Map integer to binary
AnsweredI am want to model a situation that:
N is an integer variable, and n0,n1,n2 are binary variables.
I wish that when N % 3 == 0, n0 = 1 and others =0; when N % 3 == 1, n1 = 1 and others =0; when N % 3 == 2, n2 = 1 and others =0;
Want to ask how to achieve such constraints in Gurobi. Thank you
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Hi,
It is possible with two auxiliary variables and a couple of equality constraints. First, we have to model the modulo operation
\[\begin{align}
N &= n + 3 k\\
N &\in \mathbb{Z}_{\geq 0}, n \in \{0,1,2\}, k \in \mathbb{Z}_{\geq 0}
\end{align}\]Integer variable \(n\) gives us the result of the modulo operation. Next we need to model the \(\texttt{if}\)-relationships.
\[\begin{align}
2 n_0 &+ 3 n_1 + 4 n_2 = n+2 \\
&n_0, n_1, n_2 \in \{0,1\}
\end{align}\]The above equality constraint states that, when \(n=0\), then only \(n_0=1\), if \(n=1\), then only \(n_1=1\), and if \(n=2\), then only \(n_2=1\).
Please note that the above is just one of many possible formulations and is not guaranteed to be the best one.
Best regards,
Jaromił0 -
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Thank you Jaromił! This solution really inspires me!
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