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Generalized coefficient strengthening cuts for mixed integer programming

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Abstract

Cutting plane methods are an important component in solving the mixed integer programming (MIP). By carefully studying the coefficient strengthening method, which is originally a presolving method, we are able to generalize this method to generate a family of valid inequalities called generalized coefficient strengthening (GCS) inequalities. The invariant property of the GCS inequalities is established under bound substitutions. Furthermore, we develop a separation algorithm for finding the violated GCS inequalities for a general mixed integer set. The separation algorithm is proved to have the polynomial time complexity. Extensive numerical experiments are made on standard MIP test sets, which demonstrate the usefulness of the resulting GCS separator.

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Notes

  1. Shifted geometric mean, 10 s for average time and 100 for average nodes [19].

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Authors and Affiliations

  1. Institute of Computational Mathematics and Scientific/Engineering Computing, State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei-Kun Chen, Liang Chen, Mu-Ming Yang & Yu-Hong Dai

Authors
  1. Wei-Kun Chen
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  2. Liang Chen
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  3. Mu-Ming Yang
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  4. Yu-Hong Dai
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Corresponding author

Correspondence to Mu-Ming Yang.

Additional information

This work was supported by the Chinese Natural Science Foundation (Nos. 11631013, 71331001, 11331012) and the National 973 Program of China (No. 2015CB856002).

Appendix

Appendix

See Table 3.

Table 3 Detail results of nodes and time performance
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Chen, WK., Chen, L., Yang, MM. et al. Generalized coefficient strengthening cuts for mixed integer programming. J Glob Optim 70, 289–306 (2018). https://doi.org/10.1007/s10898-017-0562-5

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