[SCIP] aggregated variables

[James Cussens]

Hi Marc,

That's very helpful, thanks! But I have further questions on this topic.

1. Let me check my understanding of the behaviour of SCIPtightenVarUb when called on an aggregated variable (like <t_3 <- 1>
In my previous email). My assumption is that will lead to the upper bound on the variable to which it is aggregated ( t_3<-{1,5} in previous email) being tightened.
Is that correct?

2. If we have eg
[binary] <t_3 <- 1>: obj=-0, global bounds=[-0,1], local bounds=[-0,1], aggregated: +1<t_3<-{1,5}>
and (aggretated) variable t_3 <- 1 has a high branching priority does this affect the branching priority of t_3<-{1,5}?

3. If I have a constraint on variables some of which are aggregated variables Do the locks declared in that constraint have any effect on the variables to which the aggregated variables are aggregated? For example, if we have:

[binary] <t_3 <- 1>: obj=-0, global bounds=[-0,1], local bounds=[-0,1], aggregated: +1<t_3<-{1,5}>
[binary] <t_3 <- 5>: obj=-0, global bounds=[-0,1], local bounds=[-0,1], aggregated: +1<t_3<-{1,5}>

and the constraint adds a downlock on both of these two aggregated variables, does t_3<-{1,5} get 2 downlocks added?

James

James Cussens
Room MVB 3.26
School of Computer Science, University of Bristol
Phone: +44 (0)117 455 8723
https://jcussens.github.io/
________________________________
From: Scip <scip-bounces at zib.de> on behalf of Marc Pfetsch <pfetsch at mathematik.tu-darmstadt.de>
Sent: 03 July 2025 09:11
To: scip at zib.de <scip at zib.de>
Subject: Re: [SCIP] aggregated variables



Hi James!

> [binary] <t_3 <- 1>: obj=-0, global bounds=[-0,1], local bounds=[-0,1],
> aggregated: +1<t_3<-{1,5}>
> [binary] <t_3 <- 5>: obj=-0, global bounds=[-0,1], local bounds=[-0,1],
> aggregated: +1<t_3<-{1,5}>
>
> First question: does SCIP branch on aggregated variables?

Well, the default branching rule would avoid that because it only
considers fractional *active* variables.

But, it would be possible in principle to branch on aggregated
variables. The prerequisite is that branching actually corresponds to a
bound change of an active variable, which is the case for aggregated
variables. (This is different for multi-aggregated variables, where
several changes of bounds of active variables could correspond to the
same bound change of the multi-aggregated variable.)

> Second question: Is it correct that if, say, <t_3 <- 1> above were
> locally fixed to 0 (by some propagation) then <t_3<-{1,5}> and then
> <t_3 <- 5> would also get locally fixed to 0?

In principle yes, if you interpret "locally fixed" in the right way. the
variable <t_3 <- 1> is not active and thus not actually present in the
problem (in particular, it does not have an LP-value). If you ask for
the local variable bounds of it, SCIP would resolve the aggregation and
return the bounds using the active variable <t_3<-{1,5}>. Similarly, for
<t_3 <- 5>.

Best

Marc

P.S. I recommend to avoid characters like "<" (and ">") in variable
names, because these make it hard to correctly read the variable names
in a CIP file.

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