Hierarchical nonlinear constraint satisfaction

Abstract

Constraint programming is a method of problem solving that allows declarative specification of relations among objects. It is important to allow preferences of constraints since it is often difficult for programmers to specify all constraints without conflicts. In this paper, we propose a numerical method for solving nonlinear constraints with hierarcical preferences (i.e., constraint hierarchies) in a least-squares manner. This method finds sufficiently precise local optimal solutions by appropriately processing hierarchical preferences of constraints. To evaluate the effectiveness of our method, we present experimental results obtained with a prototype constraint solver.