Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Bogaerts, B., Gocht, S., McCreesh, C. and Nordstrom, J. (2022) Certified Symmetry and Dominance Breaking for Combinatorial Optimisation. In: 36th AAAI Conference on Artificial Intelligence (AAAI-22), 22 February - 1 March 2022, pp. 3698-3707. ISBN 9781577358763 (doi: 10.1609/aaai.v36i4.20283)

Abstract

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce efficient, machine-verifiable certificates that solutions have been computed correctly. Building on the cutting planes proof system, we develop a certification method for optimisation problems in which symmetry and dominance breaking are easily expressible. Our experimental evaluation demonstrates that we can efficiently verify fully general symmetry breaking in Boolean satisfiability (SAT) solving, thus providing, for the first time, a unified method to certify a range of advanced SAT techniques that also includes XOR and cardinality reasoning. In addition, we apply our method to maximum clique solving and constraint programming as a proof of concept that the approach applies to a wider range of combinatorial problems.

• Item Type: Conference Proceedings
• Additional Information: Bart Bogaerts was partially supported by Fonds Wetenschappelijk Onderzoek – Vlaanderen (project G070521N). Ciaran McCreesh was supported by a Royal Academy of Engineering Research Fellowship. Stephan Gocht and Jakob Nordstrom were supported by the Swedish Research ¨ Council grant 2016-00782, and Jakob Nordstrom also re- ¨ ceived funding from the Independent Research Fund Denmark grant 9040-00389B.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mccreesh, Dr Ciaran
• Authors: Bogaerts, B., Gocht, S., McCreesh, C., and Nordstrom, J.
• College/School: College of Science and Engineering > School of Computing Science
• ISSN: 2159-5399
• ISBN: 9781577358763
• Published Online: 28 June 2022
• Copyright Holders: Copyright © 2022, Association for the Advancement of Artificial Intelligence
• First Published: First published in Proceedings of the AAAI Conference on Artificial Intelligence, 36(4): 3698-3707
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Related URLs

• Organisation
• arXiv
• Publisher

• Data DOI: 10.5281/zenodo.6373986