ILOG CPLEX 11.0 User's Manual

Numeric DifficultiesILOG CPLEX is designed to handle the numeric difficulties of linear programmingautomatically. In this context, numeric difficulties mean such phenomena as:◆◆◆◆repeated occurrence of singularities;little or no progress toward reaching the optimal objective function value;little or no progress in scaled infeasibility;repeated problem perturbations; and◆ repeated occurrences of the solution becoming infeasible.While ILOG CPLEX will usually achieve an optimal solution in spite of these difficulties,you can help it do so more efficiently. This section characterizes situations in which you canhelp.Some problems will not be solvable even after you take the measures suggested here. Forexample, problems can be so poorly conditioned that their optimal solutions are beyond thenumeric precision of your computer.Numerical Emphasis SettingsThe numerical emphasis parameter controls the degree of numerical caution used duringoptimization of a model.◆◆NumericalEmphasis (bool) in Concert TechnologyCPX_PARAM_NUMERICALEMPHASIS (int) in the Callable Library◆ emphasis numerical in the Interactive OptimizerAt its default setting, ILOG CPLEX employs ordinary caution in dealing with the numericalproperties of the computations it must perform. Under the optional setting, ILOG CPLEXuses extreme caution.This emphasis parameter is different in style from the various tolerance parameters inILOG CPLEX. The purpose of the emphasis parameter is to relieve the user of the need toanalyze which tolerances or other algorithmic controls to try. Instead, the user tellsILOG CPLEX that the model about to be solved is known to be susceptible to unstablenumerical behavior and lets ILOG CPLEX make the decisions about how best to proceed.There may be a tradeoff between solution speed and numerical caution. You should not besurprised if your model solves less rapidly at the optional setting of this parameter, becauseeach iteration may potentially be noticeably slower than at the default. On the other hand, ifthe numerical difficulty has been causing the optimizer to proceed less directly to theoptimal solution, it is possible that the optional setting will reduce the number of iterations,thus leading to faster solution. When the user chooses an emphasis on extreme numericalcaution, solution speed is in effect treated as no longer the primary emphasis.ILOG CPLEX 11.0 — USER’ S MANUAL 185