[SCIP] Negative Reduced Cost Vars not in LP

[André Mazal Krauss]

Hello Gerald, Lukas,

it is impossible for branching to cause this since I've relaxed the problem
and it still happens. Still, Lukas, I have implemented my own specialized
branching rules, and have accounted for their duals on the pricing problem.
Thank you for your input anyway.

About the problem variable pricer and PRICER_DELAY, yes, I have set it to
true, following the Binpacking example on SCIP's website. However, now that
you mentioned the variable pricer, I must ask: is it always included by
default? I have verified that the value I'm getting for SCIPgetNPricers and
SCIPGetNActivePricers during solving is 1. Since this one is surely my own
pricer, what happened to the problem variable pricer?  Does it not count
for this function, or could I have failed to include it somehow? Reading
the FAQ entry "I only implemented one pricer, why is there a second one,
called variable pricer?" leads me to believer I should expect a value of 2
for SCIPgetNPricer... Note: I have called SCIPincludeDefaultPlugins.

Thanks again,
André

Em seg., 26 de set. de 2022 às 03:16, Gerald Gamrath <gamrath at zib.de>
escreveu:

> Hi André,
>
> SCIPvarIsInLp returns whether the variable is in the LP at the current
> node. As you mentioned, a variable may not be in the LP because it is
> removable and was aged out. Another reason why a variable may not be in the
> LP is if it was priced at another node of the branch-and-bound tree. Then,
> it was added to the LP there, but when SCIP jumps to another node in the
> tree, only the variables that were in the LP at its parent node will be in
> the LP initially.
>
> Did you set PRICER_DELAY to TRUE for your pricer? The problem variable
> pricer adds existing variables with negative reduced costs to the LP and
> will be called before your pricer. If PRICER_DELAY is TRUE, your pricer
> won't be called in a pricing round where already variables have been added,
> i.e., if the variable pricer found existing variables with negative reduced
> costs, those will be added, the LP will be reoptimized, and a new pricing
> round will be started. Thus, when your pricer is called, there should not
> be any columns with negative reduced costs.
>
> Best,
>
> Gerald
> On 9/26/22 08:00, André Mazal Krauss wrote:
>
> Hello SCIP team,
>
> I'm currently working on a VRP-related application, using SCIP.  I'm
> using a Set Partitioning formulation with Branch & Price, and my
> formulation is a minimization problem. In fact, I've already asked a
> question about a month ago, and this is related to the same application.
>
> At that time, I was having serious problems with duplicate routes. After
> following your suggestions and working more by myself on the problem, I've
> managed to *almost* eliminate the pricing of repeated routes. In fact,
> while previously it was a certain occurrence, now I'm finding about 100
> repeated routes across my 1500 test instances. Anyway, I wanted to
> understand what was going on and try to eliminate them entirely.
>
> Upon investigating this, I've noticed a common trait between all these
> repeated routes being found. 1. The problem persists even when I relax the
> formulation and use continuous variables; 2. The negative RC my pricing has
> computed matches exactly with the one given by SCIPgetVarRedCost; 3. the
> already existing variable is *always* active ( ie. SCIPvarIsActive is
> true), but is *never* in the LP (ie. SCIPvarIsInLp is false); 4. upon
> inspecting the other variables in the problem, I've noticed that there are
> typically several active variables with negative RCs, but not in the LP;
> it's just that sometimes I happened to price one of them again.
>
> I found this quite strange. How does this make sense? If the variables
> have negative RCs, shouldn't SCIP put them in the LP and use them? I'm not
> sure I understand exactly what SCIPvarIsInLp means. How does it relate to
> the variable being removable and/or deletable? I've tried changing my
> variable creation to make them *not *removable and *not* deletable, but
> this had no impact whatsoever. If I price a variable and it isn't in the LP
> anymore, should it be added again? When and why would SCIP decide to remove
> a variable RC from the LP?
>
> I was thinking for some time that this could maybe be explained by my
> primal problem having multiple optimal solutions, which could, in turn,
> mean the dual has multiple optimal solutions, and my pricing algorithm
> would be somehow affected by this. But then again, I may be overthinking
> this and the problem may be simpler, or maybe not a problem at all. It
> really depends on what SCIPvarIsInLp actually means.
>
> Note: I have read the FAQ entry "Why are not all variables in the LP?",
> but it does not seem to address my case since I have tested without
> branching and the problem persists even when I set removable to false in
> all variables.
>
> Thanks again for your help,
> André
>
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