ILOG CPLEX 11.0 User's Manual

solution the value for the variable must be either exactly zero or else be between the lowerand upper bounds (and further subject to the restriction that the value be an integer, in thecase of semi-integer variables).A problem may be changed to a mixed integer problem, even if all its variables arecontinuous.Note: It is not required to specify explicit bounds on general integer variables. However, ifduring the branch and cut algorithm a variable exceeds 2,100,000,000 in magnitude of itssolution, an error termination will occur. In practice, it is wise to limit integer variables tovalues far smaller than the stated limit, or numeric difficulties may occur; trying to enforcethe difference between 1,000,000 and 1,000,001 on a finite precision computer might workbut could be difficult due to roundoff.Using the Mixed Integer OptimizerThe ILOG CPLEX Mixed Integer Optimizer solves MIP models using a very general androbust algorithm based on branch & cut. While MIP models have the potential to be muchmore difficult than their continuous LP, QCP, and QP counterparts, it is also the case thatlarge MIP models are routinely solved in many production applications. A great deal ofalgorithmic development effort has been devoted to establishing default ILOG CPLEXparameter settings that achieve good performance on a wide variety of MIP models.Therefore, it is recommended to try solving your model by first calling the Mixed IntegerOptimizer in its most straightforward form.To invoke the Mixed Integer Optimizer, use one of these approaches:◆ In the Interactive Optimizer, use the mipopt command.◆◆In Concert Technology, with the IloCplex method solve.In the Callable Library, use the CPXmipopt routine.Emphasizing Feasibility and OptimalityThe following section, Tuning Performance Features of the Mixed Integer Optimizer, goesinto great detail about the algorithmic features, controlled by parameter settings, that areavailable in ILOG CPLEX to achieve performance tuning on difficult MIP models.However, there is an important parameter, MIPEmphasis, that is oriented less toward theuser understanding the algorithm being used to solve the model, and more toward the usertelling the algorithm something about the underlying aim of the optimization being run. Thatparameter is discussed here.Optimizing a MIP model involves:ILOG CPLEX 11.0 — USER’ S MANUAL 261