Questions tagged [integer-programming]

For questions about mathematical optimization problems involving binary or general integer variables.

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18
votes
1answer
263 views

Combinatorial Optimization: Metaheuristics, CP, IP — “versus” or “and”?

"Recently" someone asked on Twitter whether "people still use genetic algorithms for integer programs". The "majority answer", i.e., 1 out of 1, was: "Yes" . So, my follow-up question is: With all ...
17
votes
5answers
3k views

When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs

Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
13
votes
1answer
202 views

Symmetry-breaking ILP constraints for square binary matrix

Setup I have a binary $N \times N$ matrix. The objective is to minimize the number of ones in the matrix, subject to various constraints. This leads to symmetries by rotating 90 degrees and/or ...
22
votes
3answers
3k views

What is the difference between integer programming and constraint programming?

At first glance both approaches appear to be very similar. What are the major differences between integer programming and constraint programming?
9
votes
1answer
213 views

How to get bounds on ILP optimal solution quality

Often, ILP formulations are just too complicated to solve optimally in reasonable time. In those cases, you can still run a solver for some fixed time and simply take the best solution that the solver ...
11
votes
2answers
867 views

In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?

Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where $a_i$ and $b$ are constants and $x_i$ are decision variables. Suppose also that we want the constraint to hold if $y=1$ (...
25
votes
3answers
5k views

In an integer program, how I can force a binary variable to equal 1 if some condition holds?

Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like If $x \gtreqless b$, then $y = 1$. How can we write this ...

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