How can I formulate a constraint that reflects that a variable can equal only -1 or 1?
回答済みI am trying to create an ILP formulation that represents newman's idea.
I formulated the objective function, but I would like to require the variables to be -1 or 1.
How can I do that?
Thanks
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Gurobi Staff
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You can use a normal binary variable \(b \in \{0,1\}\) and define a new integer variable \(b_{-}\) as \(b_{-} = 2\cdot b -1\). \(b_-\) can only take values \(\{-1,1\}\).
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Thank you!
Another question if it is ok:How can I make a new variable y_ij that is 1 iff x_i == x_j ==1?
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You can use Gurobi's addGenConstrAnd method for this.
# construct yij = 1 <=> xi=1 and xj=1 constraint
model.addGenConstrAnd(yij, [xi,xj],name="andconstr)1 -
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Hi, thanks for the answer, it really helped!
if I want in addition a variable z_ij which is 0 iff x_i == x_j ==0,
can I write it this way? (of course xi,xj,zij are binary variables)
# construct zij = 0 <=> xi=0 and xj=0 constraint
model.addGenConstrAnd(zij, [1-xi,1-xj],name="andconstr")0 -
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can I write it this way? (of course xi,xj,zij are binary variables)
# construct zij = 0 <=> xi=0 and xj=0 constraint
model.addGenConstrAnd(zij, [1-xi,1-xj],name="andconstr")No, it is not directly possible, because the addGenConstrAnd method accepts only single variable objects, i.e., it does not accept LinExpr objects such as \(1-x_i\).
You have to introduce 2 auxiliary binary variables \(y_i,y_j\) with \(y_i=1-x_i, y_j=1-x_j\) and then you can go with
# construct zij = 0 <=> xi=0 and xj=0 constraint
model.addConstr(yi == 1-xi)
model.addConstr(yj == 1-xj)
model.addGenConstrAnd(zij, [yi, yj],name="andconstr")1 -
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