[SCIP] Obtaining Bound Constraints from variables

[André Mazal Krauss]

Hello Rolf, Ambros,

thanks for your responses. Using lazy upper bounds, as you've both pointed
out, has helped a lot. Turns out the problem I was having was a consequence
of this as also the fact that I was using the wrong sign for some of the
duals. I believe I have sorted it out now.

Thanks again for your help!
André

Em sex., 2 de set. de 2022 às 07:51, Ambros Gleixner <gleixner at zib.de>
escreveu:

> Hi André,
>
> Just to add a bit to Rolf's reply:
>
> Yes, lazy bounds are the way to go.  I would not add explicit linear
> constraints for bounds, and I am not sure that you could even get the
> duals since these constraints should be converted into bounds during
> presolving.
>
> If you want to have variable bounds explicitly in your model, then you
> can use the method SCIPgetVarRedcost() to get the dual multiplier for
> the bound constraints of the variable.  Depending on the sign it will
> correspond to upper or lower bound.
>
> Best,
> Ambros
>
>
> Am 31.08.22 um 17:03 schrieb 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
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