Quadratic Reformulation of Nonlinear Pseudo-Boolean Functions via the Constraint Composite Graph

  • Ka Wa YipEmail author
  • Hong XuEmail author
  • Sven Koenig
  • T. K. Satish Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11494)


Nonlinear pseudo-Boolean optimization (nonlinear PBO) is the minimization problem on nonlinear pseudo-Boolean functions (nonlinear PBFs). One promising approach to nonlinear PBO is to first use a quadratization algorithm to reduce the PBF to a quadratic PBF by introducing intelligently chosen auxiliary variables and then solve it using a quadratic PBO solver. In this paper, we develop a new quadratization algorithm based on the idea of the constraint composite graph (CCG). We demonstrate its theoretical advantages over state-of-the-art quadratization algorithms. We experimentally demonstrate that our CCG-based quadratization algorithm outperforms the state-of-the-art algorithms in terms of both effectiveness and efficiency on randomly generated instances and a novel reformulation of the uncapacitated facility location problem.


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Authors and Affiliations

  1. 1.University of Southern CaliforniaLos AngelesUSA

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