Arc Consistency for Constrained Lexicographic Preference Trees

Abstract

Many AI applications such as recommendation systems and personalized planning require handling both constraints and preferences. In such applications, constraints can be viewed as restrictions to the solution space where preferences are the medium to identify preferred solutions. We consider here the problem of constrained Lexicographic Preference Tree (LP-tree) where a set of constraints co-exist with the preference information represented as LP-tree. The goal is to return the most preferred and feasible solution. We show that applying a well-known constraint propagation technique known as Arc Consistency (AC) simplifies the problem and can be utilized to construct an updated version of the original LP-tree that is much simpler. Furthermore, an important computational task in LP-trees is the dominance testing which asserts, given two solutions, which one is better according to the preference information. We formally show that the naive Backtracking algorithm can be adopted to solve the problem without performing any dominance testing in case variables and their domains are ordered based on the LP-tree. The empirical results conducted on the new structure show the feasibility of applying AC to further simplify the problem and solve it.