Realizing a Global Hyperpolyhedron Constraint via LP Techniques

Combination of AI/OR methods is gaining a great deal of attention because many combinatorial problems especially in planning and scheduling areas can be solved by means of combined AI/OR techniques. Many of these combinatorial problems can be expressed in a natural way as a Constraint Satisfaction Problem (CSP). It is well known that a non-binary CSP can be transformed into an equivalent binary one using some of the actual techniques. However, when the CSP is not discrete or the number of constraints is high, these techniques become impractical. In this paper, we propose an heuristic called "N-face Hyperpolyhedron Heuristic" as an incremental and non-binary CSP solver. This non-binary CSP solver carries out the search through OR techniques and maintains, in a hyperpolyhedron, those solutions that satisfy all metric non-binary constraints. Thus, we can manage more complex and expressive problems with high number of constraints and very large domains.