Undercover: a primal MINLP heuristic exploring a largest sub-MIP

We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programs (MINLPs) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a smallest set of variables to fix, a so-called cover , such that each constrai...

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Bibliographic Details
Published in:Mathematical programming Vol. 144; no. 1-2; pp. 315 - 346
Main Authors: Berthold, Timo, Gleixner, Ambros M.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2014
Springer Nature B.V
Subjects:
Algorithms
Analysis
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Complement
Domain propagation
Full Length Paper
Heuristic
Integer programming
Linear programming
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematics
Mathematics and Statistics
Mathematics of Computing
Neighborhoods
Numerical Analysis
Optimization
Solvers
State of the art
Studies
Theoretical
Variables
90C20
Primal heuristic
Nonconvex optimization
90C30
Mixed-integer nonlinear programming
Large neighborhood search
90C11
90C26
90C59
Mixed-integer quadratically constrained programming
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:We present Undercover, a primal heuristic for nonconvex mixed-integer nonlinear programs (MINLPs) that explores a mixed-integer linear subproblem (sub-MIP) of a given MINLP. We solve a vertex covering problem to identify a smallest set of variables to fix, a so-called cover , such that each constraint is linearized. Subsequently, these variables are fixed to values obtained from a reference point, e.g., an optimal solution of a linear relaxation. Each feasible solution of the sub-MIP corresponds to a feasible solution of the original problem. We apply domain propagation to try to avoid infeasibilities, and conflict analysis to learn additional constraints from infeasibilities that are nonetheless encountered. We present computational results on a test set of mixed-integer quadratically constrained programs (MIQCPs) and MINLPs. It turns out that the majority of these instances allows for small covers. Although general in nature, we show that the heuristic is most successful on MIQCPs. It nicely complements existing root-node heuristics in different state-of-the-art solvers and helps to significantly improve the overall performance of the MINLP solver SCIP .
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-013-0635-2