Questions tagged [symmetry]

For questions about invariance under transformations, in OR usually the transformation of a solution into other solutions of the same objective value.

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Excluding non-preferable solutions from a MILP

I have a model which delivers the following results (other combinations are also possible, all Xs have 50 as an upper bound): Case I $X1 = 50.0$ $X2 = 13.750$ $X3 = 50.0$ $X4 = 50.0$ Case II (obtained ...
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How can preferences be modelled in MILPs?

Suppose a MILP model includes the following constraint: $ \begin{gather*} B_{1} + B_{2} + B_{3} \le 100 \end{gather*} $, where $B_{1},B_{2},B_{3}$ are nonnegative reals. Suppose that $\begin{...
13
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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 ...
19
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How can I best handle symmetries in my MIP?

When dealing with mixed-integer-programs with many symmetric solutions it can take very long until the branch-and-bound-tree search is finished because symmetric optimal solutions cannot be pruned. ...