[SCIP] implementation of a benders decomposition

[Alexandre Dupont-Bouillard]

Dear SCIP community,

I modelized a problem as an ILP having a block diagonal structure and I 
am trying to solve it
using a benders decomposition. I am collaborating with someone who 
implemented other algorithms in Python which makes it mandatory for me 
to use Pyscipopt. I implemented the compact model using Pyscipopt.

I know that integrality constraints are mandatory inside these 
subproblems but the first step would be to implement that model relaxing 
the integrality constraints of the subproblems.

I tried to use the example given in bendersflp.py and adapt it to my 
case. The obtained program runs until convergence but does not give the 
same optimal value as the compact model with a relaxation of the 
integrality constraints of the variables associated with subproblems.

For one week, I have been looking for differences in both model sets of 
linear constraints and cannot find any difference. Is there any reason 
for that phenomenon to appear besides a mistake in the code?

Also, I would like to know the best way to implement the full branching 
process and deal with the integrality constraints of the subproblems 
using SCIP. Is it necessary to implement a dedicated branching process?


The code can be found in that repository if needed: 
https://github.com/alexandredupontbouillard/ambulance

Thanks a lot for your attention
Alexandre Dupont-Bouillard