Monday, 15:15 - 15:40 h, Room: H 2032

 

Giacomo Nannicini
On the safety of Gomory cut generators

Coauthors: Gérard Cornuéjols, Francois Margot

 

Abstract:
Gomory mixed-integer cuts are one of the key components
in branch-and-cut solvers for mixed-integer linear programs. The
textbook formula for generating these cuts is not used directly in
open-source and commercial software due to the limited numerical
precision of the computations: Additional steps are performed to avoid
the generation of invalid cuts. This paper studies the impact of some
of these steps on the safety of Gomory mixed-integer cut
generators. As the generation of invalid cuts is a relatively rare
event, the experimental design for this study is particularly
important. We propose an experimental setup that allows statistically
significant comparisons of generators. We also propose a parameter
optimization algorithm and use it to find a Gomory mixed-integer cut generator that is as safe as a benchmark cut generator from a commercial solver even though it rejects much fewer cuts.

 

Talk 1 of the invited session Mon.3.H 2032
"Trends in mixed integer programming I" [...]
Cluster 11
"Integer & mixed-integer programming" [...]

 

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