Search Space Reduction and Russian Doll Search

In a constraint optimization problem (COP), many feasible valuations lead to the same objective value. This often means a huge search space and poor performance in the propagation between the objective and problem variables. In this paper, we propose a different modeling and search strategy which focuses on the cost function. We show that by constructing a dual model on the objective variables, we can get strong propagation between the objective variables and the problem variables which allows search on the objective variables. We explain why and when searching on the objective variables can lead to large gains. We present a new Russian Doll Search algorithm, ORDS, which works on objective variables with dynamic variable ordering. Finally, we demonstrate using the hard Still-Life optimization problem the benefits of changing to the objective function model and ORDS.