How to model the indicator function in Gurobi

Answered

ibtissam labriji

• March 05, 2020 08:49

Hello, 

I would like to model the following constraint :

f_r are problem variables declared as follows :

for i in range(R):

     f[i] = m.addVar( lb=0.0, vtype=GRB.CONTINUOUS, name="CPU frequency"+ " " +str(i))

and I need to make sure that the number of elements of the vector f = (f_1 , f_2 , f_3, ...) strictly greater than zero is less than C. 

I thought of introducing a binary variable i_r which takes the value 1 if f_r> 0, 0 if f_r = 0 and adding the following conditions: 

for i in range(R):

    m.addConstrs(ind[i] == 1 if f[i] != 0 else 0)

so that then I can control the number of variables f_r different from zero in my vector f:

m.addConstr( quicksum( i[j] for j in range(R))<= C), but I can't do that because of != operator. 

in the documentation, I found this option:

Model.addGenConstrIndicator()

but it seems like it's kind of the opposite of what I want to do. is there any way to adapt it? 

# f_r > 0 -> i_r = 1

Thank you in advance !
Ibtissam

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• 

  Tobias Achterberg

  Gurobi Staff

  • March 05, 2020 17:00

  Yes, using an indicator is the right way to go. And it is very easy, you just need to invert the direction of the indicator. Instead of

  f_r > 0 -> i_r = 1

  you would enforce

  i_r = 0 -> f_r <= 0

  This is mathematically equivalent, and it fits to how indicators in Gurobi are defined.

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