  In this paper, we propose an effective search procedure that interleaves two
steps: subproblem generation and subproblem solution. We mainly focus on the
first part. It consists of a variable domain value ranking based on reduced
costs. Exploiting the ranking, we generate, in a Limited Discrepancy Search
tree, the most promising subproblems first. An interesting result is that
reduced costs provide a very precise ranking that allows to almost always find
the optimal solution in the first generated subproblem, even if its dimension
is significantly smaller than that of the original problem. Concerning the
proof of optimality, we exploit a way to increase the lower bound for
subproblems at higher discrepancies. We show experimental results on the TSP
and its time constrained variant to show the effectiveness of the proposed
approach, but the technique could be generalized for other problems.
