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Computational study of separation algorithms for clique inequalities

  • Francesca Marzi
  • Fabrizio Rossi
  • Stefano SmriglioEmail author
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Abstract

Clique inequalities appear in linear descriptions of many combinatorial optimisation problems. In general, they form an exponential family and, in addition, the associated separation problem is strongly NP-hard, being equivalent to a maximum weight clique problem. Therefore, most of the known (both exact and heuristic) separation procedures follow the decomposition scheme of a maximum clique algorithm. We introduce a new heuristic, aimed at constructing a collection of (violated) clique inequalities covering all the edges of the underlying graph. We present an extensive computational experience showing that this closely approximates the results of an exact separation oracle while being faster than standard heuristics.

Keywords

Clique inequalities Separation problem Cutting plane algorithm 

Notes

Acknowledgements

This study was funded by Italian Ministry of Education and Research, National Research Program PRIN 2015, Grant No. 20153TXRX9.

Compliance with ethical standards

Conflict of interest

All authors declare that they have no conflict of interest

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.DISIM, University of L’AquilaL’AquilaItaly

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