CPLEX IIS

This page is part of the CPLEX Manual. See CPLEX.

IIS is obsolete in the latest version of TOMLAB /CPLEX

If TOMLAB /CPLEX reports that your problem is infeasible, then you can invoke the TOMLAB /CPLEX infeasibility finder to help you analyze the source of the infeasibility. This diagnostic tool computes a set of infeasible constraints and column bounds that would be feasible if one of them (a constraint or variable) were removed. Such a set is known as an irreducibly inconsistent set (IIS).

To work, the infeasibility finder must have a problem that satisfies two conditions:

• the problem has been optimized by the primal or dual simplex optimizer or by the barrier optimizer with crossover, and

• the optimizer has terminated with a declaration of infeasibility.

Correcting Multiple Infeasibilities

The infeasibility finder will find only one irreducibly inconsistent set (IIS), though a given problem may contain many independent IISs. Consequently, even after you detect and correct one such IIS in your problem, it may still remain infeasible. In such a case, you need to run the infeasibility finder more than once to detect those multiple causes of infeasibility in your problem.

Interpreting IIS Output

The size of the IIS reported by TOMLAB /CPLEX depends on many factors in the model. If an IIS contains hundreds of rows and columns, you may find it hard to determine the cause of the infeasibility. Fortunately, there are tactics to help you interpret IIS output:

• Consider selecting an alternative IIS algorithm. The default algorithm emphasizes computation speed, and it may give rise to a relatively large IIS. See parameter IISIND.

• If the problem contains equality constraints, examine the cumulative constraint consisting of the sum of the equality rows.

• Try preprocessing with the TOMLAB /CPLEX presolver and aggregator. The presolver may even detect infeasibility by itself. If not, running the infeasibility finder on the presolved problem may help by reducing the problem size and removing extraneous constraints that do not directly cause the infeasibility but still appear in the IIS. Similarly, running the infeasibility finder on an aggregated problem may help because the aggregator performs substitutions that may remove extraneous variables that clutter the IIS output. More generally, if you perform substitutions, you may simplify the output so that it can be interpreted more easily.

• Other simplifications of the constraints in the IIS, such as combining variables, multiplying constraints by constants, and rearranging sums, may make it easier to interpret the IIS.