[Scip] Pricing generates an already existing column

[Martin Bergner]

Hi Cristina, (cc Marco, since that was the same question)

> I'm working on a B&Price algorithm for a minimization MIP and I realized
> that sometimes the algorithm generates already existing columns.
whenever I read that, my experience is that one of the following hold
(in order of appearance from my experience.

1. Your reduced cost computation is wrong. In this case, check it
   again. And then again, because usually, that's really the case.

2. The check for variables with negative reduced costs is wrong:
   Do you use an floating point check for the reduced costs, i.e.,
   if( SCIPisNegative(scip, redcost) ) instead of if( redcost < 0? )

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 ... .

I hope I could give you another hint.

Regards,
Martin

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