I have become interested in using PoolSearchMode for enumerating all integer feasible solutions of a MIP and have a related question.
For many problems, there are key decision variables, let's call them x. For modeling reasons, it may be convenient to define and use auxiliary variables y. This may give an extended formulation of the form Ax + Gy <= b.
Suppose I am only interested in the different x solutions, with no interest in the different y's that may come with them. Is there a way to exploit this in Gurobi? Or, is the only approach to apply PoolSearchMode and filter the results to find the distinct x values?
I ask because in my application, a particular x solution may pair with exponentially many y solutions, with significant time savings to be had.
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