How to define if constraint with decision varibales?

回答済み

Ariel W

2023年10月25日 07:42

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How do i express that "If w[d,0,j]==1 then p[d,j]==0, where w[d,i,j] is a decision variable"?

 

関連

• Indicator Constraints

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  Jaromił Najman

  • Gurobi Staff

  2023年10月25日 09:58

  If \(w_{d,0,j}\) is a binary variable then you can use an indicator constraint.

  The code

  model.addGenConstrIndicator(w, True, p, GRB.EQUAL, 0)

  would introduce the indicator constraint

  \[\begin{align*}
  w = 1 \rightarrow p = 0
  \end{align*}\]

  meaning "if w = 1 then p = 0".

  Is \(w\) a binary variable in your case?

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  Ariel W

  2023年10月25日 10:26

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  Thanks for your answer. Yes, w is a binary variable and p is a continous variable. For p is also a decision variable, is the method to define still the same?

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  Jaromił Najman

  • Gurobi Staff

  2023年10月25日 15:06

  For p is also a decision variable, is the method to define still the same?

  Yes, it is no problem that \(p\) is an optimization variable.

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  Ariel W

  2023年10月26日 07:34

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  I got it! Thank you, Jaromił Najman!

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  Ariel W

  2023年10月26日 10:31

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  Hello, Jaromił: I still have a question: when ∑i∈S (w[d,i,j]) = 0, p[d,j]=0. How do i define this situation?

  I tried to follow the way you wrote above, but it proposed "TypeError: 0.0 is not a variable".

  for d in range(1, 3):
      for j in range(1,4):
          expr = quicksum(w[d,i,j] for i in range(1,2) if i < j)
          model.addGenConstrIndicator(expr, False, p[d, j], GRB.EQUAL, 0)
          expr.clear()

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  Jaromił Najman

  • Gurobi Staff

  2023年10月26日 11:40

  Hi Ariel,

  Your approach does not work because the addGenConstrIndicator method accepts only a single variable as input for the binary indicator, i.e., a sum or any other expression is not allowed.

  You will have to model your conditional by hand. To do that you can introduce a new binary variable \(b\) and a constant parameter \(M\) which equals the number of \(w\) variables in your sum. You can then model

  \[\begin{align*}
  \sum w \geq b\\
  \sum w \leq M\cdot b\\
  b = 0 \rightarrow p = 0
  \end{align*}\]

  In the above \(b\) is forced to \(0\) when \(\sum w = 0\) and to \(1\) when \(\sum w > 0\). The last term can be introduced via the addGenConstrIndicator method  because \(b\) is a single binary optimization variable.

  Best regards, 
  Jaromił

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