Certified dominance and symmetry breaking for combinatorial optimisation

Bogaerts, B., Gocht, S., McCreesh, C. and Nordström, J. (2023) Certified dominance and symmetry breaking for combinatorial optimisation. Journal of Artificial Intelligence Research, 77, pp. 1539-1589. (doi: 10.1613/jair.1.14296)

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 is 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 cardinality and parity (XOR) 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: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mccreesh, Dr Ciaran
• Authors: Bogaerts, B., Gocht, S., McCreesh, C., and Nordström, J.
• College/School: College of Science and Engineering > School of Computing Science
• Journal Name: Journal of Artificial Intelligence Research
• Publisher: AAAI Press
• ISSN: 1076-9757
• ISSN (Online): 1943-5037
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Journal of Artificial Intelligence Research 77:1539-1589
• Publisher Policy: Reproduced under a Creative Commons license