Skip to main content

Temporal Planning through Mixed Integer Programming: A Preliminary Report

  • Conference paper
  • First Online:
Book cover Principles and Practice of Constraint Programming - CP 2002 (CP 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2470))

Abstract

Temporal planning is an important problem, as in many real world planning domains actions have different durations and the goals should be achieved by a specified deadline, or as soon as possible. This paper presents a novel approach to temporal planning that is based on Mixed Integer Programming. In the new framework, a temporal planning domain is modeled by two sets of linear inequalities. The first set involves integer variables and is a Graphplan-like encoding of a simplification of the original problem where the duration of the actions is ignored. The second set involves both integer and real valued variables, and models the temporal aspects of the problem. The two sets interact through the common integer variables, and their combination can be solved by using available Mixed Integer Programming software. The new method aims at generating good solutions quickly, under different minimization objectives. Preliminary experimental results illustrate the effectiveness of our approach.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Allen. Temporal reasoning and planning. In J. Allen, H. Kautz, R. Pelavin, and J. Tenenberg, editors, Reasoning about Plans, San Mateo, CA, 1991. Morgan Kaufmann.

    Google Scholar 

  2. P. Barth and A. Bockmayr. Modelling discrete optimisation problems in constraint logic programming. Annals of Operations Research, 81, 1998.

    Google Scholar 

  3. Y. Dimopoulos. Improved integer programming models and heuristic search for AI planning. In Proceedings of ECP-01. Springer Verlag, 2001.

    Google Scholar 

  4. M. B. Do and S. Kambhampati. Sapa: A domain-independent heuristic metric temporal planner. In Proceedings of ECP-01. Springer Verlag, 2001.

    Google Scholar 

  5. M. Fox and D. Long. The automatic inference of state invariants in TIM. JAIR, 9:367–421, 1998.

    MATH  Google Scholar 

  6. M. Fox and D. Long. PDDL2.1: An extension to PDDL for expressing temporal planning domains. Technical report, University of Durham, UK, 2001.

    Google Scholar 

  7. A. Gerevini and L. Schubert. Inferring state constraints for domain-independent planning. In Proceedings of AAAI-98, 1998.

    Google Scholar 

  8. A. Gerevini and L. Schubert. Discovering state constraints in DISCOPLAN: Some new results. In Proceedings of AAAI-00, 2000.

    Google Scholar 

  9. A. Gerevini and I. Serina. LPG: a planner based on planning graphs with action costs. In Proceedings of AIPS’02, 2002.

    Google Scholar 

  10. P. Haslum and H. Geffner. Heuristic planning with time and resources. In Proceedings of ECP-01. Springer Verlag, 2001.

    Google Scholar 

  11. H. Kautz and J. Walser. State-space planning by integer optimization. In Proceedings of AAAI-99, 1999.

    Google Scholar 

  12. J. Penberthy and D. Weld. Temporal planning with continuous change. In Proceedings of AAAI-94, pages 1010–1015, Seattle, WA, 1994. Morgan Kaufmann.

    Google Scholar 

  13. D. Smith and D. Weld. Temporal planning with mutual exclusive reasoning. In Proceedings of IJCAI-99, 1999.

    Google Scholar 

  14. E. Tsang. Plan generation in a temporal framework. In Proceedings of ECAI-96, pages 479–493, 1986.

    Google Scholar 

  15. T. Vossen, M. Ball, A. Lotem, and D. Nau. On the use of integer programming models in AI planning. In Proceedings of IJCAI-99, 1999.

    Google Scholar 

  16. D. Weld. Recent advances in AI planning. AI Magazine, 20(2), 1999.

    Google Scholar 

  17. S. Wolfman and D. Weld. The LPSAT engine and its application to resource planning. In Proceedings of IJCAI-99, 1999.

    Google Scholar 

  18. L. Wolsey. Integer Programming. John Wiley and Sons, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dimopoulos, Y., Gerevini, A. (2002). Temporal Planning through Mixed Integer Programming: A Preliminary Report. In: Van Hentenryck, P. (eds) Principles and Practice of Constraint Programming - CP 2002. CP 2002. Lecture Notes in Computer Science, vol 2470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46135-3_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-46135-3_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44120-5

  • Online ISBN: 978-3-540-46135-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics