Add a new lazy constraint to a MIP model from within a callback function.
Note that this method can only be invoked when the
where value on the callback function is
GRB.Callback.MIPSOL (see the
Callback Codes section
for more information).
Lazy constraints are typically used when the full set of constraints for a MIP model is too large to represent explicitly. By only including the constraints that are actually violated by solutions found during the branch-and-cut search, it is sometimes possible to find a proven optimal solution while only adding a fraction of the full set of constraints.
You would typically add a lazy constraint by first querying the
current node solution (by calling
cbGetSolution from a
GRB.Callback.MIPSOL callback, or
cbGetNodeRel from a
GRB.Callback.MIPNODE callback), and then calling
cbLazy() to add a
constraint that cuts off the solution. Gurobi guarantees that you
will have the opportunity to cut off any solutions that would
otherwise be considered feasible.
MIP solutions may be generated outside of a MIP node. Thus, generating
lazy constraints is optional when the
where value in the callback
GRB.Callback.MIPNODE. To avoid this, we recommend to
always check when the
where value equals
Your callback should be prepared to cut off solutions that violate any of your lazy constraints, including those that have already been added. Node solutions will usually respect previously added lazy constraints, but not always.
Note that you must set the LazyConstraints parameter if you want to use lazy constraints.
sense: Sense for new lazy constraint (GRB.LESS_EQUAL, GRB.EQUAL, or GRB.GREATER_EQUAL).
def mycallback(model, where): if where == GRB.Callback.MIPSOL: sol = model.cbGetSolution([model._vars, model._vars]) if sol + sol > 1.1: model.cbLazy(model._vars + model._vars <= 1) model._vars = model.getVars() model.optimize(mycallback)