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

  • 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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Author:Timo Berthold, Ambros M. Gleixner
Editor:Pierre Bonami, Leo Liberti, Andrew J. Miller, Annick Sartenaer
Document Type:In Proceedings
Parent Title (English):Proceedings of the European Workshop on Mixed Integer Nonlinear Programming, April 12-16, 2010, Marseilles, France
First Page:103
Last Page:112
Year of first publication:2010

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