[Scip] integer variables get assigned non-integer values

[Stefan Lörwald]

Hi Timo,

if the user requires binary variables any solution having non-binary
results are per definition infeasible.
Therefore SCIP shouldn't report 0.9999999 as a feasible solution (even
w.r.t. tolerances), if it isn't 0/1 feasible.
Either it should report as infeasible because the best value (0.999999)
doesn't satisfy the 0/1 constraint, or it should report as infeasible
because rounding to 1 would be infeasible.

However I'd very much like to actually see a case in which 0.9999999 is
feasible, but 1 is not. Do you have an example at hand?

Stefan

One amendment to Stefan's reply:
> > There is a small thing SCIP could do better actually: sometimes you'll
> get
> > 0.9999999 instead of 1 (which is representable as double) for e.g. binary
> > variables. In theory such output could be enforced to 0/1 or integral
> > value once the solving process is completed.
>
> This is not correct in general. As argued below, it might be that the
> 0.9999999 solution is feasible (w.r.t. tolerances), whereas the 0/1
> solution is not.
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