How to set two sets of binary variables equal to each other when they have different keys?

Answered

Emily You

August 05, 2020 00:34

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I have two sets of binary variables, aux and aux1. I am using them to make sure that two other variables only take on certain values from different lists.

 

aux looks like this (with 1 of them being 1 and the rest 0):

aux = m.addVars(allowed_values, vtype=GRB.BINARY, name='aux')

and aux1 looks like this (again, with only one of them being 1 and the rest 0):

aux1 = m.addVars(allowed_vals_occ, vtype=GRB.BINARY, name='aux1')

 

As you can see, the two sets of variables have different keys (they have the same length). I want to make sure they are both 1 at the same location. For example, if the first element of aux is 1, I want the first element of aux1 to be 1.

 

I tried: m.addConstrs(aux[i]==aux1[i] for i in range(len(aux)))

But this gives me an error because aux and aux1 have different keys.

m.addConstr(aux==aux1) gives a generator error.

How can I solve this problem?

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• Official comment

  

  Simranjit Kaur

  • Gurobi Staff

  June 23, 2025 03:09 Edited

  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?.
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  Eli Towle

  • Gurobi Staff

  August 05, 2020 01:36 Edited

  The keys for \( \texttt{aux} \) are \( \texttt{allowed_values} \), and the keys for \( \texttt{aux1} \) are \( \texttt{allowed_vals_occ} \). Thus, we have to map back to these values when adding the constraints:

  m.addConstrs(aux[allowed_values[i]] == aux1[allowed_vals_occ[i]] for i in range(len(aux)))

  This is a bit messy. It would be much cleaner to use the same indices for each of these variables. The keys themselves don't need to be anything special, since we can easily map from an index to a specific "allowed" value with the \( \texttt{allowed_values} \) and \( \texttt{allowed_vals_occ} \) lists. So, we can use:

  n = len(allowed_values)
  aux = m.addVars(n, vtype=GRB.BINARY, name='aux')
  aux1 = m.addVars(n, vtype=GRB.BINARY, name='aux1')
  m.addConstrs((aux[i] == aux1[i] for i in range(n)), name='set_aux1')

  Even better, we could completely remove the \( \texttt{aux1} \) variables. Wherever we would use \( \texttt{aux1} \), we can just use the corresponding \( \texttt{aux} \) variable (since they would be equal anyways):

  n = len(allowed_values)
  aux = m.addVars(n, vtype=GRB.BINARY, name='aux')

   

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  Emily You

  August 05, 2020 02:28

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  Thank you so much, Eli! This is very helpful.

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