ILOG CPLEX 11.0 User's Manual

1. finding a succession of improving integer feasible solutions (solutions satisfying thelinear and quadratic constraints and the integrality conditions); while2. also working toward a proof that no better feasible solution exists and is undiscovered.For most models, a balance between these two sometimes-competing aims works well, andthis is another way of stating the philosophy behind the default MIPEmphasis setting: itbalances optimality and integer feasibility.At this default MIPEmphasis setting of 0 (that is, MIPEmphasisBalanced in ConcertTechnology or CPX_MIPEMPHASIS_BALANCED in the Callable Library), ILOG CPLEX usestactics intended to find a proven optimal solution quickly, for models of a broad range ofdifficulty. That is, considerable analysis of the model is performed before branching everbegins, in the expectation that the investment will result in a faster total run time, yet notevery possible analysis is performed. And then branching is performed in a manner thatseeks to find good quality feasible solutions, without sacrificing too much time that could bespent proving the optimality of any solution that has already been found.In many situations, the user will desire a greater emphasis on feasibility and less emphasison analysis and proof of optimality. For instance, a restrictive time limit (set by the userusing the TiLim parameter) may be in force due to a real-time application deployment,where a model is of sufficient difficulty that a proof of optimality is unlikely, and the userwants to have simply as good a solution as is practicable when the time limit is reached. TheMIPEmphasis setting of 1 (MIPEmphasisFeasibility in Concert Technology or, in theCallable Library, CPX_MIPEMPHASIS_FEASIBILITY) directs ILOG CPLEX to adopt thisemphasis. Less computational effort is applied at the outset toward the analyses that aid inthe eventual proof of optimality, and more effort is spent in immediately beginningcomputations that search for early (and then improved) feasible solutions. It is likely on mostmodels that an eventual proof of optimality would take longer by setting MIPEmphasis to 1,but since the user has given ILOG CPLEX the additional information that this proof is ofless importance than usual, the user's needs will actually be met more effectively.Another choice for MIPEmphasis is 2 (MIPEmphasisOptimality in Concert Technologyor, in the Callable Library, CPX_MIPEMPHASIS_OPTIMALITY), which results in a greateremphasis on optimality than on feasibility. The search for feasible solutions is not ignoredcompletely, but the balance is shifted toward moving the Best Bound (described in thefollowing paragraph) more rapidly, at the likely expense of feasible solutions being foundless rapidly, and improved feasible solutions less frequently, than under the defaultemphasis.The fourth choice for MIPEmphasis, 3 (MIPEmphasisBestBound in Concert Technologyor, in the Callable Library, CPX_MIPEMPHASIS_BESTBOUND), works exclusively at movingthe Best Bound. The Best Bound represents the objective function value at which an integerfeasible solution could still potentially exist. As possibilities are eliminated, this Best Boundvalue will move in the opposite direction to that of any improving series of integer feasiblesolutions. The process of moving the Best Bound will eventually result in the optimalfeasible solution being discovered, at which point the optimization is complete, and feasible262 ILOG CPLEX 11.0 — USER’ S MANUAL