Nonlinear Pseudo-Boolean Optimization: Relaxation or Propagation?

  • Authors:
  • Timo Berthold;Stefan Heinz;Marc E. Pfetsch

  • Affiliations:
  • Zuse Institute Berlin, Berlin, Germany 14195;Zuse Institute Berlin, Berlin, Germany 14195;Institut für Mathematische Optimierung, Technische Universität Braunschweig, Braunschweig, Germany 38106

  • Venue:
  • SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
  • Year:
  • 2009

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Abstract

Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver.