Planning with h +  in Theory and Practice

  • Christoph Betz
  • Malte Helmert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5803)

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.

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References

  1. 1.
    Fox, M., Long, D.: PDDL2.1: An extension to PDDL for expressing temporal planning domains. JAIR 20, 61–124 (2003)MATHGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Hoffmann, J., Nebel, B.: The FF planning system: Fast plan generation through heuristic search. JAIR 14, 253–302 (2001)MATHGoogle Scholar
  4. 4.
    Bylander, T.: The computational complexity of propositional STRIPS planning. AIJ 69(1–2), 165–204 (1994)MathSciNetMATHGoogle Scholar
  5. 5.
    Bonet, B., Geffner, H.: Planning as heuristic search. AIJ 129(1), 5–33 (2001)MathSciNetMATHGoogle Scholar
  6. 6.
    Mirkis, V., Domshlak, C.: Cost-sharing approximations for h  + . In: Proc. ICAPS 2007, pp. 240–247 (2007)Google Scholar
  7. 7.
    Keyder, E., Geffner, H.: Heuristics for planning with action costs revisited. In: Proc. ECAI 2008, pp. 588–592 (2008)Google Scholar
  8. 8.
    Keyder, E., Geffner, H.: Trees of shortest paths vs. Steiner trees: Understanding and improving delete relaxation heuristics. In: Proc. IJCAI 2009 (2009)Google Scholar
  9. 9.
    Richter, S., Helmert, M., Westphal, M.: Landmarks revisited. In: Proc. AAAI 2008, pp. 975–982 (2008)Google Scholar
  10. 10.
    Karpas, E., Domshlak, C.: Cost-optimal planning with landmarks. In: Proc. IJCAI 2009 (2009)Google Scholar
  11. 11.
    Haslum, P., Bonet, B., Geffner, H.: New admissible heuristics for domain-independent planning. In: Proc. AAAI 2005, pp. 1163–1168 (2005)Google Scholar
  12. 12.
    Katz, M., Domshlak, C.: Optimal additive composition of abstraction-based admissible heuristics. In: Proc. ICAPS 2008, pp. 174–181 (2008)Google Scholar
  13. 13.
    Coles, A., Fox, M., Long, D., Smith, A.: Additive-disjunctive heuristics for optimal planning. In: Proc. ICAPS 2008, pp. 44–51 (2008)Google Scholar
  14. 14.
    Helmert, M., Geffner, H.: Unifying the causal graph and additive heuristics. In: Proc. ICAPS 2008, pp. 140–147 (2008)Google Scholar
  15. 15.
    Helmert, M., Haslum, P., Hoffmann, J.: Flexible abstraction heuristics for optimal sequential planning. In: Proc. ICAPS 2007, pp. 176–183 (2007)Google Scholar
  16. 16.
    Hoffmann, J.: Where ‘ignoring delete lists’ works: Local search topology in planning benchmarks. JAIR 24, 685–758 (2005)MATHGoogle Scholar
  17. 17.
    Helmert, M., Mattmüller, R.: Accuracy of admissible heuristic functions in selected planning domains. In: Proc. AAAI 2008, pp. 938–943 (2008)Google Scholar
  18. 18.
    Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and Approximation. Springer, Heidelberg (1999)CrossRefMATHGoogle Scholar
  19. 19.
    Helmert, M.: Understanding Planning Tasks – Domain Complexity and Heuristic Decomposition. LNCS (LNAI), vol. 4929. Springer, Heidelberg (2008)MATHGoogle Scholar
  20. 20.
    Betz, C.: Komplexität und Berechnung der h + -Heuristik. Diplomarbeit, Albert-Ludwigs-Universität Freiburg (2009)Google Scholar
  21. 21.
    Gupta, N., Nau, D.S.: On the complexity of blocks-world planning. AIJ 56(2–3), 223–254 (1992)MathSciNetMATHGoogle Scholar
  22. 22.
    Helmert, M., Mattmüller, R., Röger, G.: Approximation properties of planning benchmarks. In: Proc. ECAI 2006, pp. 585–589 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Christoph Betz
    • 1
  • Malte Helmert
    • 1
  1. 1.Institut für InformatikAlbert-Ludwigs-Universität FreiburgFreiburgGermany

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