ILOG CPLEX 11.0 User's Manual

simplex optimizer. While the barrier optimizer is often extremely fast, particularly on verylarge problems, numeric difficulties occasionally arise with it in certain classes of problems.For that reason, it is a good idea to run simplex optimizers in conjunction with the barrieroptimizer to verify solutions. At its default settings, the ILOG CPLEX Barrier Optimizeralways crosses over after a barrier solution to a simplex optimizer, so this verification occursautomatically.Numerical Emphasis SettingsBefore you try tactics that apply to specific symptoms, as described in the followingsections, a useful ILOG CPLEX parameter to try is the numerical emphasis parameter.◆◆NumericalEmphasis (bool) in Concert TechnologyCPX_PARAM_NUMERICALEMPHASIS (int) in the Callable Library◆ emphasis numerical in the Interactive OptimizerUnlike the following suggestions, which deal with knowledge of the way the barrieroptimizer works or with details of your specific model, this parameter is intended as a way totell ILOG CPLEX to exercise more than the usual caution in its computations. When you setit to its nondefault value specifying extreme numerical caution, various tactics are invokedinternally to try to avoid loss of numerical accuracy in the steps of the barrier algorithm.Be aware that the nondefault setting may result in slower solution times than usual. Theeffect of this setting is to shift the emphasis away from fastest solution time and towardnumerical caution. On the other hand, if numerical difficulty is causing the barrier algorithmto perform excessive numbers of iterations due to loss of significant digits, it is possible thatthe setting of extreme numerical caution could actually result in somewhat faster solutiontimes. Overall, it is difficult to project the impact on speed when using this setting.The purpose of this parameter setting is not to generate "more accurate solutions"particularly where the input data is in some sense unsatisfactory or inaccurate. Thenumerical caution is applied during the steps taken by the barrier algorithm during itsconvergence toward the optimum, to help it do its job better. On some models, it may turnout that solution quality measures are improved (Ax-b residuals, variable-bound violations,dual values, and so forth) when ILOG CPLEX exercises numerical caution, but this wouldbe a secondary outcome from better convergence.Difficulties in the Quality of SolutionUnderstanding Solution Quality from the Barrier LP Optimizer on page 205 lists the itemsthat ILOG CPLEX displays about the quality of a barrier solution. If the ILOG CPLEXBarrier Optimizer terminates its work with a solution that does not meet your qualityrequirements, you can adjust parameters that influence the quality of a solution. Thoseadjustments affect the choice of barrier algorithm, the limit on barrier corrections, and the212 ILOG CPLEX 11.0 — USER’ S MANUAL