期刊
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
卷 134, 期 2, 页码 353-370出版社
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1007/s10957-007-9263-4
关键词
Bilevel linear programming; Gomory cuts; linear mixed 0-1 integer programming; branch-and-cut algorithms
Linear mixed 0-1 integer programming problems may be reformulated as equivalent continuous bilevel linear programming (BLP) problems. We exploit these equivalences to transpose the concept of mixed 0-1 Gomory cuts to BLP. The first phase of our new algorithm generates Gomory-like cuts. The second phase consists of a branch-and-bound procedure to ensure finite termination with a global optimal solution. Different features of the algorithm, in particular, the cut selection and branching criteria are studied in details. We propose also a set of algorithmic tests and procedures to improve the method. Finally, we illustrate the performance through numerical experiments. Our algorithm outperforms pure branch-and-bound when tested on a series of randomly generated problems.
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