A Constraint Directed Model for Partial Constraint Satisfaction Problems

For many constraint satisfaction problems, finding complete solutions is impossible (i.e. problems may be over-constrained). In such cases, we want a partial solution that satisfies as many constraints as possible. Several backtracking and local search algorithms exist that are based on the assignment of values to variables in a fixed order, until a complete solution or a reasonably good partial solution is obtained. In this study, we examine the dual graph approach for solving CSPs. The idea of dual graphs can be naturally extended to another structure-driven approach to CSPs, constraint directed backtracking that inherently handles k-ary constraints. In this paper, we present a constraint directed branch and bound (CDBB) algorithm to address the problem of over-constrained-ness. The algorithm constructs solutions of higher arity by joining solutions of lower arity. When computational resources are bounded, the algorithm can return partial solutions in an anytime fashion. Some interesting characteristics of the proposed algorithm are discussed. The algorithm is implemented and tested on a set of randomly generated problems. Our experimental results demonstrate that the CDBB consistently finds better solutions more quickly than backtracking with branch and bound. Our algorithm can be extended with intelligent backtracking schemes and local consistency maintenance mechanisms just like backtracking has been in the past.