Symmetry groups are certainly an issue in integer programming. [Orbital branching][1] is one way of dealing with it. [Core][2] [points][3] are another relevant concept.


  [1]: http://dx.doi.org/10.1007/s10107-009-0273-x
  [2]: http://arxiv.org/abs/1202.0435
  [3]: http://arxiv.org/abs/1401.3638