How to make cuts added in a preIntsol callback globally valid (root node) instead of local to the current subtree?

Dear Emanuele,

Your approach is correct. Your cuts should be added at integral tree nodes (soltype==0) if the integral solution violates one of your constraints. If the infeasible solution stems from a heuristic (soltype!=0), you can only reject it, not derive a cut from it. In addition, you can hook into the optnode callback to generate violated constraints.

There are a few examples on separating lazy constraints, including in this community: https://community.fico.com/s/question/0D54W00008P73MsSAJ/lazy-cut-callback-in-java. Also check examples around the traveling salesman problem and subtour elimination constraints, available for different APIs: https://examples.xpress.fico.com/example.pl?id=tsp_java.

For the moment, cuts in Xpress are managed locally — it is not possible to add global cuts in the sense of an automation that keeps a cut permanently enforced at the root. We are aware of this limitation and are actively working on solutions that would address use-cases like yours.

Best regards,

Christian Raack