How Gurobi implements judgment(if) and assignment(=)

回答済み

Victor

2023年06月28日 17:00

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Hey everyone,

I have a question described as follows.

I want to realize the following code.

But in Gurobi, I cannot find any grammar that can implements the following function.

flag_chosedPoint_each_set is a 2D numpy and its value can be 0 or 1.

Could you give me a support?

x = self.model.addVars(len(A), vtype=GRB.BINARY, name='x')
for i in range(Len(B)): # count the elements
    t = [x[j] * flag_chosedPoint_each_set[j][i] for j in range(len(A))]
     t = sum(t)
    if t > 0:
         selected[i]=1
    else:
        selected [i]= 0

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  Maliheh Aramon

  • Gurobi Staff

  2023年06月29日 17:43 編集済み

  Hi Victor, 

  It seems to me that you would like to implement the following two constraints:

  \[\mbox{if}~~ \sum_j c_{ij} x_j > 0 \rightarrow s_i = 1, ~~\forall i\]

  \[\mbox{if}~~ \sum_j c_{ij} x_j \leq 0 \rightarrow s_i = 0, ~~\forall i\]

  In Gurobi Python API, you can use the Model.addGenConstrIndicator() method to implement these indicator constraints. Since the indicator variable in this method should be a binary variable and not a linear expression, you can implement their equivalent contrapositives:

  \[\mbox{if}~~ s_i \neq 1 \rightarrow \sum_j c_{ij} x_j \ngtr 0, ~~\forall i ~~\mbox{which equals} ~~ \mbox{if}~~ s_i = 0 \rightarrow \sum_j c_{ij} x_j \leq 0, ~~\forall i \]

  \[\mbox{if}~~ s_i \neq 0 \rightarrow \sum_j c_{ij} x_j \nleq 0, ~~\forall i ~~\mbox{which equals} ~~ \mbox{if}~~ s_i = 1 \rightarrow \sum_j c_{ij} x_j \geq 1, ~~\forall i \]

  The last inequality \(\sum_j c_{ij} x_j \geq 1\) holds true because all \(c_{ij}\) coefficients and \(x_j\) variables are either 0 or 1. 

  See an example implementation below:

  n, m = 10, 20
  c = np.random.randint(low=0, high=2, size=(n, m))
  
  model = gp.Model()
  x = model.addVars(m, vtype=GRB.BINARY, name="x")
  s = model.addVars(n, vtype=GRB.BINARY, name="s")
  
  for i in range(n):
      expr = gp.quicksum(c[i][j] * x[j] for j in range(m))
      model.addGenConstrIndicator(s[i], 0, expr <= 0, name=f"ind0_{i}")
      model.addGenConstrIndicator(s[i], 1, expr >= 1, name=f"ind1_{i}")
  
      # Instead of using addGenConstrIndicator, you can use the overloaded form too
      # model.addConstr((s[i] == 0) >> (expr <= 0))
      # model.addConstr((s[i] == 1) >> (expr >= 1))

  Best regards,

  Maliheh

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  Victor

  2023年06月29日 08:04

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  Hey Maliheh @Maliheh Aramon ,

  Thank you for your reply. The first method work.

  But the 2nd doesn't works and give me feedback: 

  gurobipy.GurobiError: Constraint comparison not implemented

  Thank you again.

  Victor

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  Maliheh Aramon

  • Gurobi Staff

  2023年06月29日 17:45

  My bad, I am sorry. I was missing parentheses around the linear expression. I edited the implementation. 

  Thanks for noticing this.

  Maliheh

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  Victor

  2023年07月01日 13:14

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  Hey Maliheh，

  Thank you for your suggestion.

   

  Have a nice day,

  Victor

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