Abstract
Models are used in science and engineering for experimentation, analysis, model-based diagnosis, design and planning/sheduling applications. Many of these models are overconstrained Numeric Constraint Satisfaction Problems (NCSP), where the numeric constraints could have linear or polynomial relations. In practical scenarios, it is very useful to know which parts of the overconstrained NCSP instances cause the unsolvability.
Although there are algorithms to find all optimal solutions for this problem, they are computationally expensive, and hence may not be applicable to large and real-world problems. Our objective is to improve the performance of these algorithms for numeric domains using structural analysis. We provide experimental results showing that the use of the different strategies proposed leads to a substantially improved performance and it facilitates the application of solving larger and more realistic problems.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bailey, J., Stuckey, P.J.: Discovery of Minimal Unsatisfiable Subsets of Constraints using Hitting set dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) Practical Aspects of Declarative Languages. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)
Bruni, R.: Approximating minimal unsatisfiable subformulae by means of adaptive core search. Discrete Applied Mathematics 130, 85–100 (2003)
Ceballos, R., Gómez-López, M.T., Gasca, M.T.R.M., del Valle, C.: Integración de técnicas basadas en modelos para la determinación de la diagnosis mínima de un sistema. Inteligencia Artificial. Revista Iberoamericana de Inteligencia Artificial No. 31, pp. 41–51 (2006)
Chinneck, J., Dravnieks, E.: Locating minimal infeasible constraint sets in linear programs. ORSA Journal on Computing 3, 157–168 (1991)
de la Banda, M.G., Stuckey, P.J., Wazny, J.: Finding all minimal unsatisfiable subsets. In: PPDP 2003. Proceedings of the 5th ACM SIGPLAN international conference on Principles and practice of declaritive programming, pp. 32–43. ACM Press, New York (2003)
Gómez, M.T., Ceballos, R., Gasca, R.M., Del Valle, C.: Constraint Databases Technology for Polynomial Models Diagnosis. In: Proceedings DX 2004 (2004)
Grégoire, É., Mazure, B., Piette, C.: Local-Search Extraction of MUSes. Constraints 12(3) (2007)
Junker, U.: QuickXPlain. In: Conflict Detection for Arbitatrary Constraint Propagation Algorithms Proceedings IJCAI 2001 (2001)
Liffiton, M., Sakallah, K.: On finding all minimally unsatisfiable subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 173–186. Springer, Heidelberg (2005)
Mauss, J., Tatar, M.: Computing Minimal Conflicts for Rich Constraint Languages. In: ECAI, pp. 151–155 (2002)
Moffitt, M.D., Pollack, M.E.: Applying Local Search to Disjunctive Temporal Problems. In: Proced. IJCAI (2005)
Liffiton, M.H., Moffitt, M.D., Pollack, M.E., Sakallah, K.A.: Identifying Conflicts in Overconstrained Temporal Problems. In: Proceedings IJCAI 2007 (2007)
Oh, Y., Mneimneh, M.N., Andraus, Z.S., Sakallah, K.A., Markov, I.L.: AMUSE: A Minimally-Unsatisfiable Subformula Extractor. In: DAC 2004. Proceedings of the Design Automation Conference, ACM/IEEE, pp. 518–523 (2004)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gasca, R.M., Del Valle, C., Gómez-López, M.T., Ceballos, R. (2007). NMUS: Structural Analysis for Improving the Derivation of All MUSes in Overconstrained Numeric CSPs. In: Borrajo, D., Castillo, L., Corchado, J.M. (eds) Current Topics in Artificial Intelligence. CAEPIA 2007. Lecture Notes in Computer Science(), vol 4788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75271-4_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-75271-4_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75270-7
Online ISBN: 978-3-540-75271-4
eBook Packages: Computer ScienceComputer Science (R0)