Orbital shrinking is a newly developed technique in the MIP community to deal with symmetry issues, which is based on aggregation rather than on symmetry breaking. In a recent work, a hybrid MIP/CP scheme based on orbital shrinking was developed for the multi-activity shift scheduling problem, showing significant improvements over previous pure MIP approaches. In the present paper we show that the scheme above can be extended to a general framework for solving arbitrary symmetric MIP instances. This framework naturally provides a new way for devising hybrid MIP/CP decompositions. Finally, we specialize the above framework to the multiple knapsack problem. Computational results show that the resulting method can be orders of magnitude faster than pure MIP approaches on hard symmetric instances.


Knapsack Problem Master Problem Steiner Triple System Multiple Knapsack Problem Symmetry Breaking Constraint 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Domenico Salvagnin
    • 1
  1. 1.DEIUniversity of PadovaItaly

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