Abstract
MAX-SAT, the optimisation variant of the satisfiability problem in propositional logic, is an important and widely studied combinatorial optimisation problem with applications in AI and other areas of computing science. In this paper, we present a new stochastic local search (SLS) algorithm for MAX-SAT that combines Iterated Local Search and Tabu Search, two well-known SLS methods that have been successfully applied to many other combinatorial optimisation problems. The performance of our new algorithm exceeds that of current state-of-the-art MAX-SAT algorithms on various widely studied classes of unweighted And weighted MAX-SAT instances, particularly for Random-3-SAT instances with high variance clause weight distributions. We also report promising results for various classes of structured MAX-SAT instances.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
P. Asirelli, M. de Santis, and A. Martelli. Integrity constraints in logic databases. J. of Logic Programming, 3:221–232, 1985.
R. Battiti and M. Protasi. Reactive search, a history-basedh euristic for MAXSAT. ACM Journal of Experimental Algorithmics, 2, 1997.
B. Borchers and J. Furman. A two-phase exact algorithm for MAX-SAT and weighted M AX-SAT problems. Journal of Combinatorial Optimization, 2(4):299–306, 1999.
B. Randerath et al. A satisfiability formulation of problems on level graphs. Technical Report 40-2001, Rutgers Center for Operations Research, Rutgers University, Piscataway, NJ, USA, June 2001.
M. R. Garey and D. S. Johnson. Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, San Francisco, CA, 1979.
I. P. Gent and T. Walsh. Towards an understanding of hill-climbing procedures for SAT. In Proceedings of AAAI’93, pages 28–33. MIT Press, 1993.
J. Gu and R. Puri. Asynchronous circuit synthesis with boolean satisfiability. IEEE Transact. of Computer-Aided Design of Integrated Circuits and Systems, 14(8):961–973, 1995.
P. Hansen and B. Jaumard. Algorithms for the maximum satisfiability problem. Computing, 44: 279–303, 1990. Kevin Smyth et al.
H. H. Hoos. On the run-time behaviour of stochastic local search algorithms for SAT. In Proc. AAAI-99, pages 661–666. MIT Press, 1999.
H. H. Hoos and T. Stutzle. Evaluating Las Vegas algorithms — pitfalls and remedies. In Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI-98), pages 238–245. Morgan Kaufmann, San Francisco, 1998.
Y. Jiang, H. Kautz, and B. Selman. Solving problems with hard and soft constraints using a stochastic algorithm for MAX-SAT. In Proceedings of the 1st International Joint Workshop on Artificial Intelligence and Operations Research, 1995.
S. Joy, J. Mitchell, and B. Borchers. A branch and cut algorithm for MAX-SAT and weighted MA X-SAT. In D. Du, J. Gu, and P. M. Pardalos, editors, Satisfiability problem: Theory and Applications, volume 35 of DIMACS Series on Discrete Mathematics and Theoretical Computer Science, pages 519–536. American Mathematical Society, 1997.
A. P. Kamath, N. K. Karmarkar, K. G. Ramakrishnan, and M. G. C. Resende. A continuous approach to inductive inference. Mathematical Programming, 57:215–238, 1992.
H. R. Lourenço, O. Martin, and T. Stützle. Iterated local search. In F. Glover and G. Kochenberger, editors, Handbook of Metaheuristics, volume 57 of International Series in Operations Research and Management Science, pages 321–353. Kluwer Academic Publishers, Norwell, MA, 2002.
P. Mills and E. Tsang. Guided local search for solving SAT and weighted MAXSAT problems. In I. P. Gent, H. van Maaren, and T. Walsh, editors, SAT2000 — Highlights of Satisfiability Research in the Year 2000, pages 89–106. IOS Press, 2000.
D. Mitchell, B. Selman, and H. Levesque. Hard and easy distributions of SAT problems. In Proc. of AAAI’92, pages 459–465. MIT Press, 1992.
James Park. Using weighted MAX-SAT to approximate MPE. In Proc. of AAAI-02, pages 682–687. AAAI Press, 2002.
M. G. C. Resende, L. S. Pitsoulis, and P. M. Pardalos. Approximate solution of Weighted MAX-SAT problems using GRASP. In D. Du, J. Gu, and P. M. Pardalos, editors, Satisfiability problem: Theory and Applications, volume 35, pages 393–405. AMS, 1997.
Y. Shang and B. W. Wah. Discrete lagrangian-based search for solving MAX-SAT problems. In Proc. of IJCAI’97, volume 1, pages 378–383. Morgan Kaufmann Publishers, San Francisco, CA, USA, 1997.
É. D. Taillard. Robust taboo search for the quadratic assignment problem. Parallel Computing, 17:443–455, 1991.
Z. Wu and B. W. Wah. Trap escaping strategies in discrete lagrangian methods for solving hard satisfiability and maximum satisfiability problems. In Proc. of AAAI’99, pages 673–678. MIT Press, 1999.
M. Yagiura and T. Ibaraki. Effecient 2 and 3-flip neighborhoods seach algorithms for the MAX SAT. In W.-L. Hsu and M.-Y. Kao, editors, Computing and Combinatorics, volume 1449 of Lecture Notes in Computer Science, pages 105–116. Springer Verlag, Berlin, Germany, 1998.
M. Yagiura and T. Ibaraki. Effecient 2 and 3-flip neighborhood search algorithms for the MAX SAT: Experimental evaluation. Journal of Heuristics, 7(5):423–442, 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Smyth, K., Hoos, H.H., Stützle, T. (2003). Iterated Robust Tabu Search for MAX-SAT. In: Xiang, Y., Chaib-draa, B. (eds) Advances in Artificial Intelligence. Canadian AI 2003. Lecture Notes in Computer Science, vol 2671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44886-1_12
Download citation
DOI: https://doi.org/10.1007/3-540-44886-1_12
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40300-5
Online ISBN: 978-3-540-44886-0
eBook Packages: Springer Book Archive