Abstract
Many heuristic estimators for classical planning are based on the so-called delete relaxation, which ignores negative effects of planning operators. Ideally, such heuristics would compute the actual goal distance in the delete relaxation, i.e, the cost of an optimal relaxed plan, denoted by h + . However, current delete relaxation heuristics only provide (often inadmissible) estimates to h + because computing the correct value is an NP-hard problem.
In this work, we consider the approach of planning with the actual h + heuristic from a theoretical and computational perspective. In particular, we provide domain-dependent complexity results that classify some standard benchmark domains into ones where h + can be computed efficiently and ones where computing h + is NP-hard. Moreover, we study domain-dependent implementations of h + which show that the h + heuristic provides very informative heuristic estimates compared to other state-of-the-art heuristics.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Fox, M., Long, D.: PDDL2.1: An extension to PDDL for expressing temporal planning domains. JAIR 20, 61–124 (2003)
Gazen, B.C., Knoblock, C.A.: Combining the expressivity of UCPOP with the efficiency of Graphplan. In: Steel, S. (ed.) ECP 1997. LNCS, vol. 1348, pp. 221–233. Springer, Heidelberg (1997)
Hoffmann, J., Nebel, B.: The FF planning system: Fast plan generation through heuristic search. JAIR 14, 253–302 (2001)
Bylander, T.: The computational complexity of propositional STRIPS planning. AIJ 69(1–2), 165–204 (1994)
Bonet, B., Geffner, H.: Planning as heuristic search. AIJ 129(1), 5–33 (2001)
Mirkis, V., Domshlak, C.: Cost-sharing approximations for h + . In: Proc. ICAPS 2007, pp. 240–247 (2007)
Keyder, E., Geffner, H.: Heuristics for planning with action costs revisited. In: Proc. ECAI 2008, pp. 588–592 (2008)
Keyder, E., Geffner, H.: Trees of shortest paths vs. Steiner trees: Understanding and improving delete relaxation heuristics. In: Proc. IJCAI 2009 (2009)
Richter, S., Helmert, M., Westphal, M.: Landmarks revisited. In: Proc. AAAI 2008, pp. 975–982 (2008)
Karpas, E., Domshlak, C.: Cost-optimal planning with landmarks. In: Proc. IJCAI 2009 (2009)
Haslum, P., Bonet, B., Geffner, H.: New admissible heuristics for domain-independent planning. In: Proc. AAAI 2005, pp. 1163–1168 (2005)
Katz, M., Domshlak, C.: Optimal additive composition of abstraction-based admissible heuristics. In: Proc. ICAPS 2008, pp. 174–181 (2008)
Coles, A., Fox, M., Long, D., Smith, A.: Additive-disjunctive heuristics for optimal planning. In: Proc. ICAPS 2008, pp. 44–51 (2008)
Helmert, M., Geffner, H.: Unifying the causal graph and additive heuristics. In: Proc. ICAPS 2008, pp. 140–147 (2008)
Helmert, M., Haslum, P., Hoffmann, J.: Flexible abstraction heuristics for optimal sequential planning. In: Proc. ICAPS 2007, pp. 176–183 (2007)
Hoffmann, J.: Where ‘ignoring delete lists’ works: Local search topology in planning benchmarks. JAIR 24, 685–758 (2005)
Helmert, M., Mattmüller, R.: Accuracy of admissible heuristic functions in selected planning domains. In: Proc. AAAI 2008, pp. 938–943 (2008)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (1999)
Helmert, M.: Understanding Planning Tasks – Domain Complexity and Heuristic Decomposition. LNCS (LNAI), vol. 4929. Springer, Heidelberg (2008)
Betz, C.: Komplexität und Berechnung der h + -Heuristik. Diplomarbeit, Albert-Ludwigs-Universität Freiburg (2009)
Gupta, N., Nau, D.S.: On the complexity of blocks-world planning. AIJ 56(2–3), 223–254 (1992)
Helmert, M., Mattmüller, R., Röger, G.: Approximation properties of planning benchmarks. In: Proc. ECAI 2006, pp. 585–589 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Betz, C., Helmert, M. (2009). Planning with h + in Theory and Practice. In: Mertsching, B., Hund, M., Aziz, Z. (eds) KI 2009: Advances in Artificial Intelligence. KI 2009. Lecture Notes in Computer Science(), vol 5803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04617-9_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-04617-9_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04616-2
Online ISBN: 978-3-642-04617-9
eBook Packages: Computer ScienceComputer Science (R0)