Abstract
We extend a planning algorithm to cover simple forms of arithmetics. The operator preconditions can refer to the values of numeric variables and the operator postconditions can modify the values of numeric variables. The basis planning algorithm is based on techniques from propositional satisfiability testing and does not restrict to forward or backward chaining. When several operations affect a numeric variable by increasing and decreasing its value in parallel, the effects have to be combined in a meaningful way. This problem is especially acute in planning algorithms that maintain an incomplete state description of every time point of a plan execution. The approach we take requires that for operators that are executed in parallel, all linearizations of the operations to total orders behave equivalently. We provide an efficient and general solution to the problem.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Blum, A.L., Furst, M.L.: Fast planning through planning graph analysis. Artificial Intelligence 90(1-2), 281–300 (1997)
Dimopoulos, Y., Nebel, B., Koehler, J.: Encoding planning problems in nonmonotonic logic programs. In: Steel, S. (ed.) ECP 1997. LNCS, vol. 1348, pp. 169–181. Springer, Heidelberg (1997)
Kautz, H., Selman, B.: Pushing the envelope: planning, propositional logic, and stochastic search. In: Proceedings of the Thirteenth National Conference on Artificial Intelligence and the Eighth Innovative Applications of Artificial Intelligence Conference, Menlo Park, pp. 1194–1201. AAAI Press / The MIT Press (1996)
Kautz, H., Walser, J.: State-space planning by integer optimization. In: Proceedings of the Sixteenth National Conference on Artificial Intelligence, pp. 526–533 (1999)
Koehler, J.: Planning under resource constraints. In: Proceedings of the 13th European Conference on Artificial Intelligence, pp. 489–493. John Wiley & Sons, Chichester (1998)
Li, C.M., Anbulagan: Heuristics based on unit propagation for satisfiability problems. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence, Nagoya, Japan, August 1997, pp. 366–371 (1997)
McAllester, D.A., Rosenblitt, D.: Systematic nonlinear planning. In: Dean, T.L., McKeown, K. (eds.) Proceedings of the 9th National Conference on Artificial Intelligence, Anaheim, California, pp. 634–639. The MIT Press, Cambridge (1991)
Rintanen, J.: A planning algorithm not based on directional search. In: Cohn, A.G., Schubert, L.K., Shapiro, S.C. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference (KR 1998), Trento, Italy, pp. 617–624. Morgan Kaufmann Publishers, San Francisco (1998)
Vossen, T., Ball, M., Lotem, A., Nau, D.: On the use of integer programming models in AI planning. In: Dean, T. (ed.) Proceedings of the 16th International Joint Conference on Artificial Intelligence, Stockholm, vol. I, pp. 304–309. Morgan Kaufmann Publishers, San Francisco (1999)
Wolfman, S.A.: email correspondence (August 1999)
Wolfman, S.A., Weld, D.S.: The LPSAT engine & its application to resource planning. In: Dean, T. (ed.) Proceedings of the 16th International Joint Conference on Artificial Intelligence, Stockholm, vol. I, pp. 310–315. Morgan Kaufmann Publishers, San Francisco (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Rintanen, J., Jungholt, H. (2000). Numeric State Variables in Constraint-Based Planning. In: Biundo, S., Fox, M. (eds) Recent Advances in AI Planning. ECP 1999. Lecture Notes in Computer Science(), vol 1809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10720246_9
Download citation
DOI: https://doi.org/10.1007/10720246_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67866-3
Online ISBN: 978-3-540-44657-6
eBook Packages: Springer Book Archive