Three enhancements for optimization-based bound tightening

Ambros M. Gleixner, Timo Berthold, Benjamin Müller, Stefan Weltge

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

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 17–19 % on average. Most importantly, more instances can be solved when using OBBT.

Original languageEnglish
Pages (from-to)731-757
Number of pages27
JournalJournal of Global Optimization
Volume67
Issue number4
DOIs
StatePublished - 1 Apr 2017
Externally publishedYes

Keywords

  • Bound tightening
  • MINLP
  • OBBT
  • Optimality-based bound tightening
  • Optimization-based bound tightening
  • Propagation

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