Three Enhancements for Optimization-Based Bound Tightening

Please always quote using this URN: urn:nbn:de:0297-zib-57803
accepted for publication on 2016-05-28
  • Optimization-based bound tightening (OBBT) is one of the most effective procedures to reduce variable domains of nonconvex mixed-integer nonlinear programs (MINLPs). At the same time it is one of the most expensive bound tightening procedures, since it solves auxiliary linear programs (LPs)—up to twice the number of variables many. The main goal of this paper is to discuss algorithmic techniques for an efficient implementation of OBBT. Most state-of-the-art MINLP solvers apply some restricted version of OBBT and it seems to be common belief that OBBT is beneficial if only one is able to keep its computational cost under control. To this end, we introduce three techniques to increase the efficiency of OBBT: filtering strategies to reduce the number of solved LPs, ordering heuristics to exploit simplex warm starts, and the generation of Lagrangian variable bounds (LVBs). The propagation of LVBs during tree search is a fast approximation to OBBT without the need to solve auxiliary LPs. We conduct extensive computational experiments on MINLPLib2. Our results indicate that OBBT is most beneficial on hard instances, for which we observe a speedup of 17% to 19% on average. Most importantly, more instances can be solved when using OBBT.

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Metadaten
Author:Ambros M. Gleixner, Timo Berthold, Benjamin Müller, Stefan Weltge
Document Type:ZIB-Report
Tag:MINLP; OBBT; bound tightening; optimality-based bound tightening; optimization-based bound tightening; propagation
MSC-Classification:90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING
CCS-Classification:G. Mathematics of Computing
Date of first Publication:2016/03/08
Series (Serial Number):ZIB-Report (15-16)
ISSN:1438-0064
Published in:accepted for publication in Journal of Global Optimization
DOI:http://dx.doi.org/10.1007/s10898-016-0450-4

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