MIP Tools Branch and Cut with Callbacks Lazy Constraint Callback Solve a linear program relaxation Solve Callback Incumbent Callback Do all integer variables have integer values? Update the incumbent yes no Cut Callback Add cuts MIP Callback Apply heuristics Heuristic Callback This is the branch and cut algorithm as applied to a MILP. The darker gold callbacks are used to override CPLEX procedures. The pale gold MIP callback can be used to terminate optimization or for reporting, for example to update a progress graph or terminate optimization when a good enough solution has been reached. The Solve callback is only available in the Callable Library. Choose an integer variable and create two new sub-problems Branch Callback Select a sub-problem to solve Node Callback