Totally-Ordered多重背包集的多重覆盖不等式：理论与计算
Multi-cover Inequalities for Totally-Ordered Multiple Knapsack Sets: Theory and Computation
摘要：
我们提出了一种方法来产生切割平面从多个覆盖的背包约束。如果不同的背包不等式中的权构成一个全序集，则覆盖可以来自不同的背包不等式。因此，我们引入并研究了全序多重背包集的结构。对于它的凸包，我们得到的有效的多重覆盖不等式具有许多有趣的性质。首先，推广了著名的（1，k）-构型不等式.其次，它们不是总量削减。第三，它们不能从由背包约束及其所有最小覆盖不等式组成的不等式系统中生成为秩1 Chvatal-Gomory割。给出了不等式是全序背包集的凸包的刻面的条件，以及这些不等式充分刻画全序背包集的凸包的条件.我们给出了一个整数规划来解决分离，并提供数值实验，展示这些新的不等式的强度。
英文摘要：
We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and study the structure of a totally-ordered multiple knapsack set. The valid multi-cover inequalities we derive for its convex hull have a number of interesting properties. First, they generalize the well-known (1, k)-configuration inequalities. Second, they are not aggregation cuts. Third, they cannot be generated as a rank-1 Chvatal-Gomory cut from the inequality system consisting of the knapsack constraints and all their minimal cover inequalities. We also provide conditions under which the inequalities are facets for the convex hull of the totally-ordered knapsack set, as well as conditions for those inequalities to fully characterize its convex hull. We give an integer program to solve the separation and provide numerical experiments that showcase the strength of these new inequalities.
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