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optimizationpyomomixed-integer-programming

Restricting one variable in my variable vector to integer in Pyomo

I have a minimization problem that currently has only continuous variables

min Cx
s.t. Ax <= b
lb <= x <= ub

Where C is my cost vector, A is my coefficient matrix and b is my fixed vector. X is my variable vector of continuous variables.

A = 24x29, x = 29x1, b = 24x1

I want to force one of the x variables to be an integer, how can that be done in Pyomo?

I am new to the package, any help is appreciated

Solution

  • Pyomo offers a way to set the domain of your variables. Let me prove it to you in this example that you can entirely run in a Python console with copy/paste.

    Suppose you want to change x[1] to integers, you can use (1 being part of set S = {1,2,3}):

    from pyomo.environ import ConcreteModel, Set, Var, Integers
# Create your model here (set params, vars, constraint...)
model = ConcreteModel()
model.S = Set(initialize={1,2,3})
model.x = Var(model.S)

    Let's pause the example here and type model.x.display() in the Python console. You should see that the domain of all elements in model.x is set by default to Real. Let's continue. 

    # Here, we suppose your model is created.
# You can change the domain of one lement of your var using this line:
model.x[1].domain = Integers

    Now, type model.x.display() in your Python console and you should see this:

    x : Size=3, Index=S
Key : Lower : Value : Upper : Fixed : Stale : Domain
  1 :  None :  None :  None : False :  True : Integers
  2 :  None :  None :  None : False :  True :    Reals
  3 :  None :  None :  None : False :  True :    Reals

    So, only x[1] is integer.