Advertisement

Abstract

The lexicographically-ordered CSP (“lexicographic CSP” for short) combines a simple representation of preferences with the feasibility constraints of ordinary CSPs. Preferences are defined by a total ordering across all assignments, such that a change in assignment to variable k is more important than any change in assignment to any variable that comes after it in the ordering. In this paper, we show how this representation can be extended to handle conditional preferences. This can be done in two ways. In the first, for each conditional preference relation, the parents have higher priority than the children in the original lexicographic ordering. In the second, the relation between parents and children need not correspond to the basic ordering of variables. For problems of the first type, any of the algorithms originally devised for ordinary lexicographic CSPs can also be used when some of the domain orderings are dependent on the assignments to “parent” variables. For problems of the second type, algorithms based on lexical orders can be used if the representation is augmented by variables and constraints that link preference orders to assignments. In addition, the branch-and-bound algorithm originally devised for ordinary lexicographic CSPs can be extended to handle CSPs with conditional domain orderings.

Keywords

Total Order Constraint Satisfaction Problem Lexicographic Order Soft Constraint Satisfying Assignment 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Boutilier, C., Brafman, R.I., Hoos, H.H., Poole, D.: Reasoning with conditional ceteris paribus preference statements. In: Proc. Fifteenth Annual Conf. on Uncertainty in Artif. Intell., pp. 71–80 (1999)Google Scholar
  2. 2.
    Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H.H., Poole, D.: CP-nets: A tool for representing and reasoning with conditional ceteris paribus preference statements. Journal of Artificial Intelligence Research, 135–191 (2004)Google Scholar
  3. 3.
    Wellman, M.P., Doyle, J.: Preferential semantics for goals. In: Proc. Nineth Nat. Conf. on Artif. Intell., pp. 698–703 (1991)Google Scholar
  4. 4.
    Freuder, E.C., Wallace, R.J., Heffernan, R.: Ordinal constraint satisfaction. In: Fifth Internat. Workshop on Soft Constraints - SOFT 2002 (2003)Google Scholar
  5. 5.
    Boutilier, C., Brafman, R.I., Domshlak, C., Hoos, H., Poole, D.: Preference-based constrained optimization with CP-nets. Computational Intelligence, 137–157 (2004)Google Scholar
  6. 6.
    Schiex, T., Fargier, H., Verfaillie, G.: Valued constraint satisfaction problems: Hard and easy problems. In: Proc. Fourteenth Internat. Joint Conf. on Artif. Intell., pp. 631–637 (1995)Google Scholar
  7. 7.
    Brafman, R.I., Domshlak, C.: Introducing variable importance tradeoffs into CP-nets. In: Proc. Eighteenth Annual Conf. on Uncertainty in Artif. Intell. (2002)Google Scholar
  8. 8.
    Wilson, N.: Consistency and constrained optimisation for conditional preferences. In: Proc. Sixteenth Europ. Conf. on Artific. Intell., pp. 888–892 (2004)Google Scholar
  9. 9.
    Wilson, N.: Extending CP-nets with stronger conditional preference statements. In: Proc. Nineteenth Nat. Conf. on Artif. Intell., pp. 735–741 (2004)Google Scholar
  10. 10.
    Domshlak, C., Brafman, R.I.: CP-nets - reasoning and consistency testing. In: Proc. Eighth Conf. on Principles of Knowledge Representation and Reasoning, pp. 121–132 (2002)Google Scholar
  11. 11.
    Goldsmith, J., Lang, J., Truszczynski, M., Wilson, N.: The computational complexity of dominance and consistency in CP-nets. In: Proc. Nineteenth Int. Jt. Conf. on Artif. Intell (IJCAI 2005), pp. 144–149 (2005)Google Scholar
  12. 12.
    Freuder, E.C., Heffernan, R., Prestwich, S., Wallace, R.J., Wilson, N.: Lexicographically-ordered constraint satisfaction problems (2005) (unpublished)Google Scholar
  13. 13.
    Junker, U.: Preference-based search and multi-criteria optimization. In: Proc. Eighteenth Nat. Conf. on Artif. Intell., pp. 34–40 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Richard J. Wallace
    • 1
  • Nic Wilson
    • 1
  1. 1.Cork Constraint Computation Center and Department of Computer ScienceUniversity College CorkCorkIreland

Personalised recommendations