Search Space Reduction for Constraint Optimization Problems

Abstract

In a constraint optimization problem (COP), many feasible assignments have the same objective value. This usually means huge search space and poor propagation among the objective variables (which appear in the objective function) and the problem variables (which do not). In this paper, we investigate a search strategy that focuses on the objective function, namely, the objective variables are assigned before the problem variables. Despite the larger search space, we may indeed solve a COP faster, provided that the constraint propagation is strong — the search can reach the optimal objective value faster in the objective space, and by strong propagation it knows if the constraints are unsatisfiable with little search in the problem space. To obtain strong propagation, we study the use of dual encoding [1] for COPs. Our COP formulation and search strategy are general and can handle any dual COPs.