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Orbital shrinking: a new tool for hybrid MIP/CP methods. (English) Zbl 1382.90066
Gomes, Carla (ed.) et al., Integration of AI and OR techniques in constraint programming for combinatorial optimization problems. 10th international conference, CPAIOR 2013, Yorktown Heights, NY, USA, May 18–22, 2013. Proceedings. Berlin: Springer (ISBN 978-3-642-38170-6/pbk). Lecture Notes in Computer Science 7874, 204-215 (2013).
Summary: 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.
For the entire collection see [Zbl 1263.68017].

MSC:
90C11 Mixed integer programming
68T20 Problem solving in the context of artificial intelligence (heuristics, search strategies, etc.)
90C27 Combinatorial optimization
Software:
CPLEX; Gecode
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