Abstract
In this study, a nonlinear optimization model is proposed to determine the constraint propagation (CP) of qualitative constraint sets to minimize search backtracking points. The model gives answers to the questions of what the optimal sequence is in the case that there is a set of variables with known values and, alternatively, what variable sequence is optimal to be able to have an optimal value propagation (what variable values should be known to have optimum variable sequence). In order to improve the solution performance, a constraint activation analysis is initiated for the constraints that are defined for the variables with known values by sign algebraic Karush-Kuhn-Tucker conditions. The optimization model and the qualitative activity analysis carried out can be applied to any constraint propagation problem where the variables have a limited set of values.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Berkholz, C., & Verbitsky, O. (2018). On the speed of constraint propagation and the time complexity of arc consistency testing. Journal of Computer and System Sciences, 91, 104–114. https://doi.org/10.1016/j.jcss.2017.09.003.
De Kleer, J., & Brown, J. S. (2013). A qualitative physics based on confluences. In Readings in Qualitative Reasoning About Physical Systems (pp. 88–126). https://doi.org/10.1016/B978-1-4832-1447-4.50013-4.
Dechter, R. (2003). Constraint processing. Elsevier Morgan Kaufmann.
Dechter, R., & Pearl, J. (1989). Tree clustering for constraint networks. Artificial Intelligence, 38(3), 353–366. https://doi.org/10.1016/0004-3702(89)90037-4.
Forbus, K. D. (2013). Qualitative process theory. In Readings in Qualitative Reasoning About Physical Systems (pp. 178–219). https://doi.org/10.1016/B978-1-4832-1447-4.50016-X.
Freuder, E. C. (1982). A sufficient condition for backtrack-free search. Journal of the ACM. https://doi.org/10.1145/322290.322292.
Fu, Z., Lu, Z., Ip, H. H. S., Lu, H., & Wang, Y. (2015). Local similarity learning for pairwise constraint propagation. Multimedia Tools and Applications, 74(11), 3739–3758. https://doi.org/10.1007/s11042-013-1796-y.
Guadarrama, S., Muñoz, S., & Vaucheret, C. (2004). Fuzzy prolog: A new approach using soft constraints propagation. Fuzzy Sets and Systems, 144(1), 127–150. https://doi.org/10.1016/j.fss.2003.10.017.
Hocaoğlu, M. F. (2000). Qualitative constraint propagation in constraint based qualitative simulation. Sakarya University.
Kuhn, H. W., & Tucker, A. (1951). Nonlinear programming. In Proceedings of the Second Symposium on Mathematical Statistics and Probability (Vol. x, pp. 481–492). https://doi.org/10.1007/BF01582292.
Kuipers, B. (1994). Qualitative reasoning: Modeling and simulation with incomplete knowledge. New York, Cambridge, Massachusetts: MIT Press.
Kumar, V. (1992). Algorithms for constraint-satisfaction problems: A survey. AI Magazine, 13(1), 32–44. https://doi.org/10.1.1.39.8020.
Mayoh, B., Tyugu, E., & Uustalu, T. (1994). Constraint satisfaction and constraint programming: A brief lead-in (pp. 1–16). Berlin Heidelberg: Springer. https://doi.org/10.1007/978-3-642-85983-0_1.
Nait Abdallah, A., & Van Emden, M. H. (2013). Constraint propagation as information maximization. Artificial Intelligence, 197, 25–38. https://doi.org/10.1016/j.artint.2013.02.002.
Vanderplaats, G. N. (1984). Numerical optimization techniques for engineering design: With applications. McGraw Hill College.
Vescovi, M. R., Lamega, M. M., & Farquhar, A. (1997). Modeling and simulation of a complex industrial process. IEEE Expert, 12(3), 42–46. https://doi.org/10.1109/64.590073.
Williams, B. C., & Cagan, J. (1996a). Activity analysis: Simplifying optimal design problems through qualitative partitioning. International Journal of Engineering Optimization, 27, 109–137.
Williams, B. C., & Cagan, J. (1996b). Activity analysis: The qualitative analysis of stationary points for optimal reasoning. International Journal of Engineering Optimization, 27, 109–137.
Zheng, J., & Horsch, M. C. (2003). A comparison of consistency propagation algorithms in constraint optimization. In 16th Conference of the Canadian Society for Computational Studies of Intelligence, June 11–13 2003 (Vol. 2671, pp. 160–174).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Hocaoğlu, M.F. (2019). An Optimization Model for Variable Ordering in Qualitative Constraint Propagation. In: Calisir, F., Cevikcan, E., Camgoz Akdag, H. (eds) Industrial Engineering in the Big Data Era. Lecture Notes in Management and Industrial Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-03317-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-03317-0_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-03316-3
Online ISBN: 978-3-030-03317-0
eBook Packages: EngineeringEngineering (R0)