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BDDs in a Branch and Cut Framework

  • Bernd Becker
  • Markus Behle
  • Friedrich Eisenbrand
  • Ralf Wimmer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3503)

Abstract

Branch & Cut is today’s state-of-the-art method to solve 0/1-integer linear programs. Important for the success of this method is the generation of strong valid inequalities, which tighten the linear programming relaxation of 0/1-IPs and thus allow for early pruning of parts of the search tree.

In this paper we present a novel approach to generate valid inequalities for 0/1-IPs which is based on Binary Decision Diagrams (BDDs). BDDs are a datastructure which represents 0/1-vectors as paths of a certain acyclic graph. They have been successfully applied in computational logic, hardware verification and synthesis.

We implemented our BDD cutting plane generator in a branch-and-cut framework and tested it on several instances of the MAX-ONES problem and randomly generated 0/1-IPs. Our computational results show that we have developed competitive code for these problems, on which state-of-the-art MIP-solvers fall short.

Keywords

Variable Order Longe Path Valid Inequality Separation Problem Linear Programming Relaxation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Bernd Becker
    • 1
  • Markus Behle
    • 2
  • Friedrich Eisenbrand
    • 2
  • Ralf Wimmer
    • 1
  1. 1.Albert-Ludwigs-UniversitätFreiburg im BreisgauGermany
  2. 2.Max-Planck-Institut für InformatikSaarbrückenGermany

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