Branch and cut benders decomposition

[Saeede Hosseini]

Hi Guys,

I have a benders decomposition algorithm that runs similar branch and cut algorithm. In other words, my master problem is searched by a branch and bound tree, and if it finds an integer feasible solution, the feasibility of solution is checked by Cp subproblems and if is required it adds infeasibility cut to the master problem, and continues the searching algorithm. 

However, I don't know if it is possible to implement this by using mip package. Could you please guile me in this regard?

best 

[HAROLDO GAMBINI SANTOS]

Hi,

This is possible using the Lazy Constraints:

https://docs.python-mip.com/en/latest/custom.html

See the example with Lazy constraints for the TSP.

Cheers

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[Saeede Hosseini]

Thanks for your help.

In the example of lazy constraint,  there is only one main problem which is incomplete. However, I have one master problem and some subproblems that have different variables and constraints. Also, I want to use a different solver, for example, a CP-SAT solver of google for solving subproblems. So, given this, is it possible to use lazy_constraints and if yes how can I do it?

Best