ILOG CPLEX 11.0 User's Manual

depends on the current basis. Consequently, if you use the primal simplex optimizer withvarious parameter settings, an infeasible problem will produce different objective valuesand different solutions.◆ In the case of the dual simplex optimizer, termination with a status of infeasibility occursonly during Phase II. Therefore, all solution values are relative to the problem's natural(primal) formulation, including the values related to the objective function, such as thedual variables and reduced costs. As with the primal simplex optimizer, the basis inwhich the detection of infeasibility occurred may not be unique.ILOG CPLEX provides tools to help you analyze the source of the infeasibility in yourmodel. Those tools include the conflict refiner and FeasOpt:◆The conflict refiner is invoked by the routine CPXrefineconflict in the CallableLibrary or by the method refineConflict in Concert Technology. It finds a set ofconflicting constraints and bounds in a model and refines the set to be minimal in a sensethat you declare. It then reports its findings for you to take action to repair that conflict inyour infeasible model. For more about this feature, see Diagnosing Infeasibility byRefining Conflicts on page 391.◆ FeasOpt is implemented in the Callable Library by the routine CPXfeasopt and inConcert Technology by the method feasOpt. For more about this feature, see RepairingInfeasibility: FeasOpt on page 194.With the help of those tools, you may be able to modify your problem to avoid infeasibility.Coping with an Ill-Conditioned Problem or Handling Unscaled InfeasibilitiesBy default, ILOG CPLEX scales a problem before attempting to solve it. After it finds anoptimal solution, it then checks for any violations of optimality or feasibility in the original,unscaled problem. If there is a violation of reduced cost (indicating nonoptimality) or of abound (indicating infeasibility), ILOG CPLEX reports both the maximum scaled andunscaled feasibility violations.Unscaled infeasibilities are rare, but they may occur when a problem is ill-conditioned. Forexample, a problem containing a row in which the coefficients have vastly differentmagnitude is ill-conditioned in this sense and may result in unscaled infeasibilities.It may be possible to produce a better solution anyway in spite of unscaled infeasibilities, orit may be necessary for you to revise the coefficients. To decide which way to go, considerthese steps in such a case:1. Use the command display solution quality in the Interactive Optimizer to locatethe infeasibilities.2. Examine the coefficient matrix for poorly scaled rows and columns.3. Evaluate whether you can change unnecessarily large or small coefficients.190 ILOG CPLEX 11.0 — USER’ S MANUAL