[Scip] Branching on variables in the original problem

[Gerald Gamrath]

Dear Shahin,

yes, if you have these constraints in your master problem, you also need 
to take these constraints into account in the pricing problem objective.
But this has nothing to do with SCIP, it is just about the definition of 
reduced costs and how branch-and-price works.

You can image this constraint as x_j = x_j, with the left-hand side 
replaced by the \lambda variables. Therefore, a variable will be added 
to the constraint if and only if it represents a solution of the pricing 
problem in which x_j is set to 1. Thus, you need to subtract (or add, 
depending on your objective sense) the dual solution value of this 
constraint from the objective of variable x_j in the pricing problem.

Best,
Gerald

Am 27.04.2014 00:53, schrieb Shahin Gelareh:
> Dear SCIPers
>
> It is clean that one can explicitly express the original variables as  
> combination of the master variables.
> My original variables are binary.
> But when one has \sum_i(\lambda_ij_x_ij )= x_j \in {0,1} there will be 
> dual variables associated to these sets of constraint.
> How are these constraints which also include the lambdas would 
> contribute in some way in building the  pricing problem objective?
>
> My results show that they cannot be  neglected even if they are 
> equality constraints otherwise it may never converge. So how we do we 
> actually handle them in  SCIP ?
>
> Cheers
> Shahin
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> On Thu, Jan 10, 2013 at 8:44 AM, Marco Luebbecke 
> <marco.luebbecke at rwth-aachen.de 
> <mailto:marco.luebbecke at rwth-aachen.de>> wrote:
>
>     Dear Victor,
>
>     the easiest way is to explicitly express the original variables as
>     combination of your master variables. You can then directly branch on
>     these original variables, also the elimination of master variables
>     that are incompatible to the branching decisions is for free then (in
>     the binary case). You only need to tell your pricing problem about
>     branching decisions, see
>
>     http://scip.zib.de/doc/html/FAQ.shtml#Q5.3
>
>
>     Best regards,
>     Marco
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