Pruning Rules for Constrained Optimisation for Conditional Preferences

Abstract

Access to the full text of the published version may require a subscription. Abstract. A depth-first search algorithm can be used to find optimal solutions of a Constraint Satisfaction Problem (CSP) with respect to a set of conditional preferences statements (e.g., a CP-net). This involves checking at each leaf node if the corresponding solution of the CSP is dominated by any of the optimal solutions found so far; if not, then we add this solution to the set of optimal solutions. This kind of algorithm can clearly be computationally expensive if the number of solutions is large. At a node N of the search tree, with associated assignment b to a subset of the variables B, it may happen that, for some previously found solution α, either (a) α dominates all extensions of b; or (b) α does not dominate any extension of b. The algorithm can be significantly improved if we can find sufficient conditions for (a) and (b) that can be efficiently checked. In case (a), we can backtrack since we need not continue the search below N ; in case (b), α does not need to be considered in any node below the current node N . We derive a sufficient condition for (b), and three sufficient conditions for (a). Our experimental testing indicates that this can make a major difference to the efficiency of constrained optimisation for conditional preference theories including CP-nets. Rights

Lexicographically-ordered constraint satisfaction problems

“…With (T)CP-nets, the constrained optimisation problem involves finding the undominated feasible outcomes. For an acyclic CP-net [8], (and similarly, for an acyclic TCP-net [10,47]) one can use a CSP search algorithm to find a single undominated solution, by instantiating variables in an ordering compatible with the parent-child ordering. A "staged lexical" algorithm (see Section 6.2) can also be adapted for this purpose.…”

Sorted Pareto Dominance: An Extension to Pareto Dominance and Its Application in Soft Constraints

“…This improves on the previous algorithm by further eliminating unnecessary dominance checks, but at the cost of performing this extra test. A similar idea in [26] has been shown to be effective in optimisation with respect to comparative preferences.…”

Arc Consistency for Constrained Lexicographic Preference Trees

“…Preferences guide our decisions and every day's activities, hence, they have been a subject of active research in many areas including economics, operation research, artficial intelligence and social choice [1]. Moreover, there are many decision making scenarios where the system is expected to handle users' preferences in a constrained environment [2], [3]. For instance, in product configuration, the user has preferences on different components of the product but some components are not compatible with the each other.…”