Journal of Heuristics

, Volume 12, Issue 4, pp 263–285

Hard and soft constraints for reasoning about qualitative conditional preferences


  • C. Domshlak
    • William Davidson Faculty of Industrial Engineering and ManagementTechnion—Israel Institute of Technology
  • S. Prestwich
    • Department of Computer ScienceUniversity College Cork
  • F. Rossi
    • Department of MathematicsUniversity of Padova
    • Department of MathematicsUniversity of Padova
  • T. Walsh
    • National ICT Australia and School of Computer Science and EngineeringUniversity of New South Wales

DOI: 10.1007/s10732-006-7071-x

Cite this article as:
Domshlak, C., Prestwich, S., Rossi, F. et al. J Heuristics (2006) 12: 263. doi:10.1007/s10732-006-7071-x


Many real life optimization problems are defined in terms of both hard and soft constraints, and qualitative conditional preferences. However, there is as yet no single framework for combined reasoning about these three kinds of information. In this paper we study how to exploit classical and soft constraint solvers for handling qualitative preference statements such as those captured by the CP-nets model. In particular, we show how hard constraints are sufficient to model the optimal outcomes of a possibly cyclic CP-net, and how soft constraints can faithfully approximate the semantics of acyclic conditional preference statements whilst improving the computational efficiency of reasoning about these statements.


PreferencesHard and Soft ConstraintsCP-nets

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© Springer Science + Business Media, LLC 2006