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Constraint satisfaction is a fundamental Artificial Intelligence technique for knowledge representation and inference. However, the formulation of a static constraint satisfaction problem (CSP) with hard, imperative constraints is insufficient to model many real problems. Fuzzy constraint satisfaction provides a more graded viewpoint. Priorities and preferences are placed on individual constraints and aggregated via fuzzy conjunction to obtain a satisfaction degree for a solution to the problem. This paper examines methods for solving an important instance of dynamic flexible constraint satisfaction (DFCSP) combining fuzzy CSP and restriction/relaxation based dynamic CSP: fuzzy rrDFCSP. This allows the modelling of complex situations where both the set of constraints may change over time and there is flexibility inherent in the definition of the problem. This paper also presents a means by which classical planning can be extended via fuzzy sets to enable flexible goals and preferences to be placed on the use of planning operators. A range of plans can be produced, trading compromises made versus the length of the plan. The flexible planning operators are close in definition to fuzzy constraints. Hence, through a hierarchical decomposition of the planning graph, the work shows how flexible planning reduces to the solution of a set of fuzzy rrDFCSPs.

This paper summarizes the main existing approaches to propagate resource constraints in Constraint-Based scheduling and identifies some of their limitations for using them in an integrated planning and scheduling framework. We then describe two new algorithms to propagate resource constraints on discrete resources and reservoirs. Unlike most of the classical work in scheduling, our algorithms focus on the precedence relations between activities rather than on their absolute position in time. They are efficient even when the set of activities is not completely defined and when the time window of activities is large. These features explain why our algorithms are particularly suited for integrated planning and scheduling approaches. All our algorithms are illustrated with examples. Encouraging preliminary results are reported on pure scheduling problems as well as some possible extensions of our framework.