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')

 

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• Official comment

  

  Simranjit Kaur

  Gurobi Staff

  • December 06, 2024 00:27

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.
• 

  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.

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• 

  Vincent

  • August 17, 2021 22:07

  

  

  

  Thanks very much for your quick and detailed response.

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