[Paradiseo-help] [Paradiseo-users] MOEO Hypervolume binary metric

Johann Dréo johann at dreo.fr
Mer 26 Juin 17:27:17 CEST 2013


I'm still working on MOEO, trying to implement a hard feasibility
constraint :)

I've seen that the class moeoHypervolumeBinaryMetric is designed to compute
the hypervolume based only on the "rho" method (compute a reference point
based on the range around the pop), but that it does not permits to use an
explicit reference point (as in other HV-related operators).

Unfortunately, I have, in my application, homogeneous populations (all
individuals having the same objectives values). This leads to a problem
when computing the range, that I solved by adding an epsilon to the
computed range (which thus cannot be null). And this leads to a problem
with the normalization of the HV (dividing by epsilon is not always a good
idea when using floats).

My question is:

Should we consider that the correct answer to homogeneous pop is to use a
static reference point (the user being responsible for choosing it wisely)?
Should we try to generalize the normalization so that it can handle
correctly floating point errors? Incidentally, what is the range of the
normalized hyper-volume: is it [-1,1]? I already get values greater than 1
with the current code…

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