Merging a binary decision variable with a continuous variable (semi-binary/continuous)

Answered

Vincent

• August 17, 2021 20:59

I have two decision variables defined as

x = m.addVars(((i, j) for i, j in arcs if f[i][j] == 0),
vtype=GRB.BINARY, name='x')

y = m.addVars(((i, j) for i, j in arcs if f[i][j] == 1),
vtype=GRB.CONTINUOUS, name='y')

As you see, what makes x be binary but y continuous depends on the if condition. Is there a way to merge them into a single variable? For instance, something like:

x = m.addVars(((i, j) for i, j in arcs),
vtype=GRB.CONTINUOUS if f[i][j] else vtype=GRB.BINARY, name='x')

 

0

• 

  Eli Towle

  Gurobi Staff

  • August 17, 2021 21:35
  • Edited

  You can do this by setting the \( \texttt{vtype} \) keyword argument to a \( \texttt{dict} \) that maps each arc to either \( \texttt{GRB.CONTINUOUS} \) or \( \texttt{GRB.BINARY} \). For example:

  import random
  
  vtypes = {(i, j): GRB.CONTINUOUS if random.random() < 0.5 else GRB.BINARY for (i, j) in arcs}
  x = m.addVars(arcs, vtype=vtypes, name='x')

  If you want the continuous variables to be bounded above by \( 1 \), you should include the argument \( \texttt{ub=1} \) in your call to Model.addVars().

  Alternatively, you could:

  • Set the \( \texttt{vtype} \) argument equal to a list that's the same length as \( \texttt{arcs} \), or
  • After calling Model.addVars(), iterate over the variables and individually set their VType attributes.

  1
• 

  Vincent

  • August 17, 2021 22:07

  

  

  

  Thanks very much for your quick and detailed response.

  0

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