Single Constraint with Sum of Binary Variable

Answered

Peter Furseth

• October 25, 2022 18:11

I am new to this community and am struggling with seemingly simple modeling question.

I would to create a single constraint that sums a set of binary variables x[i,j] where i = j for all i in V and sets it equal to a predefined value p.

Example:

x[1,1] + x[2,2] + ... +x[n,n] = p

The x[i,j] variable can be thought of as an edge on a graph, i and j are indexed on the vertices of the graph, and x[i,i] is an edge that goes back to the same vertex.

I am using python with gurobi and here is the code I tried:

m.addConstrs(x.sum(i, i) == p for i in V)

It returns a constraint for each value of i in V.

Any help would be appreciated.

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• 

  Eli Towle

  Gurobi Staff

  • October 25, 2022 18:44

  Model.addConstrs() is used to add multiple constraints to the model. To add one constraint to the model, use Model.addConstr().

  You are summing over all \(i\) in \(V\), so the \(\texttt{for}\) loop should be placed inside of the summation:

  x = m.addVars(V, V, vtype=GRB.BINARY, name='x')
  m.addConstr(gp.quicksum(x[i, i] for i in V) == p)

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• 

  Peter Furseth

  • October 25, 2022 20:53

  

  

  

  Eli - That did the trick. Thank you.

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