[SCIP] How to modify varaibles bounds, add valid cuts and reoptimize a MIP model in SCIP?

[Marc Pfetsch]

Hi Juan,

you can use reoptimization in SCIP (for MIPs) whenever you restrict the 
feasible region or change the objective, see

https://www.scipopt.org/doc-8.0.3/html/REOPT.php

I will try to comment on you individual steps below.

> (1) To *set the bounds of the copies of the master binary decision 
> variables* within the MIP model defining the sub-problem. I will use the 
> bounds to fix the values of several binary variables in the sub-problem, 
> which will be represented as continuous variables.
>
> (2) To *reoptimize* the sub-problem MILP model (get a new incumbent or 
> minimal infeasible set)
 >
 > (3) To *modify the right-hand side value of a single constraint* of the
 > sub-problem.

This will only work if you restrict the feasible region, i.e., from what 
I understand from you description, reoptimization will not work here.

> (3) To *add no-good and feasibility cuts* to the master problem.
> 
> (4) To *reoptimize* the master MILP problem.

This should work, since you only restrict the feasibility region.

> Does SCIP admit the modifications above and reoptimizing the MILP models 
> again?. How can I modify the bounds of a variable in SCIP once it has 
> been created?

See above.


You can see an example of using reoptimization in a Benders context here:

https://www.scipopt.org/doc-8.0.3/html/MINIISC_MAIN.php

https://www.scipopt.org/doc-8.0.3/html/miniisc_8c_source.php


Best

Marc