dominated_hypervolume {emoa} R Documentation

## Dominated Hypervolume calculation

### Description

dominated_hypervolume calculates the dominated hypervolume of the points in points.

### Usage

  dominated_hypervolume(points, ref)

hypervolume_contribution(points, ref)


### Arguments

 points Matrix containing the points one per column. ref Optional reference point. If not provided the maximum in each dimension is used.

### Details

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.

### Value

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.

### Author(s)

Olaf Mersmann olafm@statistik.tu-dortmund.de

### References

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.