[SCIP] Default branching rules but only over a subset of binary variables.

[Eduardo Moreno]

Hi All.  I'm coding for the first time a B&P using SCIP. Apologies if this
question already exists in the forum (I couldn't find it).

I'm coding a "kind-of" binpacking using Branch-and-Price, where instead of
Sum lambda_c >=1 my problem has a binary variable on the RHS, so Sum
lambda_c >= y (or may be, Sum lambda_c = y).  In other words, either y=0
(fixing all columns including it to zero) or y=1 (becoming a bin packing)

I also implemented a kind-of Ryan/Foster Branching rule (following the bin
packing example). However, this branching rule only applies for the case
y=1.  Hence, I need to prioritize the standard default branching but only
on the subset of binary "y" variables first, and only after that to enforce
the RyanFoster branching rule for the priced variables "lambda".

How do you recommend doing that?  Do I need to re-code some default
branching rules to deal only with a subset of variables "y"?  Or is there
another simpler way? If not, which branching rules do you recommend
to adapt? Just a simpler one like assume "branch_leastinf"? Or all of them
that apply to my problem?

BTW: I cannot relax the integrality of the priced vars, because I can
obtain optimal integer solutions for "y" vars using fractional values for
"lambda" vars. So that's not a viable solution.

Thanks for the help!

Eduardo

-----
Eduardo Moreno, Ph.D.
Professor, Universidad Adolfo Ibañez, Chile.
Visiting Researcher, Google Research, France
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