I’ve worked in the past on algorithms to approximate the hypervolume of data sets, but needed a way to generate some data sets to test the algorithms against. The algorithm to generate the data sets presented here does that, and also provides a way to generate data sets with known numbers of Pareto points as a byproduct.

The basics of the algorithm can be seen in this animation (click the graphic) which shows that new points are repeatedly created in the “corners” of the blocks. by doing this, we know exactly how much volume is added each time.

Here’s a partially constructed nest block.

And here is the Mathematica code to generate the data.

(MMA) Known HV for blog

Here’s the code in a PDF document.

(PDF) Known HV for blog