Heuristics: intelligent search strategies for computer problem solving
Heuristics: intelligent search strategies for computer problem solving
Generalized best-first search strategies and the optimality of A*
Journal of the ACM (JACM)
The traveling salesman problem with distances one and two
Mathematics of Operations Research
Exact solution of large-scale, asymmetric traveling salesman problems
ACM Transactions on Mathematical Software (TOMS)
Performance of linear-space search algorithms
Artificial Intelligence
Phase transitions and the search problem
Artificial Intelligence - Special volume on frontiers in problem solving: phase transitions and complexity
Artificial Intelligence
Asymptotic and finite size parameters for phase transitions: Hamiltonian circuit as a case study
Information Processing Letters
Constructive bounds and exact expectation for the random assignment problem
Random Structures & Algorithms
The probabilistic relationship between the assignment and asymmetric traveling salesman problems
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Statistical mechanics methods and phase transitions in optimizationproblems
Theoretical Computer Science - Phase transitions in combinatorial problems
Frozen development in graph coloring
Theoretical Computer Science - Phase transitions in combinatorial problems
The ζ (2) limit in the random assignment problem
Random Structures & Algorithms
Phase transition and finite-size scaling for the integer partitioning problem
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Generating Satisfiable Problem Instances
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Phase Transitions and Backbones of 3-SAT and Maximum 3-SAT
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Searching for backbones and fat: a limit-crossing approach with applications
Eighteenth national conference on Artificial intelligence
The Gn,mphase transition is not hard for the Hamiltonian cycle problem
Journal of Artificial Intelligence Research
Phase transitions of the asymmetric traveling salesman
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Backbones in optimization and approximation
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Clustering at the phase transition
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
Cut-and-solve: an iterative search strategy for combinatorial optimization problems
Artificial Intelligence
The backbone of the travelling salesperson
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Cut-and-solve: An iterative search strategy for combinatorial optimization problems
Artificial Intelligence
Understanding TSP difficulty by learning from evolved instances
LION'10 Proceedings of the 4th international conference on Learning and intelligent optimization
Is computational complexity a barrier to manipulation?
CLIMA'10 Proceedings of the 11th international conference on Computational logic in multi-agent systems
Self-organized combinatorial optimization
Expert Systems with Applications: An International Journal
Review: Measuring instance difficulty for combinatorial optimization problems
Computers and Operations Research
Discovering the suitability of optimisation algorithms by learning from evolved instances
Annals of Mathematics and Artificial Intelligence
Iterative patching and the asymmetric traveling salesman problem
Discrete Optimization
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In recent years, there has been much interest in phase transitions of combinatorial problems. Phase transitions have been successfully used to analyze combinatorial optimization problems, characterize their typical-case features and locate the hardest problem instances. In this paper, we study phase transitions of the asymmetric Traveling Salesman Problem (ATSP), an NP-hard combinatorial optimization problem that has many real-world applications. Using random instances of up to 1,500 cities in which intercity distances are uniformly distributed, we empirically show that many properties of the problem, including the optimal tour cost and backbone size, experience sharp transitions as the precision of intercity distances increases across a critical value. Our experimental results on the costs of the ATSP tours and assignment problem agree with the theoretical result that the asymptotic cost of assignment problem is π26 as the number of cities goes to infinity. In addition, we show that the average computational cost of the well-known branch-and-bound subtour elimination algorithm for the problem also exhibits a thrashing behavior, transitioning from easy to difficult as the distance precision increases. These results answer positively an open question regarding the existence of phase transitions in the ATSP, and provide guidance on how difficult ATSP problem instances should be generated.