How to model this "nested constraint" in gurobipy?

回答済み

Rihot Gusron

2022年12月03日 09:32 編集済み

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I have this formulation that I called it "nested constraint" (don't know if its right). What is the best way to formulate this in python gurobipy.

 

My current approach is that decompose these with three separate constraint below,

m.addConstrs(((gp.quicksum(y[i,j,l] for i in vertex if i!=j)) - (gp.quicksum(y[j,i,l] for i in vertex if i!=j)) == demand[l]
            for j in vertex for l in customer if j==l))
m.addConstrs(((gp.quicksum(y[i,j,l] for i in vertex if i!=j)) - (gp.quicksum(y[j,i,l] for i in vertex if i!=j)) == 0
            for j in customer for l in customer if j!=l))
m.addConstrs(((gp.quicksum(y[i,j,l] for i in vertex if i!=j)) - (gp.quicksum(y[j,i,l] for i in vertex if i!=j)) == -demand[l]
            for j in vertex for l in customer if j==0))

関連

• Python
• Modeling

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• 

  Jaromił Najman

  • Gurobi Staff

  2022年12月05日 09:26 編集済み

  Hi Rihot,

  The probably easiest way is to use auxiliary variables \(z_{j,l}\) and auxiliary equality constraints.

  \[\begin{align*}
  \sum_{i\in V}y_{ij}^l - \sum_{i \in V} y_{ji}^l &= z_{j,l} \quad \forall j, l \in V'\\
  z_{j,l} &= q_l \quad \forall j,l \in V' \text{ with } j = l\\
  z_{j,l} &= 0 \quad \forall j,l \in V' \text{ with } j \neq l\\
  z_{j,l} &= -q_l \quad \forall j, l \in V' \text{ with } j = 0
  \end{align*}\]

  A pseudo-code might look something like

  m.addConstrs(qp.quicksum(y[i,j,l] - y[j,i,l] for i in I) == z[j,l] for j in V, for l in V)
  for j in V:
    for l in V:
      if j == 0:
        m.addConstr(z[j,l] == -q[l])    
      else if j == l:
        m.addConstr(z[j,l] == q[l])
      else:
        m.addConstr(z[j,l] == 0)

  Best regards, 
  Jaromił

  0

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