How should INFEASIBLE and OBJLIMIT probing LPs be handled when computing a custom branching score?

[adecholaA1]

Hello,

I am implementing a custom branching rule in PySCIPOpt where candidate branches are evaluated by solving two probing LPs.

For an OPTIMAL probing LP, I compute the gain as:

gain = max(child_lp_obj - parent_lp_obj, 0.0)

However, I am unsure about the correct SCIP-compatible treatment of the following two cases:

SCIP_LPSOLSTAT.INFEASIBLE
SCIP_LPSOLSTAT.OBJLIMIT

My questions are:

1. When a probing LP is INFEASIBLE, what numerical value should be used as its gain when calling getBranchScoreMultiple()?

2. When a probing LP returns OBJLIMIT, should the gain be computed using SCIP's cutoff bound?

3. What should be used for an INFEASIBLE child before any incumbent exists and therefore before there is a finite cutoff bound?

4. In PySCIPOpt 5.4.1, Model.getCutoffbound() does not seem to be exposed. Is there another way to access SCIP's current cutoff bound?

5. Is getObjVal(original=False) equivalent to the cutoff bound once an incumbent exists, or can SCIP's internal cutoff bound differ from the incumbent objective?

I would like my custom probing-based branching score to reproduce SCIP's native strong-branching treatment of these cases as closely as possible.

Thank you!

[Joao-Dionisio]

Hey @adecholaA1 , thanks for the question! Both with INFEASIBLE and OBJLIMIT, SCIP doesn't compute a gain. If both children are infeasible, you can discard the node, and if only one of them is infeasible, then the other is a valid bound tightening.

4. Can you not update the PySCIPOpt version?
5. The internal cutoff bound can differ. You can set a cutoff bound yourself for an infeasible problem, for example.

you can see how SCIP treats this case directly in the documentation here.