ILOG CPLEX 11.0 User's Manual

Enumerating All SolutionsWith the solution pool, you can collect all solutions to a MIP model. To do so, set thesolution pool intensity parameter to its highest value, 4, and call populate.You can also enumerate all solutions that are valid for a specific criterion. For example, ifyou want to enumerate all alternative optimal solutions, do the following:1. Set the pool absolute gap parameter (SolnPoolAGap, CPX_PARAM_SOLNPOOLAGAP) to0.0 (zero).2. Set the pool intensity parameter to 4 (SolnPoolIntensity,CPX_PARAM_SOLNPOOLINTENSITY).3. Set the populate limit parameter (PopulateLim, CPX_PARAM_POPULATELIM) to a valuesufficiently large for your model; for example, 2 100 000 000.4. Call populate.Beware, however, that, even for small models, the number of possible solutions is likely tobe huge. Consequently, enumerating all of them will take time and consume a large quantityof memory.In addition, when you attempt to enumerate all solutions, some restrictions apply, asexplained in the following sections.◆ Limitations Due to Continuous Variables and Finite Precision on page 313◆ Limitations Due to Unbounded MIP Models on page 313◆ Limitations Due to Numeric Difficulties on page 314Limitations Due to Continuous Variables and Finite PrecisionThere may be an infinite number of possible values for a continuous variable, and it is notpractical to enumerate all of them on a finite-precision computer. Therefore, populate givesonly one solution for each set of binary and integer variables, even though there may existseveral solutions that have the same values for all binary and integer variables but differentvalues for continuous variables.Limitations Due to Unbounded MIP ModelsLikewise, for the same reason, populate does not generate all possible solutions forunbounded MIP models. As soon as the proof of unboundness is obtained, populate stops.ILOG CPLEX 11.0 — USER’ S MANUAL 313