Possibilistic Constraint Satisfaction Problems or "How to handle soft constraints?"
This work addresses the need for modeling uncertain constraints in real-world AI tasks such as job-shop scheduling, but it is incremental as it extends existing CSP techniques.
The paper tackles the problem of handling soft constraints in AI synthesis tasks like planning and scheduling by formalizing possibilistic constraint satisfaction problems, using possibility distributions and necessity-valued constraints to model uncertainly satisfied constraints, and demonstrates its utility on a simple design problem.
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all given constraints between these variables. However, for many real tasks such as job-shop scheduling, time-table scheduling, design?, all these constraints have not the same significance and have not to be necessarily satisfied. A first distinction can be made between hard constraints, which every solution should satisfy and soft constraints, whose satisfaction has not to be certain. In this paper, we formalize the notion of possibilistic constraint satisfaction problems that allows the modeling of uncertainly satisfied constraints. We use a possibility distribution over labelings to represent respective possibilities of each labeling. Necessity-valued constraints allow a simple expression of the respective certainty degrees of each constraint. The main advantage of our approach is its integration in the CSP technical framework. Most classical techniques, such as Backtracking (BT), arcconsistency enforcing (AC) or Forward Checking have been extended to handle possibilistics CSP and are effectively implemented. The utility of our approach is demonstrated on a simple design problem.