Create a constraints in C#
Do you have a method to implement a logic relationship between constraints in a same model?
For example: I would like to create a bound constraint a < x < b or x < b || x > a while a,b are constant numbers and x is a variable.
Thank you in advance!
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Hi Giang,
Can you clarify: are you looking for a way to model the logical condition that either \( x \geq a \) or \( x \leq b \)? This can be done if bounds on \( x \) are known. Let \( \ell \) and \( u \) be lower and upper bounds on \( x \), respectively (such that \( \ell < a \) and \( u > b \)). We can model this by introducing a binary variable \( z \), and adding the following constraints:
\( (\ell - a)z + a \leq x \leq u + (b-u)z \)
If \(z=0\), we have \( a \leq x \leq u \). The \( x \leq u \) part does not affect the problem, because \( u \) is known to be an upper bound on \( x \). Similarly, if \( z = 1 \), we have \( \ell \leq x \leq b \). Here, only the constraint \( x \leq b \) affects the problem.
In C#, you can use the GRBModel.AddGenConstrIndicator() method to do this more succinctly:
GRBVar z = model.AddVar(0.0, 1.0, 0.0, GRB.BINARY, "z");
model.AddGenConstrIndicator(z, 0, x >= a, "logicLB");
model.AddGenConstrIndicator(z, 1, x <= b, "logicUB");Does this help? Thanks!
Eli
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Hi Eli,
It really helps my problem. Can I ask how to create a object function to minimize like this: |x - a| + |y - b| + |z-c| ? x, y,z are variables, and a,b,c are constants. I dont know how to describe a abs() in C#. Thank you in advance!
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