How to add modulo constraints in gurobi

Answered

Vaibhav Dixit

• September 08, 2024 13:56

Hi Gurobi Community,

I'm trying to add a constrains which represents that \sum( x[i] for i in lst) is odd.

I have approached it in two ways but in both ways I have found errors.

First way:

model.addConstr(gp.quicksum(x[i] for i in lst) %2  == 1)

 

Second way:

By defining new integer vars odd_value[.]

model.addConstr(gp.quicksum(x[i] for i in lst) == odd_value[cnt])
model.addConstr(odd_value[cnt] % 2 == 1)

In both cases I get ,

TypeError: unsupported operand parent(s) for %: '<class 'gurobipy.LinExpr'>' and 'Integer Ring'

Related to

• Branch-and-Cut
• Big-M
• Branch-and-Price

0

• 

  Riley Clement

  Gurobi Staff

  • September 08, 2024 23:40

  Hi Vaihab,

  If I understand correctly, you are wanting to ensure that the following sum is odd.

  gp.quicksum(x[i] for i in lst)

  This sum is odd if, and only, if there is an even number 1 less than it.  If we introduce an integer variable named aux then 2*aux will be even.  Once this variable is added you can form the following constraint

  model.addVar(vtype="I", lb=-float("inf"))
  model.addConstr(gp.quicksum(x[i] for i in lst) == 1 + 2*aux)
  

  - Riley

   

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• 

  Vaibhav Dixit

  • September 09, 2024 04:33

  

  

  Hi,

  Thanks, its working now. So basically to ensure  that "gp.quicksum(x[i] for i in lst)"  is odd , the aux variable takes its values ​​accordingly, there is no need to add more constraints corresponding to the aux variable.

  So in same way I can define many such aux variables if 'x'  is 2D array.

  x=model.addVars(len(lst),len(lst), vtype="I")
  aux=model.addVars(len(lst),vtype="I", lb=-float("inf"))

  for j in range(len(lst)):
      model.addConstr(gp.quicksum(x[i,j] for i in lst) == 1 + 2*aux[j])

  pls correct me, if I'm wrong.

  -Vaibhav

  0
• 

  Riley Clement

  Gurobi Staff

  • September 09, 2024 04:39
  • Edited

  Correct!

  Only thing I have to add is that if x are non-negative then the sum can never be negative so you don't need the lower bound of -infinity on the integer variables, and can let them take their default lower bound of 0.

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