

Olaf Mersmann olafm@statistik.tu-dortmund.de

This code uses version 1.3 of the hypervolume code available from http://iridia.ulb.ac.be/~manuel/hypervolume. For a description of the algorithm see

Carlos M. Fonseca, Luis Paquete, and Manuel Lopez-Ibanez.
*An improved dimension-sweep algorithm for the
hypervolume indicator*. In IEEE Congress on Evolutionary
Computation, pages 1157-1163, Vancouver, Canada, July
2006.

`nondominated_points`

to extract the pareto
front approximation from a given set of points and
`nds_hv_selection`

for a selection strategy
based on the hypervolume contribution of each point.

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