[SCIP] Obtaining Bound Constraints from variables

[Rolf van der Hulst]

Hi André,

Although I am not sure if there is a way to explicitly get the dual 
solutions for the variables, I do have a workaround which would work for 
you.

In many branch-and-price applications, the variable bounds are 
implicitly satisfied. Thus, SCIP supports disabling them (e.g. 
preventing them from entering the LP) by setting 'lazy bounds' through 
the functions
SCIPchgVarLbLazy() and SCIPchgVarUbLazy(). In debug mode, SCIP checks if 
the variables satisfy these lazy bounds, but does not enforce them in 
the LP. In release mode, they are equivalent to unbounded variables.

In your case, you can make the bounds on relevant variables lazy, and 
then explicitly add the variable bound constraints to the master problem 
as linear constraints (rather than implicitly during variable creation).
Then, you can simply use the SCIPgetDualsolLinear() on these variable 
bound constraints to get the dual solution.

There might be an easier way to do this, as it can be some work to add 
all of the variable bounds explicitly as constraints.

Best,

Rolf

On 31-08-2022 15:48, André Mazal Krauss wrote:
> Hello SCIP team,
>
> I'm currently working on a VRP-related application, using SCIP.  I'm 
> using a Set Partioning formulation with Branch & Price, and my 
> formulation is a minimization problem. I've started having issues with 
> pricing of repeated variables and slow convergence. I suspect this is 
> happening because I'm not correctly considering the duals of bound 
> constraints on my pricing.
>
> My variables are all binary, so they should have implicit linear x > 0 
> and x < 1 constraints, right? How can I collect these constraints, 
> either during variable creation or later, so I can query their duals 
> using SCIPgetDualsolLinear? I don't believe this will actually help 
> solve the underlying issue, and I might have some reformulation to do, 
> but having this would help me diagnose the problem better and make 
> sure I understand it correctly.
>
> I have of course read the documentation but haven't found anything on 
> bound constraints. Also, functions like SCIPgetNConss(scip) do not 
> seem to account for these. I'd like to avoid creating them explicitly 
> over the binary variables since this seems redundant and I'm not sure 
> about how the solver would behave in this situation.
>
> Thanks in advance for your help,
> André Mazal Krauss