ILOG CPLEX 11.0 User's Manual

For C++ applications, see Accessing Solution Information on page 57, and for Javaapplications, see Accessing Solution Information on page 82. Those sections highlight theapplication programming details of how to retrieve statistics about the quality of a solution.Regardless of whether a solution is infeasible or optimal, the commanddisplay solution quality in the Interactive Optimizer displays the bound andreduced-cost infeasibilities for both the scaled and unscaled problem. In fact, it displays thefollowing summary statistics for both the scaled and unscaled problem:◆◆◆◆maximum bound infeasibility, that is, the largest bound violation;maximum reduced-cost infeasibility;maximum row residual;maximum dual residual;◆ maximum absolute value of a variable, a slack variable, a dual variable, and a reducedcost.When the simplex optimizer detects infeasibility in the primal or dual linear program (LP),parts of the solution it provides are relative to the Phase I linear program it solved toconclude infeasibility. In other words, the result you see in such a case is not the solutionvalues computed relative to the original objective or original righthand side vector. Keep thisdistinction in mind when you interpret solution quality; otherwise, you may be surprised bythe results. In particular, when ILOG CPLEX detects that a linear program is infeasibleusing the primal simplex method, the reduced costs and dual variables provided in thesolution are relative to the objective of the Phase I linear program it solved. Similarly, whenILOG CPLEX detects that a linear program is unbounded because the dual simplex methoddetected dual infeasibility, the primal and slack variables provided in the solution are relativeto the Phase I linear program created for the dual simplex optimizer.The following sections discuss these summary statistics in greater detail.Maximum Bound Infeasibility: Identifying Largest Bound ViolationThe maximum bound infeasibility identifies the largest bound violation. This informationmay help you discover the cause of infeasibility in your problem. If the largest boundviolation exceeds the feasibility tolerance of your problem by only a small amount, then youmay be able to get a feasible solution to the problem by increasing the parameter forfeasibility tolerance (EpRHS in Concert Technology, CPX_PARAM_EPRHS in the CallableLibrary). Its range is between 1e-9 and 0.1. Its default value is 1e-6.Maximum Reduced-Cost InfeasibilityThe maximum reduced-cost infeasibility identifies a value for the optimality tolerance thatwould cause ILOG CPLEX to perform additional iterations. It refers to the infeasibility inthe dual slack associated with reduced costs. Whether ILOG CPLEX terminated with anoptimal or infeasible solution, if the maximum reduced-cost infeasibility is only slightly192 ILOG CPLEX 11.0 — USER’ S MANUAL