Optimal Cutting Planes from the Group Relaxations

• 成果类型: Article
• 署名作者: Basu, Amitabh; Conforti, Michele; Di Summa, Marco; Zambelli, Giacomo
• 署名单位: Johns Hopkins University; University of Padua; University of London; London School Economics & Political Science
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0964
• 发表日期: 2019
• 页码: 1208-1220
• 关键词: dantzig cuts; integer

摘要

We study quantitative criteria for evaluating the strength of valid inequalities for Gomory and Johnson's finite and infinite group models, and we describe valid inequalities that are optimal for these criteria. We justify and focus on the criterion of maximizing the volume of the nonnegative orthant cut off by a valid inequality. For the finite group model of prime order, we show that the unique maximizer is an automorphism of the Gomory mixed-integer (GMI) cut for a possibly different finite group problem of the same order. We extend the notion of volume of a simplex to the infinite-dimensional case. This is used to show that in the infinite group model, the GMI cut maximizes the volume of the non-negative orthant cut off by an inequality.