# How to compute Generational Distance, Inverted Generational Distance, Epsilon Indicator, and Hypervolume for a Pareto front?

In order to find the quality indicators like Generational Distance, Inverted Generational Distance, Epsilon Indicator, and HyperVolume for a Pareto front I want to normalize the values of approximation front obtained on solving the algorithm based on reference front which I assume encloses the approximation front. Is it correct to do so?

Basically, rather than normalizing the approximation front and reference front. I have to normalize the approximate front between 0 to 1 based on max and min values of reference front?

Also how to compute reference point? Is it the maximum of each objective value in a reference front if the problem is a min-min?

The reference front is another name for the pareto front of the problem. You find it either by solving the problem symbolically, constructing a problem around some pareto front or running and global optimizer long enough. If you want to normalize the any front it is sensible to do so using the reference front. Over what (hyper) cuboid you normalize the fronts is your decision, there is no right answer just answers that don't match your usecase. The maximum of each objective value might be meaningless if it is unbounded. Consider $$\min_{x,y} x,y \ \text{ subject to: } xy = 1$$