Meaning of "Lazy constraints" in the optimization log

Answered

Tomas Pippia

• October 22, 2024 15:05

Hello, I added lazy constraints to a model enumerating them using the Lazy property instead of doing it via callback. In the optimization logs, I see first:

Extracted 400 lazy constraints

and at the end:

Cutting planes:
  Implied bound: 19
  MIR: 23
  Flow cover: 13
  Relax-and-lift: 2
  Lazy constraints: 6

What does the number 6 after "Lazy constraints:" mean? Is it the amount of lazy constraints that were pulled in (as explained here)?

By checking the "Slack" property of the enumerated lazy constraints, I see that 7 of them have a slack value of 0, three have a value of 1.42e-14 (thus, they can be regarded as 0, considering tolerances), and the rest has a non-zero value. Therefore, I assume that 10 out of the 400 constraints are active at the optimal solution. Shouldn't then the amount of lazy constraints used be 10 instead of 6? Or is it 6 because some of "missing" 4 constraints are already satisfied when pulling in some of the other 6, and as explained in the documentation, "With a value of 1, the constraint can be used to cut off a feasible solution, but it won’t necessarily be pulled in if another lazy constraint also cuts off the solution"?

Thanks in advance!

Related to

• Lazy Constraints

0

• 

  Jaromił Najman

  Gurobi Staff

  • October 24, 2024 14:05

  Hi Tomas,

  The output means that there are 6 active lazy constraint at the optimal solution point.

  Or is it 6 because some of "missing" 4 constraints are already satisfied when pulling in some of the other 6, and as explained in the documentation, "With a value of 1, the constraint can be used to cut off a feasible solution, but it won’t necessarily be pulled in if another lazy constraint also cuts off the solution"?

  Correct, this is why you see 6 instead of 10.

  Best regards, 
  Jaromił

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