Possibilistic Constraint Satisfaction Problems or "How to handle soft constraints?"

TL;DR

This paper introduces possibilistic constraint satisfaction problems (CSPs) to model and solve problems with soft constraints by incorporating uncertainty and necessity measures, extending classical CSP techniques.

Contribution

It formalizes possibilistic CSPs with possibility distributions and necessity constraints, integrating soft constraints into the classical CSP framework with extended algorithms.

Findings

Extended classical CSP algorithms to handle possibilistic constraints

Effectively implemented possibilistic CSP techniques on a design problem

Demonstrated the approach's utility in modeling uncertain constraints

Abstract

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.