Orbital Shrinking

  • Matteo Fischetti
  • Leo Liberti
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7422)


Symmetry plays an important role in optimization. The usual approach to cope with symmetry in discrete optimization is to try to eliminate it by introducing artificial symmetry-breaking conditions into the problem, and/or by using an ad-hoc search strategy. In this paper we argue that symmetry is instead a beneficial feature that we should preserve and exploit as much as possible, breaking it only as a last resort. To this end, we outline a new approach, that we call orbital shrinking, where additional integer variables expressing variable sums within each symmetry orbit are introduces and used to “encapsulate” model symmetry. This leads to a discrete relaxation of the original problem, whose solution yields a bound on its optimal value. Encouraging preliminary computational experiments on the tightness and solution speed of this relaxation are presented.


Mathematical programming discrete optimization algebra symmetry relaxation MILP convex MINLP 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Matteo Fischetti
    • 1
  • Leo Liberti
    • 2
  1. 1.DEIUniversità di PadovaItaly
  2. 2.LIX, École PolytechniquePalaiseauFrance

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