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Constraints

, Volume 23, Issue 4, pp 383–402 | Cite as

Translation-based approaches for solving disjunctive temporal problems with preferences

  • Enrico Giunchiglia
  • Marco MarateaEmail author
  • Luca Pulina
Article
  • 76 Downloads

Abstract

Disjunctive Temporal Problems (DTPs) with Preferences (DTPPs) extend DTPs with piece-wise constant preference functions associated to each constraint of the form lxyu, where x,y are (real or integer) variables, and l,u are numeric constants. The goal is to find an assignment to the variables of the problem that maximizes the sum of the preference values of satisfied DTP constraints, where such values are obtained by aggregating the preference functions of the satisfied constraints in it under a “max” semantic. The state-of-the-art approach in the field, implemented in the native DTPP solver Maxilitis, extends the approach of the native DTP solver Epilitis. In this paper we present alternative approaches that translate DTPPs to Maximum Satisfiability of a set of Boolean combination of constraints of the form lxyu, ⋈ ∈{<,≤}, that extend previous work dealing with constant preference functions only. We prove correctness and completeness of the approaches. Results obtained with the Satisfiability Modulo Theories (SMT) solvers Yices and MathSAT on randomly generated DTPPs and DTPPs built from real-world benchmarks, show that one of our translation is competitive to, and can be faster than, Maxilitis (This is an extended and revised version of Bourguet et al. 2013).

Keywords

Disjunctive temporal problems Preferences 

Notes

Acknowledgments

The authors would like to thank the reviewers for useful comments and criticisms. They would like to thank also Michael D. Moffitt for providing his solvers and the program for generating random benchmarks, and Bruno Dutertre for his support about Yices.

References

  1. 1.
    Bourguet, J.R., Maratea, M., Pulina, L. (2013). A reduction-based approach for solving disjunctive temporal problems with preferences. In M. Baldoni, C. Baroglio, G. Boella, R. Micalizio (Eds.) Proceedings of the 13th international conference of the Italian association for artificial intelligence (AI*IA): advances in artificial intelligence. Volume 8249 of lecture notes in computer science (pp. 445–456). Berlin: Springer.Google Scholar
  2. 2.
    Dechter, R., Meiri, I., Pearl, J. (1991). Temporal constraint networks. Artificial Intelligence, 49(1–3), 61–95.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Pollack, M.E. (2005). Intelligent technology for an aging population: the use of AI to assist elders with cognitive impairment. AI Magazine, 26(2), 9–24.Google Scholar
  4. 4.
    Berry, P.M., Gervasio, M.T., Uribe, T.E., Pollack, M.E., Moffitt, M.D. (2005). A personalized time management assistant: research directions. In Persistent assistants: living and working with ai, papers from the 2005 AAAI spring symposium, technical Report SS-05-05 (pp. 1–6). Stanford: AAAI.Google Scholar
  5. 5.
    Berry, P.M., Gervasio, M.T., Peintner, B., Yorke-Smith, N. (2007). A preference model for over-constrained meeting requests. In Proceedings of the AAAI 2007 workshop on preference handling for artificial intelligence (pp. 7–14).Google Scholar
  6. 6.
    Moffitt, M.D. (2011). On the modelling and optimization of preferences in constraint-based temporal reasoning. Artificial Intelligence, 175(7–8), 1390–1409.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Tsamardinos, I., & Pollack, M. (2003). Efficient solution techniques for disjunctive temporal reasoning problems. Artificial Intelligence, 151, 43–89.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Sheini, H.M., Peintner, B., Sakallah, K.A., Pollack, M.E. (2005). On solving soft temporal constraints using SAT techniques. In P. van Beek (Ed.) Proceedings of the 11th international conference on principles and practice of constraint programming (CP 2005). Volume 3709 of lecture notes in computer science (pp. 607–621). Berlin: Springer.Google Scholar
  9. 9.
    Moffitt, M.D., & Pollack, M.E. (2005). Partial constraint satisfaction of disjunctive temporal problems. In I. Russell, & Z. Markov (Eds.) Proceedings of the 18th international conference of the Florida artificial intelligence research society (FLAIRS 2005) (pp. 715–720). AAAI Press.Google Scholar
  10. 10.
    Moffitt, M.D., & Pollack, M.E. (2006). Temporal preference optimization as weighted constraint satisfaction. In Proceedings of the 21st national conference on artificial intelligence (AAAI 2006). AAAI Press.Google Scholar
  11. 11.
    Peintner, B., & Pollack, M.E. (2004). Low-cost addition of preferences to DTPs and TCSPs. In D.L. McGuinness, & G. Ferguson (Eds.) Proceedings of the 19th national conference on artificial intelligence (AAAI 2004) (pp. 723–728). AAAI Press/The MIT Press.Google Scholar
  12. 12.
    Peintner, B., Moffitt, M.D., Pollack, M.E. (2005). Solving over-constrained disjunctive temporal problems with preferences. In S. Biundo, K.L. Myers, K. Rajan (Eds.) Proceedings of the 15th international conference on automated planning and scheduling (ICAPS 2005) (pp. 202–211). AAAI.Google Scholar
  13. 13.
    Maratea, M., & Pulina, L. (2012). Solving disjunctive temporal problems with preferences using maximum satisfiability. AI Commuications, 25(2), 137–156.MathSciNetzbMATHGoogle Scholar
  14. 14.
    Stergiou, K., & Koubarakis, M. (1998). Backtracking algorithms for disjunctions of temporal constraints. In H.E. Shrobe, T.M. Mitchell, R.G. Smith (Eds.) Proceedings of the 15th national conference on artificial intelligence (AAAI 1998) (pp. 248–253). AAAI Press/The MIT Press.Google Scholar
  15. 15.
    Armando, A., Castellini, C., Giunchiglia, E. (1999). SAT-based procedures for temporal reasoning. In S. Biundo, & M. Fox (Eds.) Proceedings of the 5th European conference on planning (ICAPS 1999). Volume 1809 of lecture notes in computer science (pp. 97–108). Berlin: Springer.Google Scholar
  16. 16.
    Cimatti, A., Griggio, A., Schaafsma, B.J., Sebastiani, R. (2013). The MathSAT5 SMT solver. In N. Piterman, & S.A. Smolka (Eds.) Proceedings of the 19th international conference on tools and algorithms for the construction and analysis of systems (TACAS 2013). Volume 7795 of lecture notes in computer science (pp. 93–107). Berlin: Springer.Google Scholar
  17. 17.
    Sebastiani, R., & Trentin, P. (2015). OptiMathSAT: a tool for optimization modulo theories. In D. Kroening, & C.S. Pasareanu (Eds.) Proceedings of the 27th international conference of computer aided verification (CAV 2015). Volume 9206 of lecture notes in computer science (pp. 447–454). Berlin: Springer.Google Scholar
  18. 18.
    Dutertre, B., & Moura, L.D. (2006). A fast linear-arithmetic solver for DPLL (T). In T. Ball, & R.B. Jones (Eds.) Proceedings of the 18th international conference on computer aided verification (CAV 2006). Volume 4144 of lecture notes in computer science (pp. 81–94). Berlin: Springer.Google Scholar
  19. 19.
    Dutertre, B., & De Moura, L. (2006). The Yices SMT solver. Tool paper at http://yices.csl.sri.com/tool-paper.pdf 2(2).
  20. 20.
    Peintner, B.M. (2005). Algorithms for constraint-based temporal reasoning with preferences. Ann Arbor: University of Michigan.Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DIBRIS - University of GenovaGenovaItaly
  2. 2.POLCOMING - University of SassariSassariItaly

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