Certified Symmetry and Dominance Breaking for Combinatorial Optimisation

Bart Bogaerts, Stephan Gocht, Ciaran McCreesh, Jakob Nordström

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)1539-1589
Number of pages51
JournalJournal of Artificial Intelligence Research
Publication statusPublished - 2023


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