Binary Variable Involving Case Brackets

回答済み

Suli Adeniye

2023年05月21日 16:46

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Hi, 

I am trying to write a Gurobi expression for a binary variable X_ij which depends on another variable F_ij.

F_ij is a list of variables each of which could have a different value depending on (i, j).  I have already written in my code F_ij as a dictionary of key, value pairs - (i_j), F[i, j] but I am having a hard time translating X_ij into code. 

Please, can you give me suggestions, example codes, or resources that could help me in coding X_ij.

Thank you.

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  Jaromił Najman

  • Gurobi Staff

  2023年05月22日 09:08

  We discuss how to model conditional statements in the Knowledge Base article How do I model conditional statements in Gurobi? In the linked article, we discuss a strict inequality where we need a small tolerance \(\epsilon > 0 \). This is not required in your case because your condition \(F_{i,j} \geq 1\) is not a strict inequality.

  Best regards, 
  Jaromił

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  Suli Adeniye

  2023年05月23日 19:50

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  Thank you Jaromil.

  I would like to add that F_ij is defined as:

  

  X_ij is:

  The binary variable representing flow[(k, (i, j)] is written as:

  flow_k_on_i_j = [(k, (i, j)) for k in pmu_nodes for i in nodes for j in nodes if i != j and (i, j) in edges]
  
  flow = model.addVars(flow_k_on_i_j, vtype=GRB.BINARY, name="flow")

  Following the notes you provided, I wrote code the snippets involving F_ij, and X_ij as:

  F_ij = {}
  for edge in edges:
      F_ij[edge] = sum(flow[(k, edge)] for k in pmu_nodes)

  X = model.addVar(vtype=GRB.BINARY, name="X")

  model.addConstr((F_ij[edge] for edge in edges) >= (1 - M * (1 - X[edge] for edge in edges)), name="X_edge_equal_1")
  model.addConstr((F_ij[edge] for edge in edges) <= (M * (1 - X[edge] for edge in edges)), name="X_edge_equal_equal_0")

  # note that pmu_nodes is a list containing nodes 2 to n, and flow[(k, edge)] is a data structure storing flow from node k passing through an edge (i, j) in the graph, edges is a list containing each edge (i, j)

  My code has been throwing an error on the first constraint that should ensure X_ij be 1 when F_ij is greater than or equal to 1:

  model.addConstr((F_ij[edge] for edge in edges) >= (1 - M * (1 - X[edge] for edge in edges)), name="X_edge_equal_1")

  TypeError: unsupported operand type(s) for *: 'int' and 'generator'

  Is there anythying I am doing wrong?  Thank you.

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  Jaromił Najman

  • Gurobi Staff

  2023年05月24日 07:44

  You are trying to access \(\texttt{X[edge]}\) but you define only a single variable \(\texttt{X}\).

  F_ij = {}
  for edge in edges:
      F_ij[edge] = sum(flow[(k, edge)] for k in pmu_nodes)
      X[edge] = model.addVar(vtype=GRB.BINARY, name="X") # here the name of X should be made unique

   

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