[Scip] why no branching came up in my branch-and-price code?

[gamrath@zib.de]

Dear Xiangyong,

> I am using SCIP to develop a branch-and-price code. I tried to solve 50
> instances and found that the code terminate at the root node (say " SCIP
> Status : problem is solved [optimal solution found] "). Namely no
> branching came up and all my considered instances are optimally solved at
> the root node (so far I have not found an instances which cannot be
> optimally solved at the root node using current B&P code).  I think that
> it is impossible.

What kind of problems do you solve? Bin packing problems, for instance,
have a very strong dual bound so that the problem is solved once you find
an optimal solution. Can you model your problem as a pure MIP without
column generation and solve a small instance? perhaps, you can also
enumerate all variables in advance for a small problem? Then you could
check whether your computed solutions are optimal.

> I have checked the pricer which could produce correct new variable.
What do you mean? Did you check that your pricer works correctly or were
there still variables with negative reduced cost for the final LP
solution?
Did you set a value for the lowerbound-pointer in the pricing method?

> Further at each call of pricer, I used
> SCIPgetNLPBranchCands(scip)  to get number of branching candidates for LP
> solution branching. It returned value of zero. It seems that the LP
> relaxations at the root node always returned integer solution.

If the LP solution is always integral, then the simplerounding heuristic
should find a solution in each pricing round. This would be indicated by a
"s" in front of each line of the output. Is that the case? Could you send
me the output produced by a run of your code? If its size is too big,
please send it to me directly and not to the mailing list.

Regards, Gerald