## Conflict-Free Learning for Mixed Integer Programming

Please always quote using this URN: urn:nbn:de:0297-zib-75338

- Conflict learning plays an important role in solving mixed integer programs (MIPs) and is implemented in most major MIP solvers. A major step for MIP conflict learning is to aggregate the LP relaxation of an infeasible subproblem to a single globally valid constraint, the dual proof, that proves infeasibility within the local bounds. Among others, one way of learning is to add these constraints to the problem formulation for the remainder of the search. We suggest to not restrict this procedure to infeasible subproblems, but to also use global proof constraints from subproblems that are not (yet) infeasible, but can be expected to be pruned soon. As a special case, we also consider learning from integer feasible LP solutions. First experiments of this conflict-free learning strategy show promising results on the MIPLIB2017 benchmark set.

Author: | Jakob WitzigORCiD, Timo Berthold |
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Document Type: | ZIB-Report |

Tag: | conflict analysis; dual proof analysis; mixed integer programming; no-good learning; solution learning |

MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C10 Integer programming |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C11 Mixed integer programming | |

Date of first Publication: | 2019/12/02 |

Series (Serial Number): | ZIB-Report (19-59) |

ISSN: | 1438-0064 |