Add Feasibility Cuts for Bender's Decomposition

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Mina Valaei

2023年05月08日 16:18

I have a Bender's Decomposition problem. One of the subproblems is unbounded. I used the UnbdRay attribute to determine the direction of unboundedness. I want to add a feasibility cut to the master problem. The variables from the subproblem come to the master problem as a constant value. However, I can't retrieve the values from the subproblem by using .X function, because the model is unbounded. How can I fix this?

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Mario Ruthmair

Gurobi Staff

2023年05月16日 10:09
Hi Mina,

I guess your subproblem is an pure LP, right?
Did you set parameter InfUnbdInfo=1 to get the UnbdRay attribute?
Additionally, you might set DualReductions=0 to be sure that the model is unbounded (and not infeasible).
If the return status is indeed unbounded, then you should be able to access a feasible solution via the X attribute. Could you please show the Gurobi log of your LP subproblem?
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Mina Valaei

2023年05月22日 20:55
Hello,

Yes, my subproblem is pure LP. I think my dual subproblem is infeasible. So I want to add feasibility cuts to the MP, but I do not know how. I tried to use InfUnbdInfo, but I did not know how to write it.
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Mario Ruthmair

Gurobi Staff

2023年05月23日 07:17
If the LP subproblem is infeasible, then it is of course not possible to retrieve a feasible solution via attribute X.

You should set the following parameter for your subproblem to get a clearly defined state (unbounded or infeasible):
```
submodel.params.InfUnbdInfo = 1
submodel.params.DualReductions = 0
```
If your dual subproblem is indeed infeasible, then either there is an issue with your dual formulation or you are done, see this article for a short description of all cases.
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