naa a22 4500 510809073 CHVBK 20180411083433.0 cr unu---uuuuu 180411e20131201xx s 000 0 eng 10.1007/s12532-013-0057-4 doi (NATIONALLICENCE)springer-10.1007/s12532-013-0057-4 On the safety of Gomory cut generators [Elektronische Daten] [Gérard Cornuéjols, François Margot, Giacomo Nannicini] 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 that work in finite precision: Additional steps are performed to avoid the generation of invalid cuts due to the limited numerical precision of the computations. 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 generates many more cuts. Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society, 2013 Cornuéjols Gérard Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA aut Margot François Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA aut Nannicini Giacomo Engineering Systems and Design, Singapore University of Technology and Design, Singapore, Singapore aut Mathematical Programming Computation Springer Berlin Heidelberg 5/4(2013-12-01), 345-395 1867-2949 5:4<345 2013 5 12532 https://doi.org/10.1007/s12532-013-0057-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12532-013-0057-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Cornuéjols Gérard Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA aut NATIONALLICENCE 700 1- Margot François Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA aut NATIONALLICENCE 700 1- Nannicini Giacomo Engineering Systems and Design, Singapore University of Technology and Design, Singapore, Singapore aut NATIONALLICENCE 773 0- Mathematical Programming Computation Springer Berlin Heidelberg 5/4(2013-12-01), 345-395 1867-2949 5:4<345 2013 5 12532 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer