[Scip] integer variables get assigned non-integer values

[Marco Lübbecke]

2013/12/4 Stefan Lörwald <stefan.loerwald at gmail.com>

>
> 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.
>

I believe this is not what we want. If the user requires binary variables,
and (w.r.t. tolerances) there is no binary feasible solution, the answer to
the computation will be "there is no feasible solution". From a practical
perspective, this is not very satisfactory. And it may be a false answer.
Maybe there IS a feasible solution, but we did not find it b/c of
computations are subject to tolerance.

The solution you get from a MIP solver may be in some rare cases completely
irrelevant, wrong or otherwise flawed. Probably, this does not happen too
often, but it may happen. Now, I rather see an "almost" feasible solution
than "there is no answer". At least as a practitioner. But again, both
answers, feasible or infeasible, may be wrong, so I prefer the report "I
probably found an almost feasible solution" rather than "the correct answer
may be 'infeasible'".

Marco
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