Solving Hierarchical Soft Constraints with an SMT Solver

Constraints allow the declarative specification of various problems in many fields. In particular, constraint hierarchies that enable soft constraints with hierarchical preferences are useful for programming interactive graphical applications. However, it is still difficult to handle constraint hierarchies with nonlinear constraints. This paper proposes an algorithm for solving constraint hierarchies possibly with nonlinear constraints. Instead of directly solving a constraint hierarchy, it successively generates and solves ordinary constraint problems by using an external SMT solver. The results of our experiments show that the algorithm is able to find accurate constraint hierarchy solutions.