What is considered a good value of hypervolume indicator for a given Pareto front surface?

For the multiobjective optimization algorithm applied to a specific problem, I am optimizing for 3 objectives. I obtained a hypervolume value of the Pareto front points equal to HV= 0.014. I assume this is not a good value, is this right? When I saw sample example of 2 dimensional optimization in literature, values varied between 0.3 to 0.9. What is considered a good indicator value in my case?

Answer 1

[Alan Weiss]

The hypervolume depends on the scale of your objective functions, so there is no such thing as a "good" value. For a 3-objective problem, if you multiply all the objectives by 100 then the hypervolume changes by a factor of 1e6. Yet the underlying problem and solution have not changed at all.

Alan Weiss

MATLAB mathematical toolbox documentation

[Wiss Wiss]

I normalised all 3 objectives and obtained an HV of 0.014. Is that a bad indicator or an acceptable value?

[Alan Weiss]

I think that there is no general statement that can be made. It is not good or bad, it is just what happens with your problem.

If you are looking to get a larger extent of Pareto points, you can try setting initial points to the single-objective optima, as shown in Compare paretosearch and gamultiobj.

Good luck,

Alan Weiss

MATLAB mathematical toolbox documentation