Using indicator constraint with two variables

Answered

Saeid Ghafouri

• March 04, 2023 02:22

Hi Gurobi team,

I want to use the sum of two binary decision variables (when their sum equals to one) as the condition of Model.AddGenConstrIndicator https://www.gurobi.com/documentation/current/refman/py_model_agc_indicator.html, however, it seems to be impossible, e.g. for the minimal code below which reflects the relevant part of my real problem trying the following:

import gurobipy as gp

model = gp.Model()

x = model.addVar(vtype=gp.GRB.BINARY, name="x")
y = model.addVar(vtype=gp.GRB.BINARY, name="y")

z = model.addVar(vtype=gp.GRB.CONTINUOUS, name="z")

model.update()
constr = model.addConstr((x + y == 1) >> (z <= 20))

model.setObjective(z, gp.GRB.MAXIMIZE)

# Solve the model
model.optimize()

Will result in the following error:

    constr = model.addConstr((x + y == 1) >> (z <= 20))
  File "src/gurobipy/model.pxi", line 3632, in gurobipy.Model.addConstr
gurobipy.GurobiError: Indicator constraints can only be triggered by a single binary variable at a given value

Is there a workaround for this?

Related to

• Indicator Constraints

0

• 

  Saeid Ghafouri

  • March 04, 2023 02:41

  

  

  

  Just a quick fix to the above example, what I want as the constraint is the following (I want it to equal to two instead one - that I have in the above):

  constr = model.addConstr((x + y == 2) >> (z <= 20))

  0
• 

  Jonasz Staszek

  Community Moderator

  • March 04, 2023 06:13

  

  

  

  Hi Saeid,

  if you are sure that either \(x = 1 \land y = 1\) or \(x=0 \land y=0\), you can try "Big-M" kind of constraint:

  a = model.addVar(vtype="B")
  model.addLConstr(x+y, GRB.LESS_EQUAL, 2*a)

  If you are sure the condition above is too strict, you can resort to another general constraint, the AND-constraint:

  a = model.addVar(vtype="B")
  model.addGenConstrAnd(a, [x, y], "andconstr")

   

  Regardless of the approach you choose, you can then use the binary \(a\) variable with your indicator constraint.

  Hope this helps.

  Best regards
  Jonasz

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• 

  Jue Xue

  Gurobi Staff

  • March 06, 2023 13:59

  Hi Saeid,

  See the bold part in the error message you get: "gurobipy.GurobiError: Indicator constraints can only be triggered by a single binary variable at a given value". So you may want to use an additional binary variable, say w, and an additional constraint w = x+y to work around. Similarly, to have "x+y = 2", you can add a constraint "2*w = x + y". Hope this solves your problem.

  0
• 

  Jue Xue

  Gurobi Staff

  • March 06, 2023 14:02

  a single binary variable

  0

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