How to formulate multiple conditional logical (AND and OR) constraints

回答済み

Babooshka Shavazipour

2023年09月15日 10:05

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I am wondering what would be the efficient way of formulating the following constraint in (Python) Gurobi:

# The big-M
M = 10**9
# Constraints
for i in range(n):
    for k inrange(n):
        if (i!=k) and (x[i]==1) and (x[k]==1):
            # OR constraints already linearized via Big-M
            px[i] - px[k] +M*eta <= M-l[i]
            px[k] - px[i] -M*eta <= -l[k]

x_i  (i=1,...,n), eta, and gamma are binary variables and px_i (i=1,...,n) are integer variables. 

関連

• General Constraints

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• 

  Maliheh Aramon

  • Gurobi Staff

  2023年09月16日 00:43

  Hi, 

  You can define an auxiliary variable \(z_{ik} = x_i \land x_k\, ~~ \forall i, k\). The logical And constraints can be implemented using the Model.addGenConstrAnd() method in Gurobi Python API. 

  You can then use the Model.addGenConstrIndicator() method to implement the following two constraints for all \(i\) and \(k\) indices where \(i \neq k\):

  • \(\mbox{if}~ z_{ik} = 1 \rightarrow px_i - px_k + M \eta \leq M - l_i\)
  • \(\mbox{if}~ z_{ik} = 1 \rightarrow px_i - px_k - M \eta \leq - l_k\)

  Best regards,

  Maliheh

  0

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