Sequential pairing of mixed integer inequalities

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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. © 2007.

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Guan, Y., Ahmed, S., & Nemhauser, G. L. (2007). Sequential pairing of mixed integer inequalities. Discrete Optimization, 4(1), 21–39. https://doi.org/10.1016/j.disopt.2006.10.003

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