Some results and experiments in programming techniques for propositional logic
Computers and Operations Research - Special issue: Applications of integer programming
Mathematical Programming: Series A and B
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
Noise strategies for improving local search
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Improvements to propositional satisfiability search algorithms
Improvements to propositional satisfiability search algorithms
Linear programming 1: introduction
Linear programming 1: introduction
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
New upper bounds for maximum satisfiability
Journal of Algorithms
A machine program for theorem-proving
Communications of the ACM
Chaff: engineering an efficient SAT solver
Proceedings of the 38th annual Design Automation Conference
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Random MAX SAT, random MAX CUT, and their phase transitions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Enhancing Maximum Satisfiablility Algorithms with Pure Literal Strategies
AI '96 Proceedings of the 11th Biennial Conference of the Canadian Society for Computational Studies of Intelligence on Advances in Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Generic ILP versus specialized 0-1 ILP: an update
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Inference methods for a pseudo-boolean satisfiability solver
Eighteenth national conference on Artificial intelligence
Using weighted MAX-SAT engines to solve MPE
Eighteenth national conference on Artificial intelligence
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time
Journal of the ACM (JACM)
Introduction to Operations Research and Revised CD-ROM 8
Introduction to Operations Research and Revised CD-ROM 8
Study of lower bound functions for MAX-2-SAT
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Heuristics based on unit propagation for satisfiability problems
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Integer optimization by local search: a domain-independent approach
Integer optimization by local search: a domain-independent approach
Hard and easy distributions of SAT problems
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
Experimental results on the crossover point in satisfiability problems
AAAI'93 Proceedings of the eleventh national conference on Artificial intelligence
Evidence for invariants in local search
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Symmetry Breaking for Maximum Satisfiability
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Branch and Bound for Boolean Optimization and the Generation of Optimality Certificates
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
Partial max-SAT solvers with clause learning
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
MiniMaxSAT: a new weighted Max-SAT solver
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
On inconsistent clause-subsets for Max-SAT solving
CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
AI'07 Proceedings of the 20th Australian joint conference on Advances in artificial intelligence
Some simplified forms of reasoning with distance-based entailments
Canadian AI'08 Proceedings of the Canadian Society for computational studies of intelligence, 21st conference on Advances in artificial intelligence
Using learnt clauses in MAXSAT
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A Framework for Certified Boolean Branch-and-Bound Optimization
Journal of Automated Reasoning
Journal of Automated Reasoning
Semiring-induced propositional logic: definition and basic algorithms
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
On SAT modulo theories and optimization problems
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A complete calculus for Max-SAT
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
The power of semidefinite programming relaxations for MAX-SAT
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Conflict-Directed a* search for soft constraints
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
A SAT-based approach to cost-sensitive temporally expressive planning
ACM Transactions on Intelligent Systems and Technology (TIST) - Special Section on Intelligent Mobile Knowledge Discovery and Management Systems and Special Issue on Social Web Mining
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Maximum Boolean satisfiability (max-SAT) is the optimization counterpart of Boolean satisfiability (SAT), in which a variable assignment is sought to satisfy the maximum number of clauses in a Boolean formula. A branch and bound algorithm based on the Davis-Putnam-Logemann-Loveland procedure (DPLL) is one of the most competitive exact algorithms for solving max-SAT. In this paper, we propose and investigate a number of strategies for max-SAT. The first strategy is a set of unit propagation or unit resolution rules for max-SAT. We summarize three existing unit propagation rules and propose a new one based on a nonlinear programming formulation of max-SAT. The second strategy is an effective lower bound based on linear programming (LP). We show that the LP lower bound can be made effective as the number of clauses increases. The third strategy consists of a binary-clause first rule and a dynamic-weighting variable ordering rule, which are motivated by a thorough analysis of two existing well-known variable orderings. Based on the analysis of these strategies, we develop an exact solver for both max-SAT and weighted max-SAT. Our experimental results on random problem instances and many instances from the max-SAT libraries show that our new solver outperforms most of the existing exact max-SAT solvers, with orders of magnitude of improvement in many cases.