Certified Symmetry and Dominance Breaking for Combinatorial Optimisation
This provides a unified, machine-verifiable certification method for advanced SAT techniques, addressing correctness concerns in combinatorial optimization for researchers and practitioners.
The paper tackled the problem of verifying the correctness of symmetry and dominance breaking techniques in combinatorial optimization by developing a certification method based on the cutting planes proof system, resulting in efficient verification for Boolean satisfiability (SAT) solving and applicability to problems like maximum clique and constraint programming.
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.