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Valid inequalities for a single constrained 0-1 MIP set intersected with a conflict graph

机译：与冲突图相交的单个约束0-1 MIP集的有效不等式

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摘要

In this paper a mixed integer set resulting from the intersection of a single constrained mixed 0-1 set with the vertex packing set is investigated. This set arises as a subproblem of more general mixed integer problems such as inventory routing and facility location problems. Families of strong valid inequalities that take into account the structure of the simple mixed integer set and that of the vertex packing set simultaneously are introduced. In particular, the well-known mixed integer rounding inequality is generalized to the case where incompatibilities between binary variables are present. Exact and heuristic algorithms are designed to solve the separation problems associated to the proposed valid inequalities. Preliminary computational experiments show that these inequalities can be useful to reduce the integrality gaps and to solve integer programming problems. (C) 2016 Elsevier B.V. All rights reserved.
机译：本文研究了一个混合整数集，该集合是由单个约束混合0-1集与顶点压缩集的交集得到的。该集合是更常见的混合整数问题（例如库存路由和设施位置问题）的子问题。介绍了同时考虑简单混合整数集和顶点填充集结构的强有效不等式的族。特别地，众所周知的混合整数舍入不等式被推广到二进制变量之间存在不兼容的情况。设计精确和启发式算法来解决与建议的有效不等式相关的分离问题。初步的计算实验表明，这些不等式可用于减少积分差距并解决整数规划问题。 （C）2016 Elsevier B.V.保留所有权利。

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