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.

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Metadaten
Author:Timo Berthold, Ambros M. Gleixner
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

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