FCP-Nets: extending constrained CP-nets with objective functions

CP-Nets are a framework for dealing with qualitative preferences, both conditional and unconditional. They have received a lot of attention recently, and many extensions have been provided. In particular, the framework of constrained CP-Nets aims to choose, amongst the solutions that satisfy a set of constraints, the preferred one. While the semantics of CP-Nets allows for cycles (and, indeed, cyclic CP-Nets occur in real-life problems), current algorithms are not always able to select the preferred solution in the presence of cycles. This means that, although there might exist feasible solutions, current algorithms are unable (in unlucky instances) to provide a preferred solution, and they simply fail, providing no answer to the user. In this work, we propose FCP-Net, that is, a framework that adds an objective function to a constrained CP-Net. The objective function (essential in many constraint applications) is able to convey quantitative information into the CP-Net. Besides the higher expressivity of FCP-Nets, we are able to provide a single, best preferred solution in all feasible instances (those in which there is at least a solution), paving the way to a wider use of CP-Nets in practical applications.