Matthias Poloczek
David P. Williamson
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Abstract
We evaluate the performance of fast approximation algorithms for MAX SAT on the comprehensive benchmark sets from the SAT and MAX SAT contests. Our examination of a broad range of algorithmic techniques reveals that greedy algorithms offer particularly striking performance, delivering very good solutions at low computational cost. Interestingly, their relative ranking does not follow their worst-case behavior. Johnson’s deterministic algorithm is consistently better than the randomized greedy algorithm of Poloczek et al. [2017], but in turn is outperformed by the derandomization of the latter: this two-pass algorithm satisfies more than 99% of the clauses for instances stemming from industrial applications. In general, it performs considerably better than nonoblivious local search, Tabu Search, WalkSat, and several state-of-the-art complete and incomplete solvers, while being much faster. But the two-pass algorithm does not achieve the excellent performance of Spears’s computationally intense simulated annealing. Therefore, we propose a new hybrid algorithm that combines the strengths of greedy algorithms and stochastic local search to provide outstanding solutions at high speed: in our experiments, its performance is as good as simulated annealing, achieving an average loss with respect to the best-known assignment of less that 0.5%, while its speed is comparable to the greedy algorithms.
- Andre Abrame and Djamal Habet. 2015. Ahmaxsat: Description and evaluation of a branch and bound Max-SAT Solver. J. Satisfiability Boolean Modeling Comput. 9 (2015), 89--128. The code is available at www.lsis.org/habetd/Djamal_Habet/MaxSAT.html.Google Scholar
Cross Ref
- Benjamin Andres, Benjamin Kaufmann, Oliver Matheis, and Torsten Schaub. 2012. Unsatisfiability-based optimization in Clasp. In Technical Communications of the 28th International Conference on Logic Programming (ICLP’12). 211--221.Google Scholar
- Josep Argelich, Chu Min Li, Felip Manyà, and Jordi Planes. 2014. MAX-SAT 2014: Ninth Max-SAT Evaluation. Retrieved from http://www.maxsat.udl.cat/14/. Last accessed on September 4, 2016.Google Scholar
- Josep Argelich, Chu Min Li, Felip Manyà, and Jordi Planes. 2015. MAX-SAT 2015: Tenth Max-SAT Evaluation. Retrieved from http://www.maxsat.udl.cat/15/. Last accessed on September 6, 2016.Google Scholar
- Anton Belov, Daniel Diepold, Marijn J. H. Heule, and Matti Järvisalo. 2014. Proceedings of SAT COMPETITION 2014: Solver and Benchmark Descriptions. See also http://satcompetition.org/edacc/sc14/. Last accessed on September 5, 2016.Google Scholar
- Niv Buchbinder and Moran Feldman. 2016. Deterministic algorithms for submodular maximization problems. In Proceedings of the 27th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’16). 392--403. Google ScholarDigital Library
- Niv Buchbinder, Moran Feldman, Joseph Naor, and Roy Schwartz. 2015. A tight linear time (1/2)-approximation for unconstrained submodular maximization. SIAM J. Comput. 44 (2015), 1384--1402. Google ScholarCross Ref
- Shaowei Cai, Chuan Luo, Jinkun Lin, and Kaile Su. 2016. New local search methods for partial MaxSAT. Artif. Intell. 240 (2016), 1--18. Google ScholarCross Ref
- Shaowei Cai, Chuan Luo, John Thornton, and Kaile Su. 2014. Tailoring local search for partial MaxSAT. In Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI’16). 2623--2629. The code is available at http://lcs.ios.ac.cn/∼caisw/MaxSAT.html. Google ScholarDigital Library
- Jianer Chen, Donald K. Friesen, and Hao Zheng. 1999. Tight bound on Johnson’s algorithm for maximum satisfiability. J. Comput. System Sci. 58, 3 (1999), 622--640. Google ScholarDigital Library
- Kevin P. Costello, Asaf Shapira, and Prasad Tetali. 2011. Randomized greedy: New variants of some classic approximation algorithms. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’11). 647--655. Google ScholarDigital Library
- Martin Gebser, Roland Kaminski, Benjamin Kaufmann, Javier Romero, and Torsten Schaub. 2015. Progress in Clasp Series 3. In Proceedings of the 13th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR’15). 368--383. Google ScholarCross Ref
- Martin Gebser, Roland Kaminski, Benjamin Kaufmann, and Torsten Schaub. 2011. Multi-criteria optimization in answer set programming. In Technical Communications of the 27th International Conference on Logic Programming (ICLP’11). 1--10.Google Scholar
- Jun Gu, Paul W. Purdom, John Franco, and Benjamin W. Wah. 1996. Algorithms for the satisfiability (SAT) problem: A survey. In Satisfiability Problem: Theory and Applications. 19--152.Google Scholar
- Marijn Heule and Sean Weaver (Eds.). 2015. In Proceedings of the 18th International Conference on Theory and Applications of Satisfiability Testing (SAT’15). Lecture Notes in Computer Science, Vol. 9340. Springer.Google Scholar
- David S. Johnson. 1974. Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9, 3 (1974), 256--278. Google ScholarDigital Library
- David S. Johnson and Lyle A. McGeoch. 1997. The traveling salesman problem: A case study in local optimization. Local Search Combin. Optim. 1 (1997), 215--310.Google Scholar
- Benjamin Kaufmann. 2015a. Personal communication.Google Scholar
- Benjamin Kaufmann. 2015b. Clasp: A conflict-driven nogood learning answer set solver (version 3.1.3). The code is available at http://www.cs.uni-potsdam.de/clasp/.Google Scholar
- Henry Kautz. 2014. WalkSat (version 51). The code is available at http://www.cs.rochester.edu/u/kautz/walksat/. See the source code for further references.Google Scholar
- Sanjeev Khanna, Rajeev Motwani, Madhu Sudan, and Umesh V. Vazirani. 1998. On syntactic versus computational views of approximability. SIAM J. Comput. 28, 1 (1998), 164--191. Google ScholarDigital Library
- Chuan Luo, Shaowei Cai, Kaile Su, and Wenxuan Huang. 2017. CCEHC: An efficient local search algorithm for weighted partial maximum satisfiability. Artif. Intell. 243 (2017), 26--44. Google ScholarDigital Library
- Chuan Luo, Shaowei Cai, Wei Wu, Zhong Jie, and Kaile Su. 2015. CCLS: An efficient local search algorithm for weighted maximum satisfiability. IEEE Trans. Comput. 64, 7 (2015), 1830--1843. The code is available at http://lcs.ios.ac.cn/∼caisw/MaxSAT.html. Google ScholarDigital Library
- Ruben Martins. 2015. (2015). Personal communication.Google Scholar
- Ruben Martins, Saurabh Joshi, Vasco M. Manquinho, and Inês Lynce. 2014a. Incremental cardinality constraints for MaxSAT. In Principles and Practice of Constraint Programming (CP’14). 531--548. Google ScholarCross Ref
- Ruben Martins, Vasco Manquinho, and Ines Lynce. 2015. Open-WBO: An open source version of the MaxSAT solver WBO (version 1.3.0). The code is available at http://sat.inesc-id.pt/open-wbo/index.html.Google Scholar
- Ruben Martins, Vasco M. Manquinho, and Inês Lynce. 2014b. Open-WBO: A Modular MaxSAT Solver. In Proceedings of the 17th International Conference on Theory and Applications of Satisfiability Testing (SAT’14). Lecture Notes in Computer Science, vol. 8561. Springer. Google ScholarCross Ref
- Monaldo Mastrolilli and Luca Maria Gambardella. 2004. MAX-2-SAT: How good is Tabu Search in the worst-case? In Proceedings of the 19th National Conference on Artificial Intelligence, 16th Conference on Innovative Applications of Artificial Intelligence (AAAI’04). 173--178. Google ScholarDigital Library
- Shuichi Miyazaki, Kazuo Iwama, and Yahiko Kambayashi. 1996. Database queries as combinatorial optimization problems. In CODAS. 477--483.Google Scholar
- António Morgado, Federico Heras, Mark H. Liffiton, Jordi Planes, and João Marques-Silva. 2013. Iterative and core-guided MaxSAT solving: A survey and assessment. Constraints 18, 4 (2013), 478--534. Google ScholarDigital Library
- Nina Narodytska and Fahiem Bacchus. 2014. Maximum satisfiability using core-guided MaxSAT resolution. In Proceedings of the 28th AAAI Conference on Artificial Intelligence (AAAI’14). 2717--2723. Google ScholarDigital Library
- Nina Narodytska and Fahiem Bacchus. 2015. EvaSolver. The code is available at https://www.cse.unsw.edu.au/∼ninan/.Google Scholar
- Denis Pankratov and Allan Borodin. 2010. On the relative merits of simple local search methods for the MAX-SAT problem. In Proceedings of the 13th International Conference on Theory and Applications of Satisfiability Testing (SAT’10). Lecture Notes in Computer Science, Vol. 6175. Springer. Google ScholarDigital Library
- Matthias Poloczek. 2011. Bounds on greedy algorithms for MAX SAT. In Algorithms -- ESA 2011, Camil Demetrescu and Magnús M. Halldórsson (Eds.). Lecture Notes in Computer Science, Vol. 6942. Springer, 37--48. Google ScholarDigital Library
- Matthias Poloczek and Georg Schnitger. 2011. Randomized variants of Johnson’s algorithm for MAX SAT. In Proceedings of the 22nd Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’11). 656--663. Google ScholarDigital Library
- Matthias Poloczek, Georg Schnitger, David P. Williamson, and Anke van Zuylen. 2017. Greedy algorithms for the maximum satisfiability problem: Simple algorithms and inapproximability bounds. SIAM Journal on Computing (SICOMP) 46, 3 (2017), 1029--1061. Google ScholarCross Ref
- Matthias Poloczek, David P. Williamson, and Anke van Zuylen. 2014. On some recent approximation algorithms for MAX SAT. In Latin American Theoretical Informatics Symposium (LATIN’14) (Lecture Notes in Computer Science), Alberto Pardo and Alfredo Viola (Eds.), Vol. 8392. Springer, 598--609. Google ScholarCross Ref
- Bart Selman, Henry A. Kautz, and Bram Cohen. 1993. Local search strategies for satisfiability testing. In Cliques, Coloring, and Satisfiability: 2nd DIMACS Implementation Challenge. 521--532.Google Scholar
- William M. Spears. 1993. Simulated annealing for hard satisfiability problems. In Cliques, Coloring and Satisfiability: 2nd DIMACS Implementation Challenge. 533--558.Google Scholar
- Daniel A. Spielman and Shang-Hua Teng. 2009. Smoothed analysis: An attempt to explain the behavior of algorithms in practice. Commun. ACM 52, 10 (2009), 76--84. Google ScholarDigital Library
- Anke van Zuylen. 2011. Simpler 3/4-approximation algorithms for MAX SAT. In Workshop on Approximation and Online Algorithms (WAOA’11) (Lecture Notes in Computer Science), Roberto Solis-Oba and Giuseppe Persiano (Eds.), Vol. 7164. Springer, 188--197. Google ScholarDigital Library
- David P. Williamson. 1999. Lecture Notes in Approximation Algorithms, Fall 1998. IBM Research Report RC 21409. IBM Research.Google Scholar
- Ya Zhang, Hongyuan Zha, Chao-Hsien Chu, and Xiang Ji. 2005. Protein Interaction Interference as a Max--Sat Problem. In Proceedings of the IEEE Workshop on Computer Vision Methods for Bioinformatics (CVPR’05). Google ScholarDigital Library
Index Terms
- An Experimental Evaluation of Fast Approximation Algorithms for the Maximum Satisfiability Problem
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