[Scip] How to force SCIP to branch first on integer variables before performing spatial branch and bound

[Stefan Vigerske]

Hi,

On 07/03/2013 05:27 PM, Ahmad Moradi wrote:
> Dear SCIP community,
>
> In case when a MINLP is considered, how one could force SCIP to possibly
> first do branching on integer variables before performing spatial
> branching. Is that what SCIP automatically does?

Yes, that's the default behavior. If there is a fractional discrete 
variable, SCIP is first branching on that one.
There is actually no way to change this via parameters currently.

> Actually, the non-linearity in my problem comes from a concave objective
> function. I have implemented the problem in both MINLP model and MILP model
> ( approximated by piece-wise linear function on a fixed number of
> breakpoints) to SCIP and noticed that their initial relaxations are
> identical (i.e the convex initial relaxation of the MINLP is identical to
> the LP relaxation of MILP). Then I guess the only advantages of
> implementing the problem as MINLP would be to use spatial branching. right?

Yes. With the MINLP you can identify a spatial branch-and-bound subtree 
with a "piece-wise linear approximation" of your objective function.
SCIP tries to get an accurate approximation only at "points of interest" 
(around an optimal solution), while with an a priori piece-wise 
linearization you may to be exact enough everywhere. However, the latter 
lets you choose how exact you want your objective to be approximated and 
you may benefit from more of SCIP's MIP technology than in the MINLP 
case (e.g., your approximation goes through presolve).

Stefan

> this motivates me to ask the above question.
>
> Bests, Ahmad
>
>
>
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