Hypervolume calculation in 4D doesn't handle dominated points well (one algorithm)

[naceee]

Hi, i am a student from @ttusar and I am working on converting your algorithms to a python library. During testing I figured out that your algorithm for computing hypervolume in 4D doesn't handle dominated points well.

Minimal example:

I have a set of nondominated points in 4 dimensions called points_nd.txt:

4 3 2 1
2 2 2 2
1 2 3 4

with the reference point 5 5 5 5.

Hypervolume of the given points with respect to the reference point is 93: I calculated it by hand as well as confirmed with both your algorithms for calculating hypervolume in 4D.

$ ./hvc examples/points_nd.txt -r "5 5 5 5"
93
$ ./hvc examples/points_nd.txt -r "5 5 5 5" -R
93

However if I add a point 3 3 3 3 which is obviously dominated by point 2 2 2 2, the result of one of the algorithms changes (the one without the -R flag):

4 3 2 1
2 2 2 2
1 2 3 4
3 3 3 3

$ ./hvc examples/points.txt -r "5 5 5 5" -R
93
$ ./hvc examples/points.txt -r "5 5 5 5"
97

[apguerreiro]

Hi @naceee, thank you for reaching out and for reporting this issue.

In the current implementation we were assuming that the input set was a nondominated point set and, therefore, it was expected that the calculation could be incorrect when this requirement is not satisfied.

In any case, we plan to change the code to admit dominated points (to some extent). We will try fix this issue as soon as possible.