swMATH ID: 31749
Software Authors: Fukasawa, Ricardo; Poirrier, Laurent; Xavier, Álinson S.
Description: The (not so) trivial lifting in two dimensions. When generating cutting-planes for mixed-integer programs from multiple rows of the simplex tableau, the usual approach has been to relax the integrality of the non-basic variables, compute an intersection cut, then strengthen the cut coefficients corresponding to integral non-basic variables using the so-called trivial lifting procedure. Although of polynomial-time complexity in theory, this lifting procedure can be computationally costly in practice. For the case of two-row relaxations, we present a practical algorithm that computes trivial lifting coefficients in constant time, for arbitrary maximal lattice-free sets. Computational experiments confirm that the algorithm works well in practice.
Homepage: https://rd.springer.com/article/10.1007%2Fs12532-018-0146-5
Source Code:  https://zenodo.org/record/1342771#.Xju_5cZKjmI
Keywords: integer programming; lifting; cutting planes
Related Software: MIPLIB; onerow; CPLEX; infinite group relaxation; MIPLIB2003; gmp
Cited in: 5 Documents

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