Sequence-independent lifting is a procedure for strengthening valid inequalities of an integer program. We generalize the sequence-independent lifting method of Gu, Nemhauser, and Savelsbergh (GNS lifting) for cover inequalities and correct an error in their proposed generalization. We obtain a new sequence-independent lifting technique -- piecewise-constant (PC) lifting -- with a number of interesting properties. We derive a broad set of sufficient conditions under which PC lifting is facet defining. To our knowledge, this is the first characterization of facet-defining sequence-independent liftings that are efficiently computable from the underlying cover. Finally, we demonstrate via experiments that PC lifting can be a useful alternative to GNS lifting. We test our new lifting techniques atop a number of novel cover cut generation routines, which prove to be effective in experiments with CPLEX.

翻译：序列无关提升是一种加强整数规划有效不等式的方法。我们推广了Gu、Nemhauser和Savelsbergh提出的覆盖不等式序列无关提升方法（GNS提升），并纠正了其原始推广中的一个错误。我们获得了一种具有多项有趣性质的新序列无关提升技术——分段常数提升。我们推导出一组广泛的充分条件，在此条件下分段常数提升能够定义面。据我们所知，这是首个从底层覆盖中高效计算且可定义面的序列无关提升的特征描述。最后，我们通过实验证明，分段常数提升可作为GNS提升的有效替代方案。我们将新提升技术应用于多个新型覆盖割生成程序，这些程序在CPLEX实验中表现出有效性。