Sequential-Merge Facets for Two-Dimensional Group Problems

Authors:
Santanu S. Dey;Jean-Philippe P. Richard
Affiliations:
School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47906-2023,;School of Industrial Engineering, Purdue University, 315 N. Grant Street, West Lafayette, IN 47906-2023,
Venue:
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Year:
2007

Citing 4
Cited 1

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Abstract

In this paper, we show how to generate strong cuts for unstructured mixed integer programs through the study of high-dimensional group problems. We present a new operation that generates facet-defining inequalities for two-dimensional group problems by combining two facet-defining inequalities of one-dimensional group problems. Because the procedure allows the use of a large variety of one-dimensional constituent inequalities, it yields large families of new cutting planes for MIPs that we call sequential-merge inequalities. We show that sequential-merge inequalities can be used to generate inequalities whose continuous variable coefficients are stronger than those of one-dimensional cuts and can be used to derive the three-gradient facet-defining inequality introduced by Dey and Richard [4].