Binary Search-Based Methods for Solving Constraint Hierarchies over Finite Domains

Constraint programming is a powerful tool for modeling and solving various problems. Especially, soft constraints are useful since they enable the treatment of over-and under-constrained real-world problems by relaxing conflicting constraints and introducing default constraints. Constraint hierarchies provide a soft constraint framework that introduces hierarchical preferences called strengths. In a constraint hierarchy, constraints are associated with strengths such as required, strong, medium, and weak, and a solution is obtained to maximally satisfy stronger constraints in the sense of a given solution criterion. In this paper, we propose three methods based on binary search for solving constraint hierarchies over finite domains by using a criterion called unsatisfied-count-better. Our methods solve constraint hierarchies by encoding them into ordinary constraint satisfaction problems and repeatedly solving the encoded problems with an external solver. We also present the implementations of our methods and the results of the experiment that we conducted to evaluate them.