Default CPLEX

Callbacks allow user written code to be run at select points to monitor or influence the behavior of the CPLEX solver. Before modifying the behavior of the solver, lets understand exactly how the solver works. Below is a somewhat simplified picture of the algorithm CPLEX is using to solve an integer program.

The algorithm terminates when the node stack is empty, and the best incumbent found is the new solution. The first node pushed on, the LP relaxation of the original problem is often called the root node.

LazyConstraintCallback

Lazy constraints, at a high level, are constraints that are only checked when a candidate for an integer solution has been identified. They can be added to the model at the start though the IloCplex method addLazyCut(), or they can be added on the fly with a LazyConstraintCallback (documentation here). The LazyConstraintCallback provides a user implemented routine to take a new potential incumbent solution, determine any of the Lazy constraints were violated, and if so, to add at least one of them.