TY - JOUR
T1 - Certified Dominance and Symmetry Breaking for Combinatorial Optimisation
AU - Bogaerts, Bart
AU - Gocht, Stephan
AU - McCreesh, Ciaran
AU - Nordström, Jakob
N1 - Publisher Copyright:
©2023 The Authors.
PY - 2023
Y1 - 2023
N2 - 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.
AB - 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.
U2 - 10.1613/jair.1.14296
DO - 10.1613/jair.1.14296
M3 - Article
AN - SCOPUS:85171627621
SN - 1076-9757
VL - 77
SP - 1539
EP - 1589
JO - Journal of Artificial Intelligence Research
JF - Journal of Artificial Intelligence Research
ER -