Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Depth-first iterative-deepening: an optimal admissible tree search
Artificial Intelligence
Introduction to operations research, 4th ed.
Introduction to operations research, 4th ed.
Exact solution of large-scale, asymmetric traveling salesman problems
ACM Transactions on Mathematical Software (TOMS)
Performance of linear-space search algorithms
Artificial Intelligence
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A complete anytime algorithm for number partitioning
Artificial Intelligence
Asymptotic experimental analysis for the Held-Karp traveling salesman bound
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Depth-First Branch-and-Bound versus Local Search: A Case Study
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
TSP Cuts Which Do Not Conform to the Template Paradigm
Computational Combinatorial Optimization, Optimal or Provably Near-Optimal Solutions [based on a Spring School]
Searching for backbones and fat: a limit-crossing approach with applications
Eighteenth national conference on Artificial intelligence
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Editorial: The traveling salesman problem
Discrete Optimization
Rearrangement Clustering: Pitfalls, Remedies, and Applications
The Journal of Machine Learning Research
Engineering Applications of Artificial Intelligence
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Branch-and-bound and branch-and-cut use search trees to identify optimal solutions to combinatorial optimization problems. In this paper, we introduce an iterative search strategy which we refer to as cut-and-solve and prove optimality and termination for this method. This search is different from traditional tree search as there is no branching. At each node in the search path, a relaxed problem and a sparse problem are solved and a constraint is added to the relaxed problem. The sparse problems provide incumbent solutions. When the constraining of the relaxed problem becomes tight enough, its solution value becomes no better than the incumbent solution value. At this point, the incumbent solution is declared to be optimal. This strategy is easily adapted to be an anytime algorithm as an incumbent solution is found at the root node and continuously updated during the search.Cut-and-solve enjoys two favorable properties. Since there is no branching, there are no "wrong" subtrees in which the search may get lost. Furthermore, its memory requirement is negligible. For these reasons, it has potential for problems that are difficult to solve using depth-first or best-first search tree methods.In this paper, we demonstrate the cut-and-solve strategy by implementing a generic version of it for the Asymmetric Traveling Salesman Problem (ATSP). Our unoptimized implementation outperformed state-of-the-art solvers for five out of seven real-world problem classes of the ATSE For four of these classes, cut-and-solve was able to solve larger (sometimes substantially larger) problems. Our code is available at our websites.