ILOG CPLEX 11.0 User's Manual

solutions may be discovered along the way anyway, due to branches that happen to locatefeasible solutions that do not match the Best Bound. A great deal of analysis may beperformed on the model, beyond what is done under the default emphasis. Therefore it isrecommended to use this setting only on models that are difficult for the default emphasis,and for which you do not care about interim feasible solutions that may or may not beoptimal.The final choice for MIPEmphasis is 4 (CPX_MIPEMPHASIS_HIDDENFEAS). It appliesconsiderable additional effort toward finding high quality feasible solutions that are difficultto locate, and for this reason the eventual proof of optimality may take longer than withdefault settings. This choice is intended for use on difficult models where a proof ofoptimality is unlikely, and where emphasis 1 (one) does not deliver solutions of anappropriately high quality.To make clear a point that has been alluded to so far: every choice of MIPEmphasis resultsin the search algorithm proceeding in a manner that eventually will find and prove anoptimal solution, or will prove that no integer feasible solution exists. The choice ofemphasis only guides ILOG CPLEX to produce feasible solutions in a way that is in keepingwith the user's particular purposes, but the accuracy and completeness of the algorithm is notsacrificed in the process.The MIPEmphasis parameter may be set in conjunction with any other ILOG CPLEXparameters (discussed at length in the next section). For example, if you wish to set anupward branching strategy via the BrDir parameter, this will be honored under any settingof MIPEmphasis. Of course, certain combinations of MIPEmphasis with other parametersmay be counter-productive, such as turning off all cuts with emphasis 3, but the user has theoption if that is what is wanted.Terminating MIP OptimizationILOG CPLEX terminates MIP optimization under a variety of circumstances. First,ILOG CPLEX declares integer optimality and terminates when it finds an integer solutionand all parts of the search space have been processed. Optimality in this case is relative towhatever tolerances and optimality criteria you have set. For example, ILOG CPLEXconsiders any user-supplied cutoff value (such as CutLo or CutUp) as well as the objectivedifference parameter (ObjDif) when it treats nodes during branch & cut. Thus these settingsindirectly affect termination.An important termination criterion that the user can set explicitly is the MIP gap tolerance.In fact, there are two such tolerances: a relative MIP gap tolerance that is commonly used,and an absolute MIP gap tolerance that is appropriate in cases where the expected optimalobjective function is quite small in magnitude. The default value of the relative MIP gaptolerance is 1e-4; the default value of the absolute MIP gap tolerance is 1e-6. These defaultvalues indicate to CPLEX to stop when an integer feasible solution has been proved to bewithin 0.01% of optimality. On a difficult model with input data obtained with onlyapproximate accuracy, where a proved optimum is thought to be unlikely within aILOG CPLEX 11.0 — USER’ S MANUAL 263