ILOG CPLEX 11.0 User's Manual

Difficulty Solving Subproblems: Overcoming DegeneracyThere are classes of MIPs that produce very difficult subproblems, for example, if thesubproblems are dual degenerate. In such a case, a different optimizer, such as the primalsimplex or the barrier optimizer, may be better suited to your problem than the default dualsimplex optimizer for subproblems. These alternatives are discussed in UnsatisfactoryOptimization of Subproblems on page 297. A stronger dual pricing algorithm, such as dualsteepest-edge pricing (that is, the parameter DPriInd or CPX_PARAM_DPRIIND set to thevalue 2), could also be considered.If the subproblems are dual degenerate, then consider using the primal simplex optimizer forthe subproblems. You make this change by setting the parameter NodeAlg(CPX_PARAM_SUBALG) to 1 (one).Unsatisfactory Optimization of SubproblemsIn some problems, you can improve performance by evaluating how the continous LP or QPsubproblems are solved at the nodes in the search space, and then possibly modifying thechoice of algorithm to solve them.QCP subproblems are solved only by the barrier optimizer. However, MIQCP models are notalways solved by a sequence of QCP subproblems. The MIQCP strategy parameter(MIQCPStrat, CPX_PARAM_MIQCPSTRAT) allows you to control what kinds ofsubproblems are solved in a mixed integer quadratically constrained programming model.Consequently, the following suggestions may also help that class of problem as well.You can control which algorithm ILOG CPLEX applies to the root relaxation of yourproblem separately from your control of which algorithm ILOG CPLEX applies to othersubproblems. The following sections explain those parameters more fully.RootAlg ParameterThe RootAlg algorithm parameter indicates the algorithm for ILOG CPLEX to use on theinitial subproblem. In a typical MIP, that initial subproblem is usually the linear relaxationof the original MIP. By default, ILOG CPLEX starts the initial subproblem with the dualsimplex optimizer. You may have information about your problem that indicates anotheroptimizer could be more efficient. Table 14.15 summarizes the values available for theRootAlg parameter.To set this parameter:◆◆In the Interactive Optimizer, use the command set mip strategy startalgorithmwith the value to indicate the optimizer you want.In Concert Technology, use the IloCplex method setParam with the parameterRootAlg and the appropriate algorithm enumeration value.ILOG CPLEX 11.0 — USER’ S MANUAL 297