## Undercover – a primal heuristic for MINLP based on sub-MIPs generated by set covering

Please always quote using this URN: urn:nbn:de:0297-zib-11632

- We present Undercover, a primal heuristic for mixed-integer nonlinear programming (MINLP). The heuristic constructs a mixed-integer linear subproblem (sub-MIP) of a given MINLP by fixing a subset of the variables. We solve a set covering problem to identify a minimal set of variables which need to be fixed in order to linearise each constraint. Subsequently, these variables are fixed to approximate values, e.g. obtained from a linear outer approximation. The resulting sub-MIP is solved by a mixed-integer linear programming solver. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. Although general in nature, the heuristic seems most promising for mixed-integer quadratically constrained programmes (MIQCPs). We present computational results on a general test set of MIQCPs selected from the MINLPLib.

Author: | Timo Berthold, Ambros M. Gleixner |
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Document Type: | ZIB-Report |

Tag: | MINLP; MIQCP ; Mengenüberdeckung; Nachbarschaftssuche ; Primalheuristik MIQCP ; large neighborhood search ; mixed-integer nonlinear programming ; primal heuristic ; set covering |

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

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming | |

90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C59 Approximation methods and heuristics | |

CCS-Classification: | G. Mathematics of Computing / G.1 NUMERICAL ANALYSIS / G.1.6 Optimization |

Date of first Publication: | 2009/12/16 |

Series (Serial Number): | ZIB-Report (09-40) |

ISSN: | 1438-0064 |

Published in: | App. in: Proceedings of the EWMINLP. Pierre Bonami et al. eds. 2010, pp. 103-112 |