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IIS Logging

Recall that an Irreducible Infeasible Subsystem (IIS) is a subset of the constraints and variable bounds in your infeasible model with the following properties:

  • It is still infeasible, and
  • If a single constraint or bound is removed, the subsystem becomes feasible.
The process of identifying an IIS is one of addition and subtraction. The algorithm grows a set of constraints and bounds that are known to be part of an IIS, and also a set that are known not to be. You can track the progress of this process in the IIS log.
Computing Irreducible Inconsistent Subsystem (IIS)...

           Constraints          |            Bounds           |  Runtime
      Min       Max     Guess   |   Min       Max     Guess   |
        0     17509         -         0         4         -           0s
        0     12996         -         0         4         -           5s
        0     10398        20         0         0         -          10s
        0      9749        20         0         0         -          15s
        1      9584        20         0         0         -          20s
        4      9576        20         0         0         -          25s
        6      9406        20         0         0         -          30s
        8      8432        40         0         0         -          35s
       11      8422        40         0         0         -          40s
       15      8413        60         0         0         -          45s
       18      8241        60         0         0         -          50s
       21      7908        50         0         0         -          55s
       24      7735        50         0         0         -          60s
The first two columns show the minimum and maximum sizes of the set of constraints in the IIS. The fourth and fifth column give the same information for the set of variable bounds. The final column shows elapsed runtime.

The third and sixth columns in the IIS log provide guesses at the final size of the IIS. Computing an IIS can be quite time-consuming, and it is often useful to have a sense of how large the result will be. These guesses can be quite accurate in some cases, but unfortunately there are some models that can fool our heuristic. You should treat these as very rough estimates.

When the process completes, the algorithm outputs the size of the IIS (the number of constraints and bounds in the irreducible subsystem):

IIS computed: 102 constraints, 0 bounds
IIS runtime: 129.91 seconds
Note in this case that early guesses were in the neighborhood of 50 constraints, but the IIS contained 102.

If you terminate the process early, you will get a non-minimal infeasible subsystem instead:

Non-minimal IIS computed: 3179 constraints, 0 bounds
IIS runtime: 120.29 seconds

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