The OPL optimization programming language
The OPL optimization programming language
A linear-time transformation of linear inequalities into conjunctive normal form
Information Processing Letters
A comparative study of two Boolean formulations of FPGA detailed routing constraints
Proceedings of the 2001 international symposium on Physical design
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Generic ILP versus specialized 0-1 ILP: an update
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
A fast pseudo-boolean constraint solver
Proceedings of the 40th annual Design Automation Conference
ShatterPB: symmetry-breaking for pseudo-Boolean formulas
Proceedings of the 2004 Asia and South Pacific Design Automation Conference
Solving strategies for highly symmetric CSPs
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Efficient symmetry breaking for boolean satisfiability
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
CGRASS: a system for transforming constraint satisfaction problems
ERCIM'02/CologNet'02 Proceedings of the 2002 Joint ERCIM/CologNet international conference on Constraint solving and constraint logic programming
Solving difficult instances of Boolean satisfiability in the presence of symmetry
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On implementing symmetry detection
Constraints
A novel approach for detecting symmetries in CSP models
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Scheduling social golfers with memetic evolutionary programming
HM'06 Proceedings of the Third international conference on Hybrid Metaheuristics
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We introduce a framework for studying and solving a class of CSP formulations. The framework allows constraints to be expressed as linear and non-linear equations, then compiles them into SAT instances via Boolean logic circuits. While in general reduction to SAT may lead to the loss of structure, we specifically detect several types of structure in high-level input and use them in compilation. Linearity is preserved by the use of pseudo-Boolean (PB) constraints in conjunction with a 0-1 ILP solver that extends common SAT-solving techniques. Symmetries are detected in high-level constraints by solving the graph automorphism problem on parse trees. Symmetry-breaking predicates are added during compilation. Our system generalizes earlier work on symmetries in SAT and 0-1 ILP problems. Empirical evaluation is performed on instances of the social golfers and Hamming code generation problems. We show substantial speedups with symmetry-breaking, especially on unsatisfiable instances. In general, our runtimes with the specialized 0-1 ILP solver Pueblo are competitive with results recently reported for ILOG Solver.