Is there a better solution than IntegralityFocus to ensure integrality of variables?

Awaiting user input

Amirhossein Moosavi

• April 24, 2023 14:20

I have an MIP model with the following parameter settings:

mdl.Params.IntegralityFocus = 1
mdl.Params.FeasibilityTol = 1e-9

The model sometimes generates variables that are not even close to integer values. For example:

k: v.X for k, v in t.items() if v.X > 0}
{(0, 1): 114.0, (0, 4): 23.558825610628386, (0, 5): 45.0, (0, 6): 111.0, (0, 7): 64.52817997001554, (0, 8): 89.45054879258372, (0, 10): 14.0, (0, 11): 29.558825610628386, (0, 12): 24.0, (0, 13): 12.000000000000016, (0, 14): 7.0, (0, 15): 76.74705379564192, (0, 16): 117.0, (0, 17): 9.000000000000016, (0, 18): 61.0, (0, 19): 18.0, (0, 21): 52.52817997001554, (0, 22): 64.5158780897043, (0, 24): 85.0, (0, 26): 71.0, (0, 27): 99.0, (0, 28): 83.45054879258372, (0, 30): 78.0, (0, 31): 35.0, (0, 32): 20.514940870192838, (0, 33): 28.0, (0, 34): 58.52817997001554, (0, 37): 84.0, (0, 38): 107.0, (0, 39): 3.000000000000016, (0, 40): 26.558825610628386, (0, 41): 6.000000000000015, (0, 43): 52.0, (0, 44): 95.45054879258372, (0, 45): 92.0, (0, 46): 12.0, (0, 48): 15.000000000000016, (0, 49): 30.0, (0, 50): 38.0, (0, 51): 68.0, (0, 52): 32.55882561062839, (0, 53): 58.0, (0, 54): 6.0, (0, 55): 35.558825610628446, (0, 56): 90.0, (0, 58): 55.0, (0, 59): 21.0}

However, the integrality of variables is important in my application and rounding them after the solution process might not be sufficient. What would be your suggestion?

Related to

• MIP
• Parameters

0

• 

  Eli Towle

  Gurobi Staff

  • April 24, 2023 16:36

  How exactly do you define your \(\texttt{t}\) variables? It looks like at least some of them are not defined as integer variables:

  (0, 4): 23.558825610628386
  (0, 7): 64.52817997001554
  (0, 8): 89.45054879258372
  (0, 11): 29.558825610628386
  (0, 15): 76.74705379564192
  (0, 21): 52.52817997001554
  (0, 22): 64.5158780897043
  (0, 28): 83.45054879258372
  (0, 32): 20.514940870192838
  (0, 34): 58.52817997001554
  (0, 40): 26.558825610628386
  (0, 44): 95.45054879258372
  (0, 52): 32.55882561062839
  (0, 55): 35.558825610628446

  You can define integer variables by adding the keyword argument \(\texttt{vtype=GRB.INTEGER}\) to your call to Model.addVars() or Model.addVar().

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