non zero variable

Answered

Zahra Hoobakht

April 19, 2024 19:16

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Hi 

I have a variable that is in the interval of -1 and 1 but it cannot be zero. I would be appreciate if you help me to define the constraints properly.

m = gp.Model()
phi_0 = m.addVar(vtype=gp.GRB.CONTINUOUS,lb=-1,ub=1,name=("phi_0"))
phi_1 = m.addVar(vtype=gp.GRB.CONTINUOUS,lb=-1,ub=1,name=("phi_1"))

m.addConstr(phi_0 >= 1e-3  or phi_0 <= -1e-3 )
m.addConstr(phi_0 >= 1e-3  or phi_0 <= -1e-3 )

gurobipy.GurobiError: Constraint has no bool value (are you trying "lb <= expr <= ub"?)

Related to

• General Constraints

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  Bot Marley (with AI contributions)

  April 21, 2024 01:52 Edited

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  Hi Zahra,

  To define your variable phi_0 such that it can never be zero but lies within the interval [−1,1], you can utilize auxiliary variables.  In your case, you want to enforce that phi_0 is either greater than a small positive threshold or less than a small negative threshold.

  Here's how you can modify your code to implement this constraint correctly:

  import gurobipy as gp
  
  m = gp.Model()
  phi_0 = m.addVar(vtype=gp.GRB.CONTINUOUS, lb=-1, ub=1, name="phi_0")
  
  # Create a helper variable to manage the or constraint
  phi_0_positive = m.addVar(vtype=gp.GRB.BINARY, name="phi_0_positive")
  phi_0_negative = m.addVar(vtype=gp.GRB.BINARY, name="phi_0_negative")
  
  # Add constraints that link these binary variables with phi_0 ranges
  m.addConstr(phi_0 >= 1e-3 - (1 - phi_0_positive), name="phi_0_pos_constr")
  m.addConstr(phi_0 <= -1e-3 + (1 - phi_0_negative), name="phi_0_neg_constr")
  
  # Ensure that one of the binary variables must be true, so phi_0 cannot be zero
  m.addConstr(phi_0_positive + phi_0_negative == 1, name="phi_0_or_constr")
  
  # Now phi_0 is constrained to be either > 1e-3 or < -1e-3

  This method uses binary helper variables (phi_0_positive and phi_0_negative) to enforce that phi_0 must be strictly positive or strictly negative, hence not zero. The constraint phi_0_positive + phi_0_negative == 1 ensures that one of these conditions is always true.

  - Bot

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