New answers tagged integer-programming
5
votes
Is there a better way of defining a constraint on positive integer variables such that no two variables are the same and are uniquely assigned a value
This is called an alldifferent constraint and is supported directly by constraint programming solvers. @Kuifje gave a traditional linear formulation (+1) that uses binary variables, but it is worth ...
- 22.7k
10
votes
Accepted
Is there a better way of defining a constraint on positive integer variables such that no two variables are the same and are uniquely assigned a value
Introduce binary variables $y_{ij}\in \{0,1\}$ that take value $1$ if and only if $x_i$ is assigned to value $j\in \{1,...,N\}$, and use the following constraints:
\begin{align}
x_i &= \sum_{j=1}^...
- 10.4k
3
votes
Accepted
How to pose the constraint for binary variable to indicate if quantity is zero or greater than zero
$$b_i \le p^i-p^{i+1} \le (N-1)b_i$$
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4
votes
Accepted
Modeling a special case of conservation of flow
Introduce binary variables $x_a,\dots,x_e,$ with each variable taking value 1 if the corresponding arc is used. To limit yourself to a single input, add the constraint $$x_a + x_b = 1$$ (or $x_a + x_b ...
- 31.1k
3
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Integer programming books
There are at least three somewhat distinct aspects to integer programming: theory (e.g., why LP solutions occur at vertices of polytopes); algorithms (branch-and-bound, decomposition, cutting plane ...
- 31.1k
3
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What is the meaning of this math formulation?
The set of equations are used to represent the conservation of flow at every node $j$ in a network. Here, $\Delta^{-}(j)$ represents the set of nodes coming into node $j$ and $\Delta^{+}(j)$ ...
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