This paper provides a technique for solving general constraint satisfaction problems (CSPs) with continuous variables. Constraints are represented by a hierarchical binary decomposition of the space of feasible values. We propose algorithms for path-and higher degrees of consistency based on logical operations defined on this representation and demonstrate that the algorithms terminate in polynomial time. We show that, in analogy to convex temporal problems and discrete row-convex problems, convexity properties of the solution spaces can be exploited to compute minimal and decomposable networks using path consistency algorithms. Based on these properties, we also show that a certain class of non binary CSPs can be solved using strong 5-consistency.

Much of preliminary engineering design is a constraint-driven non-monotonic exploration process. Initial decisions are made when information is incomplete and many goals are contradictory. Such conditions are present regardless of whether one or several designers contribute to designs. This paper presents an approach for supporting decisions in situations of incomplete and conflicting knowledge. In particular, we use assumptions and conflict management to achieve efficient search in contexts where little reliable information exists. A knowledge representation, containing a semantic differentiation between two types of assumptions, is used within a computational model based on the dynamic constraint satisfaction paradigm. Conflict management strategies consist of three generic mechanisms adapted to the type of constraints involved. These strategies may be refined through consideration of variable importance, context, and design inertia.

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