使用值析取的中间整数规划表示
Intermediate integer programming representations using value disjunctions
摘要：
我们介绍了一种通用的技术来创建一个扩展的配方的混合整数规划。我们将整数变量分成块，每个块生成一个有限集的向量值。通过为每个生成的值创建一个新的二进制变量来构造扩展公式。初步实验表明，扩展的配方可以有一个更紧凑的完整的描述比原来的配方。我们证明，使用这种重构技术，刻面描述分解成一个“连接多面体”每块和“聚合多面体”。每个多面体都可以单独分析。对于块中系数相同的情况，我们给出了连接多面体的完整描述和多项式时间分离算法。应用于具有固定数目的不同系数的背包，该定理在具有多项式数目的变量的扩展空间中提供了完整的描述。
英文摘要：
We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description than the original formulation. We prove that, using this reformulation technique, the facet description decomposes into one ``linking polyhedron'' per block and the ``aggregated polyhedron''. Each of these polyhedra can be analyzed separately. For the case of identical coefficients in a block, we provide a complete description of the linking polyhedron and a polynomial-time separation algorithm. Applied to the knapsack with a fixed number of distinct coefficients, this theorem provides a complete description in an extended space with a polynomial number of variables.
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