An efficient algorithm for the minimum capacity cut problem
Mathematical Programming: Series A and B
Artificial Intelligence
Systematic and nonsystematic search strategies
Proceedings of the first international conference on Artificial intelligence planning systems
An additive bounding procedure for the asymmetric travelling salesman problem
Mathematical Programming: Series A and B
CP '99 Proceedings of the 5th International Conference on Principles and Practice of Constraint Programming
A Hybrid Exact Algorithm for the TSPTW
INFORMS Journal on Computing
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Exploiting semidefinite relaxations in constraint programming
Computers and Operations Research
Discrepancy-Based Additive Bounding Procedures
INFORMS Journal on Computing
Combinatorial complexity: are we on the right way?
AIKED'06 Proceedings of the 5th WSEAS International Conference on Artificial Intelligence, Knowledge Engineering and Data Bases
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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 TSPan d its time constrained variant to show the effectiveness of the proposed approach, but the technique could be generalized for other problems.