1 research outputs found
Encoding Linear Constraints into SAT
Linear integer constraints are one of the most important constraints in
combinatorial problems since they are commonly found in many practical
applications. Typically, encodings to Boolean satisfiability (SAT) format of
conjunctive normal form perform poorly in problems with these constraints in
comparison with SAT modulo theories (SMT), lazy clause generation (LCG) or
mixed integer programming (MIP) solvers.
In this paper we explore and categorize SAT encodings for linear integer
constraints. We define new SAT encodings based on multi-valued decision
diagrams, and sorting networks. We compare different SAT encodings of linear
constraints and demonstrate where one may be preferable to another. We also
compare SAT encodings against other solving methods and show they can be better
than linear integer (MIP) solvers and sometimes better than LCG or SMT solvers
on appropriate problems. Combining the new encoding with lazy decomposition,
which during runtime only encodes constraints that are important to the solving
process that occurs, gives the best option for many highly combinatorial
problems involving linear constraints