K. Yip, H. Xu, S. Koenig and S. Kumar. Quadratic Reformulation of Nonlinear Pseudo-Boolean Functions via the Constraint Composite Graph. In International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR), pages 643-660, 2019.

Abstract: 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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