[Scip] Pricing generates an already existing column

[Gerald Gamrath]

Hi Martin,

> Additionally, it might be the following:
> 3. You use CPLEX as an LP solver
>    With CPLEX 12.2 and 12.2, I noticed this behaviour. The callable
>    library returned different reduced cost than reading in the master
>    problem in the CPLEX command line version. The dual values from
>    CPLEX as standalone product would be correct, that is no variable
>    would price out favorably whereas the dual values from the API lead
>    to new priced variables. You might want to try a different LP solver
>    in this case. For me, CPLEX stopped returning these useless dual
>    variables after some iterations, and since I had a set partitioning
>    master, I didn't care so much about this issue anymore since in an
>    optimal solution, the problem would go away anyway ... .
some time ago, we had an issue with CPLEX for branch-and-price related
to the fastmip setting. This should be fixed for quite some time and I
did not encounter it since then. In particular with the latest release,
the LP cutoff bound is automatically disabled for branch-and-price and
fastmip should not make a difference. However, to be on the safe side,
you could disable this and see if it helps.

Concerning the difference in the reduced costs, are you sure this really
was an issue? If your problem has some degeneracy, it might happen that
there are alternative optimal (dual) LP solutions, in particular since
using CPLEX as an LP solver within SCIP changes some things, e.g.,
starting from a basis, no presolving, tightened tolerances,...
Are you sure that the dual solution returned by the callable library was
not dual feasible or the reduced costs did not correspond to this dual
solution? Otherwise, it might just have been a different, but not
necessarily wrong dual solution.

But of course, you are right that there might also be a bug somewhere
and trying a different LP solver is always a good suggestion.

PS: If you see this issue with CPLEX again, I would be very interested
in looking into it.

Best,
Gerald