ILOG CPLEX 11.0 User's Manual

Limitations Due to Numeric DifficultiesILOG CPLEX uses numerical methods of finite-precision arithmetic. Consequently, thefeasibility of a solution depends on the value given to tolerances. Two parameters define thetolerances that assess the feasibility of a MIP solution:◆the integrality tolerance (EpInt, CPX_PARAM_EPINT);◆ the feasibility tolerance (EpRHS, CPX_PARAM_EPRHS).A solution may be considered feasible for one pair of values for these two parameters, andinfeasible for a different pair. This phenomenon is especially noticeable in models withnumeric difficulties, for example, in models with Big M coefficients.Since the definition of a feasible MIP solution is subject to tolerances, the total number ofsolutions to a MIP model may vary, depending on the approach used to enumerate solutions,and on precisely which tolerances are used. In most models, this tolerance issue is notproblematic for ILOG CPLEX. But, in the presence of numeric difficulties, ILOG CPLEXmay create solutions that are slightly infeasible or integer infeasible, and therefore createmore solutions than expected.You can find more details about the topic of numeric difficulties in the ILOG CPLEX User’sManual in Numeric Difficulties on page 185 and Slightly Infeasible Integer Variables onpage 292.Impact of Change on the Solution PoolVarious changes that you make to your model or its context may have an impact on thesolution pool and the solutions stored there. The following sections offer more informationabout changes and their effects.◆ Changes between MIP Optimization and Populate on page 314◆ Persistence of Solutions in the Solution Pool on page 315◆ Model Changes and the Solution Pool on page 315Changes between MIP Optimization and PopulateWhat might users do between a call of MIP optimization and a call of populate or betweensuccessive calls of populate?Users can continue to call populate until they have a pool of solutions they are satisfied with.Between calls, users may examine solutions. If the solutions are satisfactory, users can stopcalling populate. If the solutions are not satisfactory, then users can make changes to314 ILOG CPLEX 11.0 — USER’ S MANUAL