I am still working on a little project
in my spare time for doing branches in parallel.
One side-effect which came up in the
research of mine, that a so called "strong branching" is possible
with glpk for sparse MILP.
It is in no way straight forward how
to do it:
Convert the node you are working on
to its dual problem, in fact a new problem is created.
Fix in this new problem almost all variables
to the dual values of the original problem and use presolving. The dual
variables which are still free are only in the region of the considered
normal variable (which is now a restriction). Region can be defined via
the graph of the problem.
For sparse problems this will work.
Also possible, you can shrink first the problem before you do the conversion,
but I didn't implement it in that way.
I can publish the code, but what I did,
was first to standardize the LP first:
Only use min direction (transform objective,
No Bounds (Shall be real inequalities!)
only use <= inequalities
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[Help-glpk] Strong branching,
harald . buesching<=