[SCIP] Lazy constraints

[Marco Correia]

Hi,

I'm trying to understand the minimal requirements for adding constraints
during search to SCIP.

My toy problem is to try to enforce that two variables x1, x2, both
integral with domains {1,2}, add up to 3, only by using lazy constraints.

To this I created a constraint handler, and implemented:

* SCIP_DECL_CONSCHECK : Checks if x1 + x2 == 3, returning SCIP_FEASIBLE, or
SCIP_INFEASIBLE accordingly.

* SCIP_DECL_CONSENFOLP : Adds x1 + x2 == 3 to the model
using SCIPcreateConsBasicLinear and SCIPaddCons and returning
SCIP_CONSADDED.

* SCIP_DECL_CONSLOCK : Calls SCIPaddVarLocks() for both x1 and x2.

* SCIP_DECL_CONSENFOPS : Do nothing (only return SCIP_OKAY). I don't know
what to do here and it seems this never gets called in my example anyway.

* SCIP_DECL_CONSTRANS: Just return SCIP_OKAY.

Then I add this constraint handler using needscons=false, since if I
understand correctly, this way it will run even if I don't associate any
constraints with it.

Besides adding the constraint handler, I do not add any constraints, and
simply call minimize x1.

I get this trace:

Called CHECK with values x1=1, x2=1 (which returns false)
(repeats 6 times)
Called ENFOLP with values x1=1, x2=1 (which adds the x1+x2==3 and returns
CONSADDED)

and then SCIP stops with state "infeasible".

I was expecting instead to see SCIP branching and eventually finding x1=1,
x2=2.

I have the feeling I'm missing something obvious. I can't find a simple
enough example in the documentation, all examples there seem to require
that constraints are added to the constraint handler, and are much more
involved. I am essentially looking for something as simple as the gurobi
callback mechanism: just call a function at each node that can add global
constraints to the search tree.

Any hints?

As a second question, why is CHECK called 7 times with the same variable
values? Is SCIP expecting that CHECK is non-deterministic?

Thanks!
Marco
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