ILOG CPLEX 11.0 User's Manual

automatically perturbs the variable bounds; when stalling occurs with the dual simplexoptimizer, ILOG CPLEX perturbs the objective function.In either case, perturbation creates a different but closely related problem. OnceILOG CPLEX has solved the perturbed problem, it removes the perturbation by resettingproblem data to their original values.If ILOG CPLEX automatically perturbs your problem early in the solution process, youshould consider starting the solution process yourself with a perturbation. (Starting in thisway will save the time that would be wasted if you first allowed optimization to stall andthen let ILOG CPLEX perturb the problem automatically.)To start perturbation yourself, set the parameter PerInd to 1 instead of its default value of 0.The perturbation constant, EpPer, is usually appropriate at its default value of 1e -6 , but canbe set to any value 1e -8 or larger.If you observe that your problem has been perturbed more than once, then the perturbedproblem may differ too greatly from your original problem. In such a case, considerreducing the value of the perturbation constant (EpPer in Concert Technology,CPX_PARAM_EPPER in the Callable Library).Inability to Stay FeasibleIf a problem repeatedly becomes infeasible in Phase II (that is, after ILOG CPLEX hasachieved a feasible solution), then numeric difficulties may be occurring. It may help toincrease the Markowitz tolerance in such a case. By default, the value of the parameterEpMrk is 0.01, and suitable values range from 0.0001 to 0.99999.Sometimes slow progress in Phase I (the period when ILOG CPLEX calculates the firstfeasible solution) is due to similar numeric difficulties, less obvious because feasibility is notgained and lost. In the progress reported in the log file, an increase in the printed sum ofinfeasibilities may be a symptom of this case. If so, it may be worthwhile to set a higherMarkowitz tolerance, just as in the more obvious case of numeric difficulties in Phase II.Diagnosing LP InfeasibilityILOG CPLEX reports statistics about any problem that it optimizes. For infeasible solutions,it reports values that you can analyze to discover where your problem formulation provedinfeasible. In certain situations, you can then alter your problem formulation or changeILOG CPLEX parameters to achieve a satisfactory solution.◆When the ILOG CPLEX primal simplex optimizer terminates with an infeasible basicsolution, it calculates dual variables and reduced costs relative to the Phase I objectivefunction; that is, relative to the infeasibility function. The Phase I objective functionILOG CPLEX 11.0 — USER’ S MANUAL 189