Lexicography and degeneracy: can a pure cutting plane algorithm work?

• 成果类型: Article
• 署名作者: Zanette, Arrigo; Fischetti, Matteo; Balas, Egon
• 署名单位: University of Padua; Carnegie Mellon University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0335-0
• 发表日期: 2011
• 页码: 153-176
• 关键词: gomory cuts

摘要

We discuss an implementation of the lexicographic version of Gomory's fractional cutting plane method for ILP problems and of two heuristics mimicking the latter. In computational testing on a battery of MIPLIB problems we compare the performance of these variants with that of the standard Gomory algorithm, both in the single-cut and in the multi-cut (rounds of cuts) version, and show that they provide a radical improvement over the standard procedure. In particular, we report the exact solution of ILP instances from MIPLIB such as stein15, stein27, and bm23, for which the standard Gomory cutting plane algorithm is not able to close more than a tiny fraction of the integrality gap. We also offer an explanation for this surprising phenomenon.