At default settings, ILOG CPLEX preprocesses problems by simplifying constraints, reducing problem size, and eliminating redundancy. Its presolver tries to reduce the size of a problem by making inferences about the nature of any optimal solution to the problem. Its aggregator tries to eliminate variables and rows through substitution. For most models, preprocessing is beneficial to the total solution speed, and ILOG CPLEX reports the model's solution in terms of the user's original formulation, making the exact nature of any reductions immaterial.

Dual Formulation in Presolve

A useful preprocessing feature for performance tuning, one that is not always activated by default, can be to convert the problem to its dual formulation. The nature of the dual formulation is rooted in linear programming theory, beyond the scope of this manual, but for the purposes of this preprocessing feature it is sufficient to think of the roles of the rows and columns of the model's constraint matrix as being switched. Thus the feature is especially applicable to models that have many more rows than columns.

You can direct the preprocessor to form the dual by setting the PreDual parameter to 1 (one).

Conversely, to entirely inhibit the dual formulation for the barrier optimizer, you can set the PreDual parameter to -1. The default, automatic, setting is 0.

It is worth emphasizing, to those familiar with linear programming theory, that the decision to solve the dual formulation of your model, via this preprocessing parameter, is not the same as the choice between using the dual simplex method or the primal simplex method to perform the optimization. Although these two concepts (dual formulation and dual simplex optimizer) have theoretical foundations in common, it is valid to consider, for example, solving the dual formulation of your model with the dual simplex method; this would not simply result in the same computational path as solving the primal formulation with the primal simplex method. However, with that distinction as background, it may be worth knowing that when CPLEX generates the dual formulation, and a simplex optimizer is to be used, CPLEX will in most cases automatically select the opposite simplex optimizer to the one it would have selected for the primal formulation. Thus, if you set the PreDual parameter to 1 (one), and also select LPMethod 1 (which normally invokes the primal simplex optimizer), the dual simplex optimizer will be used in solving the dual formulation. Because solution status and the other results of an optimization are the same regardless of these settings, no additional steps need to be taken by the user to use and interpret the solution; but examination of solution logs might prove confusing if this behavior is not taken into account.

Dependency Checking in Presolve

Final Factor after Presolve

Factorization can easily be performed later by a call to a simplex optimizer with the parameter AdvInd set to a value greater than or equal to one.

Memory Use and Presolve

Controlling Passes in Preprocessing

In rare instances, a user may wish to specify the number of analysis passes that the presolver or the aggregator makes through the problem. The parameters PrePass and AggInd, respectively, control these two preprocessing features; the default, automatic, setting of -1 lets ILOG CPLEX decide the number of passes to make, while a setting of 0 directs ILOG CPLEX not to use that preprocessing feature, and a positive integer limits the number of passes to that value. At the automatic setting, ILOG CPLEX applies the aggregator just once when it is solving an LP model; for some problems, it may be worthwhile to increase the AggInd setting. The behavior under the PrePass default is less easy to predict, but if the output log indicates it is performing excessive analysis you may wish to try a limit of five passes or some other modest value.

Aggregator Fill in Preprocessing

Another parameter, which affects only the aggregator, is AggFill. Occasionally the substitutions made by the aggregator will increase matrix density and thus make each iteration too expensive to be advantageous. In such cases, try lowering AggFill from its default value of 10. ILOG CPLEX may make fewer substitutions as a consequence, and the resulting problem will be less dense.

Turning Off Preprocessing

Finally, if for some reason you wish to turn ILOG CPLEX preprocessing entirely off, set the parameter PreInd to 0.