ILOG CPLEX 11.0 User's Manual

Figure 28.1ycutting planesobjectiveoptimum ofLP relaxationIP optimumxfeasible solutionsFigure 28.1 Cuts in a typical MIPWhat Are Pools of User Cuts or Lazy Constraints?Sometimes, for a MIP formulation, a user may already know a large set of helpful cuttingplanes (user cuts), or can identify a group of constraints that are unlikely to be violated (lazyconstraints). Simply including these cuts or constraints in the original formulation couldmake the LP subproblem of a MIP optimization very large or too expensive to solve. Instead,these situations can be handled in one of these ways:◆through the cut callback described in Advanced MIP Control Interface on page 483, or◆ by setting up cut pools before MIP optimization begins, as explained in Adding UserCuts and Lazy Constraints on page 422.The principle in common between these two pools allows the optimization algorithm toperform its computations on a smaller model than it otherwise might, in the hope ofdelivering faster run times. In either case (whether in the case of pools of user cuts or poolsof lazy constraints), the model starts out small, and then potentially grows as members of thepools are added to the model. Both kinds of pool may be used together in solving a MIPmodel, although that would be an unusual circumstance.420 ILOG CPLEX 11.0 — USER’ S MANUAL