Abstract
The CP-net and the LP-tree are two fundamental graphical models for representing user’s qualitative preferences. Constrained CP-nets have been studied in the past in which a very expensive operation, called dominance testing, between outcomes is required. In this paper, we propose a recursive backtrack search algorithm that we call Search-LP to find the most preferable feasible outcome for an LP-tree extended to a set of hard constraints. Search-LP instantiates the variables with respect to a hierarchical order defined by the LP-tree. Since the LP-tree represents a total order over the outcomes, Search-LP simply returns the first feasible outcome without performing dominance testing. We prove that this returned outcome is preferable to every other feasible outcome.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ahmed, S., Mouhoub, M.: Constrained optimization with partial CP-nets. In: IEEE International Conference on Systems, Man, and Cybernetics, pp. 3361–3366 (2018)
Booth, R., Chevaleyre, Y., Lang, J., Mengin, J., Sombattheera, C.: Learning conditionally lexicographic preference relations. In: Proceedings of 19th European Conference on Artificial Intelligence, pp. 269–274 (2010)
Boutilier, C., Brafman, R., Domshlak, C., Hoos, H., Poole, D.: Preference-based constrained optimization with CP-nets. Comput. Intell. 20, 137–157 (2004)
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. J. Artif. Intell. Res. (JAIR) 21, 135–191 (2004)
Freuder, E.C., Wallace, R.J., Heffernan, R.: Ordinal constraint satisfaction. In: Fifth International Workshop on Soft Constraints (2003)
Keeney, R.L., Raiffa, H.: Decisions with Multiple Objectives: Preferences and Value Trade-Offs. Cambridge University Press, New York (1993)
Wallace, R.J., Wilson, N.: Conditional lexicographic orders in constraint satisfaction problems. In: Beck, J.C., Smith, B.M. (eds.) CPAIOR 2006. LNCS, vol. 3990, pp. 258–272. Springer, Heidelberg (2006). https://doi.org/10.1007/11757375_21
Yong, K.W., Mouhoub, M.: Using conflict and support counts for variable and value ordering in CSPs. Appl. Intell. 48(8), 2487–2500 (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Ahmed, S., Mouhoub, M. (2019). Lexicographic Preference Trees with Hard Constraints. In: Meurs, MJ., Rudzicz, F. (eds) Advances in Artificial Intelligence. Canadian AI 2019. Lecture Notes in Computer Science(), vol 11489. Springer, Cham. https://doi.org/10.1007/978-3-030-18305-9_31
Download citation
DOI: https://doi.org/10.1007/978-3-030-18305-9_31
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-18304-2
Online ISBN: 978-3-030-18305-9
eBook Packages: Computer ScienceComputer Science (R0)