## 摘要

Polynomial discrete programming problems are commonly faced but hard to solve. Treating the nonconvex cross-product terms is the key. State-of-the-art methods usually convert such a problem into a 0-1 mixedinteger linear programming problem and then adopt the branch-and-bound scheme to find an optimal solution. Much effort has been spent on reducing the required numbers of variables and linear constraints as well as on avoiding unbalanced branch-and-bound trees. This study presents a set of equations that linearize the discrete cross-product terms in an extremely effective manner. It is shown that embedding the proposed "equations for linearizing discrete products" into those state-of-the-art methods in the literature not only significantly reduces the required number of linear constraints from O(h^{3}n^{3}) to O(hn) for a cubic polynomial discrete program with n variables in h possible values but also tighten these methods with much more balanced branch-and-bound trees. Numerical experiments confirm a two-order (10^{2}-times) reduction in computational time for some randomly generated cubic polynomial discrete programming problems. There is a Video Overview associated with this article, available as supplemental material.

原文 | English |
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頁（從 - 到） | 108-122 |

頁數 | 15 |

期刊 | INFORMS Journal on Computing |

卷 | 29 |

發行號 | 1 |

DOIs | |

出版狀態 | Published - 1 十二月 2017 |