Hard and soft constraints for reasoning about qualitative conditional preferences

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.

[1]  Ronen I. Brafman,et al.  UCP-Networks: A Directed Graphical Representation of Conditional Utilities , 2001, UAI.

[2]  Carmel Domshlak,et al.  Reasoning about soft constraints and conditional preferences: complexity results and approximation techniques , 2003, IJCAI.

[3]  Miroslaw Truszczynski,et al.  The computational complexity of dominance and consistency in CP-nets , 2005, IJCAI.

[4]  Francesca Rossi,et al.  Semiring-based constraint solving and optimization , 1997 .

[5]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6]  Ronen I. Brafman,et al.  Reasoning With Conditional Ceteris Paribus Preference Statements , 1999, UAI.

[7]  J. Doyle,et al.  Representing Preferences as Ceteris Paribus Comparatives , 1994 .

[8]  Jon Doyle,et al.  Efficient utility functions for ceteris paribus preferences , 2002, AAAI/IAAI.

[9]  Thomas Schiex,et al.  Semiring-Based CSPs and Valued CSPs: Basic Properties and Comparison , 1995, Over-Constrained Systems.

[10]  N. S. Barnett,et al.  Private communication , 1969 .

[11]  D. Dubois,et al.  The calculus of fuzzy restrictions as a basis for flexible constraint satisfaction , 1993, [Proceedings 1993] Second IEEE International Conference on Fuzzy Systems.

[12]  Ronen I. Brafman,et al.  CP-nets: Reasoning and Consistency Testing , 2002, KR.

[13]  Thomas Schiex,et al.  Selecting preferred solutions in Fuzzy Constraint Satisfaction Problems , 1993 .

[14]  Ronen I. Brafman,et al.  Extended Semantics and Optimization Algorithms for CP‐Networks , 2004, Comput. Intell..

[15]  Richard J. Wallace,et al.  Partial Constraint Satisfaction , 1989, IJCAI.

[16]  Jon Doyle,et al.  Background to Qualitative Decision Theory , 1999, AI Mag..

[17]  Jérôme Lang,et al.  From Preference Representation to Combinatorial Vote , 2002, KR.

[18]  Ronen I. Brafman,et al.  CP-nets: A Tool for Representing and Reasoning withConditional Ceteris Paribus Preference Statements , 2011, J. Artif. Intell. Res..

[19]  Francesca Rossi,et al.  Semiring-based constraint satisfaction and optimization , 1997, JACM.

[20]  Thomas Schiex,et al.  Possibilistic Constraint Satisfaction Problems or "How to Handle Soft Constraints?" , 1992, UAI.

[21]  Thomas Schiex,et al.  Valued Constraint Satisfaction Problems: Hard and Easy Problems , 1995, IJCAI.

[22]  Daniel Sabin,et al.  Product Configuration Frameworks - A Survey , 1998, IEEE Intell. Syst..

[23]  Toby Walsh,et al.  Constraint-Based Preferential Optimization , 2005, AAAI.

[24]  Ronen I. Brafman,et al.  Preference‐Based Constrained Optimization with CP‐Nets , 2004, Comput. Intell..