Variable ordering and constraint propagation for constrained CP-nets

Abstract

A Conditional Preferences network (CP-net) is a known graphical model for representing qualitative preferences. In many real world applications we are often required to manage both constraints and preferences in an efficient way. The goal here is to select one or more scenarios that are feasible according to the constraints while maximizing a given utility function. This problem has been modelled as a CP-net where some variables share a set of constraints. This latter framework is called a Constrained CP-net. Solving the constrained CP-net has been proposed in the past using a variant of the branch and bound algorithm called Search CP. In this paper, we experimentally study the effect of variable ordering heuristics and constraint propagation when solving a constrained CP-net using a backtrack search algorithm. More precisely, we investigate several look ahead strategies as well as the most constrained heuristic for variable ordering during search. The results of the experiments conducted on random Constrained CP-net instances generated through the RB model, clearly show a significant improvement when adopting these techniques for specific graph structures as well as the case where a large number of variables are sharing constraints.