Abstract
We consider constraint optimization problems where costs (or preferences) are all given, but some are tagged as possibly unstable, and provided with a range of alternative values. We also allow for some uncontrollable variables, whose value cannot be decided by the agent in charge of taking the decisions, but will be decided by Nature or by some other agent. These two forms of uncertainty are often found in many scheduling and planning scenarios. For such problems, we define several notions of desirable solutions. Such notions take into account not only the optimality of the solutions, but also their degree of robustness (of the optimality status, or of the cost) w.r.t. the uncertainty present in the problem. We provide an algorithm to find solutions accordingly to the considered notions of optimality, and we study the properties of these algorithms. For the uncontrollable variables, we propose to adopt a variant of classical variable elimination, where we act pessimistically rather than optimistically.
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References
Bistarelli, S., Montanari, U., Rossi, F.: Semiring-based constraint solving and optimization. Journal of the ACM 44(2), 201–236 (1997)
Dechter, R.: Constraint processing. Morgan Kaufmann, San Francisco (2003)
Dechter, R., Dechter, A.: Belief maintenance in dynamic constraint networks. In: AAAI, pp. 37–42 (1988)
Dechter, R., Mateescu, R.: And/or search spaces for graphical models. AI Journal 171(2-3), 73–106 (2007)
Dechter, R.: Bucket elimination: A unifying framework for reasoning. AI Journal 113(1-2), 41–85 (1999)
Faltings, B., Macho-Gonzalez, S.: Open constraint programming. AI Journal 161(1-2), 181–208 (2005)
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), vol. 1, pp. 175–180. AAAI Press, Menlo Park (1996)
Gelain, M., Pini, M.S., Rossi, F., Venable, K.B.: Dealing with incomplete preferences in soft constraint problems. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 286–300. Springer, Heidelberg (2007)
Lamma, E., Mello, P., Milano, M., Cucchiara, R., Gavanelli, M., Piccardi, M.: Constraint propagation and value acquisition: Why we should do it interactively. In: IJCAI, pp. 468–477 (1999)
Mateescu, R., Dechter, R.: A comparison of time-space schemes for graphical models. In: Proc. IJCAI 2007, pp. 2346–2352. Morgan Kaufmann, San Francisco (2007)
Rossi, F., Van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier, Amsterdam (2006)
Vidal, T., Fargier, H.: Handling contigency in temporal constraint networks. JETAI 11(1), 23–45 (1999)
Wilson, N., Grimes, D., Freuder, E.C.: A cost-based model and algorithms for interleaving solving and elicitation of csps. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 666–680. Springer, Heidelberg (2007)
Yorke-Smith, N., Gervet, C.: Certainty closure: A framework for reliable constraint reasoning with uncertainty. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 769–783. Springer, Heidelberg (2003)
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Pini, M.S., Rossi, F., Venable, K.B., Dechter, R. (2009). Robust Solutions in Unstable Optimization Problems. In: Oddi, A., Fages, F., Rossi, F. (eds) Recent Advances in Constraints. CSCLP 2008. Lecture Notes in Computer Science(), vol 5655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03251-6_8
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DOI: https://doi.org/10.1007/978-3-642-03251-6_8
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