Heuristics for Planning with Action Costs

  • Emil Keyder
  • Hector Geffner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4788)


We introduce a non-admissible heuristic for planning with action costs, called the set-additive heuristic, that combines the benefits of the additive heuristic used in the HSP planner and the relaxed plan heuristic used in FF. The set-additive heuristic \(h^s_a\) is defined mathematically and handles non-uniform action costs like the additive heuristic h a , and yet like FF’s heuristic \(h_{\textrm{\scriptsize FF}}\), it encodes the cost of a specific relaxed plan and is therefore compatible with FF’s helpful action pruning and its effective enforced hill climbing search. The definition of the set-additive heuristic is obtained from the definition of the additive heuristic, but rather than propagating the value of the best supports for a precondition or goal, it propagates the supports themselves, which are then combined by set-union rather than by addition. We report then empirical results on a planner that we call FF(\(h^s_a\)) that is like FF except that the relaxed plan is extracted from the set-additive heuristic. The results show that FF(\(h^s_a\)) adds only a slight time overhead over FF but results in much better plans when action costs are not uniform.


Planning Graph Action Cost Helpful Action Classical Planning Additive Heuristic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bonet, B., Geffner, H.: Planning as heuristic search. Artificial Intelligence 129(1-2), 5–33 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Hoffmann, J., Nebel, B.: The FF planning system: Fast plan generation through heuristic search. Journal of Artificial Intelligence Research 14, 253–302 (2001)zbMATHGoogle Scholar
  3. 3.
    Sapena, O., Onaindia, E.: Handling numeric criteria in relaxed planning graphs. In: Lemaître, C., Reyes, C.A., González, J.A. (eds.) IBERAMIA 2004. LNCS (LNAI), vol. 3315, pp. 114–123. Springer, Heidelberg (2004)Google Scholar
  4. 4.
    Fuentetaja, R., Borrajo, D., Linares, C.: Improving relaxed planning graph heuristics for metric optimization. In: Proc. 2006 AAAI Workshop on Heuristic Search, Memory Based Heuristics and its Applications, pp. 79–86 (2006)Google Scholar
  5. 5.
    Blum, A., Furst, M.: Fast planning through planning graph analysis. In: Proceedings of IJCAI 1995, pp. 1636–1642. Morgan Kaufmann, San Francisco (1995)Google Scholar
  6. 6.
    Haslum, P., Geffner, H.: Admissible heuristics for optimal planning. In: AIPS-2000. Proc. of the Fifth International Conference on AI Planning Systems, pp. 70–82 (2000)Google Scholar
  7. 7.
    Bonet, B., Loerincs, G., Geffner, H.: A robust and fast action selection mechanism for planning. In: Proceedings of AAAI 1997, pp. 714–719. MIT Press, Cambridge (1997)Google Scholar
  8. 8.
    Do, M.B., Kambhampati, S.: Sapa: A domain-independent heuristic metric temporal planner. In: Proc. ECP 2001, pp. 82–91 (2001)Google Scholar
  9. 9.
    Smith, D.E.: Choosing objectives in over-subscription planning. In: Proc. ICAPS 2004, pp. 393–401 (2004)Google Scholar
  10. 10.
    Bertsekas, D.: Linear Network Optimization: Algorithms and Codes. MIT Press, Cambridge (1991)zbMATHGoogle Scholar
  11. 11.
    Cormen, T.H., Leiserson, C.E., Rivest, R.L.: Introduction to Algorithms. MIT Press, Cambridge (1989)Google Scholar
  12. 12.
    Liu, Y., Koenig, S., Furcy, D.: Speeding up the calculation of heuristics for heuristic search-based planning. In: Proc AAAI 2002, pp. 484–491 (2002)Google Scholar
  13. 13.
    Blizard, W.D.: Multiset theory. Notre Dame J. Formal Logic 30(1), 36–66 (1988)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Hoffmann, J.: The metric-ff planning system: Translating ”ignoring delete lists” to numeric state variables. J. Artif. Intell. Res (JAIR) 20, 291–341 (2003)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Emil Keyder
    • 1
  • Hector Geffner
    • 2
  1. 1.Universitat Pompeu Fabra, Passeig de Circumvalació 8, 08003 BarcelonaSpain
  2. 2.ICREA & Universitat Pompeu Fabra, Passeig de Circumvalació 8, 08003 BarcelonaSpain

Personalised recommendations