Sequential pairing of mixed integer inequalities

Authors:
Yongpei Guan;Shabbir Ahmed;George L. Nemhauser
Affiliations:
School of Industrial Engineering, University of Oklahoma, 202 West Boyd, Norman, OK 73019, United States;School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332, United States;School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332, United States
Venue:
Discrete Optimization
Year:
2007

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Abstract

We investigate a scheme, called pairing, for generating new valid inequalities for mixed integer programs by taking pairwise combinations of existing valid inequalities. The pairing scheme essentially produces a split cut corresponding to a specific disjunction, and can also be derived through the mixed integer rounding procedure. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that lead to a manageable set of non-dominated inequalities. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results showing the efficiency of adding the new generated inequalities as cuts.