Abstract
In this paper we describe new local search algorithms for regular CNF formulas and investigate their suitability for solving problems from the domains of graph coloring and sports scheduling. First, we define suitable encodings for such problems in the logic of regular CNF formulas. Second, we describe Regular-GSAT and Regular-WSAT, as well as some variants, which are a natural generalization of two prominent local search algorithms -GSAT and WSAT- used to solve the prepositional satisfiability (SAT) problem in classical logic. Third, we report on experimental results that demonstrate that encoding graph coloring and sports scheduling problems as instances of the SAT problem in regular CNF formulas and then solving these instances with local search algorithms can outperform or compete with state-of-the-art approaches to solving hard combinatorial problems.
Research partially supported by the project CICYT TIC96-1038-C04-03. The first author is supported by a doctoral fellowship of the Comissionat per a Universitats i Recerca (1998FI00326).
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References
B. Beckert, R. Hähnle, and F. Manyà. Transformations between signed and classical clause logic. In Proc. International Symposium on Multiple-Valued Logics, ISMVL’99, Freiburg, Germany, pages 248–255. IEEE Press, Los Alamitos, 1999.
R. Béjar and F. Manyà. A comparison of systematic and local search algorithms for regular CNF formulas. In Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU’99, London, England, pages 22–31. Springer LNAI 1638, 1999.
R. Béjar and F. Manyà. Phase transitions in the regular random 3-SAT problem. In Proceedings of the International Symposium on Methodologies for Intelligent Systems, ISMIS’99, Warsaw, Poland, pages 292–300. Springer LNAI 1609, 1999.
J. M. Crawford and A. B. Baker. Experimental results on the application of satisfiability algorithms to scheduling problems. In Proceedings of the 12th National Conference on Artificial Intelligence, AAAI’94, Seattle, WA, USA, pages 1092–1097, 1994.
G. Escalada-Imaz and F. Manyà. The satisfiability problem for multiple-valued Horn formulae. In Proceedings of the International Symposium on Multiple-Valued Logics, ISMVL’94, Boston, MA, USA, pages 250–256. IEEE Press, Los Alamitos, 1994.
C. P. Gomes, B. Selman, K. McAloon, and C. Tretkoff. Randomization in backtrack search: Exploiting heavy-tailed profiles for solving hard scheduling problems. In Proceedings AIPS’98, Pittsburg, PA, USA, 1998.
R. Hähnle. Short conjunctive normal forms in finitely-valued logics. Journal of Logic and Computation, 4(6):905–927, 1994.
R. Hähnle. Exploiting data dependencies in many-valued logics. Journal of Applied Non-Classical Logics, 6:49–69, 1996.
R. Hähnle and G. Escalada-Imaz. Deduction in many-valued logics: A survey. Mathware and Soft Computing, 4(2):69–97, 1997.
D. S. Johnson, C. R. Aragon, L. A. McGeoch, and C. Schevon. Optimization by simulated annealing: An experimental evaluation; part II, graph coloring and number partitioning. Operations Research, 39(3):378–406, 1991.
H. A. Kautz and B. Selman. Pushing the envelope: Planning, prepositional logic, and stochastic search. In Proceedings of the 14th National Conference on Artificial Intelligence, AAAI’96, Portland, OR, USA, pages 1194–1201, 1996.
F. Manyà. The 2-SAT problem in signed CNF formulas. Multiple-Valued Logic, An International Journal, 1999. In press.
F. Manyà, R. Béjar, and G. Escalada-Imaz. The satisfiability problem in regular CNF-formulas. Soft Computing: A Fusion of Foundations, Methodologies and Applications, 2(3):116–123, 1998.
D. McAllester, B. Selman, and H. Kautz. Evidence for invariants in local search. In Proceedings of the 14th National Conference on Artificial Intelligence, AAAI’97, Providence, RI, USA, pages 321–326, 1997.
B. Selman and H. A. Kautz. Domain-independent extensions of GSAT: Solving large structured satisfiability problems. In Proceedings of the International Joint Conference on Artificial Intelligence, IJCAI’93, Chambery, France, pages 290–295, 1993.
B. Selman, H. A. Kautz, and B. Cohen. Noise strategies for improving local search. In Proceedings of the 12th National Conference on Artificial Intelligence, AAAI’94, Seattle, WA, USA, pages 337–343, 1994.
B. Selman, H. Levesque, and D. Mitchell. A new method for solving hard satisfiability problems. In Proceedings of the 10th National Conference on Artificial Intelligence, AAAI’92, San Jose, CA, USA, pages 440–446, 1992.
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Béjar, R., Manyà, F. (1999). Solving Combinatorial Problems with Regular Local Search Algorithms. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 1999. Lecture Notes in Computer Science(), vol 1705. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48242-3_3
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DOI: https://doi.org/10.1007/3-540-48242-3_3
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