Modeling Robustness in CSPs as Weighted CSPs
Many real life problems come from uncertain and dynamic environments, where the initial constraints and/or domains may undergo changes. Thus, a solution found for the problem may become invalid later. Hence, searching for robust solutions for Constraint Satisfaction Problems (CSPs) becomes an important goal. In some cases, no knowledge about the uncertain and dynamic environment exits or it is hard to obtain it. In this paper, we consider CSPs with discrete and ordered domains where only limited assumptions are made commensurate with the structure of these problems. In this context, we model a CSP as a weighted CSP (WCSP) by assigning weights to each valid constraint tuple based on its distance from the edge of the space of valid tuples. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a robust solution for the original CSP according to our assumptions.
KeywordsRobustness Uncertainty Dynamic CSPs
Unable to display preview. Download preview PDF.
- 1.Bofill, M., Busquets, D., Villaret, M.: A declarative approach to robust weighted Max-SAT. In: Proceedings of the 12th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming (PPDP 2010), pp. 67–76 (2010)Google Scholar
- 2.Climent, L., Salido, M., Barber, F.: Reformulating dynamic linear constraint satisfaction problems as weighted CSPs for searching robust solutions. In: Proceedings of the 9th Symposium of Abstraction, Reformulation, and Approximation (SARA 2011), pp. 34–41 (2011)Google Scholar
- 3.Dechter, R., Dechter, A.: Belief maintenance in dynamic constraint networks. In: Proceedings of the 7th National Conference on Artificial Intelligence (AAAI 1988), pp. 37–42 (1988)Google Scholar
- 5.Fargier, H., Lang, J., Schiex, T.: Mixed constraint satisfaction: A framework for decision problems under incomplete knowledge. In: Proceedings of the 13th National Conference on Artificial Intelligence (AAAI 1996), pp. 175–180 (1996)Google Scholar
- 7.Hays, W.: Statistics for the social sciences, 2nd edn., vol. 410. Holt, Rinehart and Winston, New York (1973)Google Scholar
- 8.Hebrard, E.: Robust Solutions for Constraint Satisfaction and Optimisation under Uncertainty. PhD thesis, University of New South Wales (2006)Google Scholar
- 9.Herrmann, H., Schneider, C., Moreira, A., Andrade Jr., J., Havlin, S.: Onion-like network topology enhances robustness against malicious attacks. Journal of Statistical Mechanics: Theory and Experiment 2011(1), P01027 (2011)Google Scholar
- 11.Mackworth, A.: On reading sketch maps. In: Proceedings of the 5th International Joint Conference on Artificial Intelligence (IJCAI 1977), pp. 598–606 (1977)Google Scholar
- 12.Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: Hard and easy problems. In: Proceedings of the 14th International Joint Conference on Artificial Intelligence (IJCAI 1995), pp. 631–637 (1995)Google Scholar
- 15.Walsh, T.: Stochastic constraint programming. In: Proceedings of the 15th European Conference on Artificial Intelligence (ECAI 2002), pp. 111–115 (2002)Google Scholar
- 16.William, F.: Topology and its applications. John Wiley & Sons (2006)Google Scholar
- 17.Winer, B.: Statistical principles in experimental design, 2nd edn. McGraw-Hill Book Company (1971)Google Scholar