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
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
Introduction to Operations Research and Revised CD-ROM 8
Introduction to Operations Research and Revised CD-ROM 8
Phase transitions and backbones of the asymmetric traveling salesman problem
Journal of Artificial Intelligence Research
Solving time-dependent planning problems
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Transforming asymmetric into symmetric traveling salesman problems
Operations Research Letters
Algorithms and Experimental Study for the Traveling Salesman Problem of Second Order
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
A Knowledge-Based Ant Colony Optimization for Flexible Job Shop Scheduling Problems
Applied Soft Computing
SplittingHeirs: inferring haplotypes by optimizing resultant dense graphs
Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology
Lower tolerance-based Branch and Bound algorithms for the ATSP
Computers and Operations Research
Proceedings of Programming Models and Applications on Multicores and Manycores
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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 ATSP. For four of these classes, cut-and-solve was able to solve larger (sometimes substantially larger) problems. Our code is available at our websites.