# Exact solution of large-scale, asymmetric traveling salesman problems

@article{Carpaneto1995ExactSO, title={Exact solution of large-scale, asymmetric traveling salesman problems}, author={Giorgio Carpaneto and Mauro Dell'Amico and Paolo Toth}, journal={ACM Trans. Math. Softw.}, year={1995}, volume={21}, pages={394-409} }

A lowest-first, branch-and-bound algorithm for the <italic>Asymmetric Traveling Salesman Problem</italic> is presented. The method is based on the <italic>Assignment Problem relaxation</italic> and on a <italic>subtour elimination branching scheme</italic>. The effectiveness of the algorithm derives from reduction procedures and parametric solution of the relaxed problems associated with the nodes of the branch-decision tree. Large-size, uniformly, randomly generated instances of complete…

## 124 Citations

A Polyhedral Approach to the Asymmetric Traveling Salesman Problem

- Computer Science
- 1997

The aim of this paper is to evaluate the effectiveness of a branch-and-cut algorithm exploiting ATSP-specific facet-defining cuts to be used to attack hard instances that cannot be solved by the AP-based procedures from the literature.

Algorithm 750: CDT: a subroutine for the exact solution of large-scale, asymmetric traveling salesman problems

- Computer ScienceTOMS
- 1995

The Fortran code CDT, implementing an algorithm for theasymmetric traveling salesman problem, based on the Assignment Problem relaxation and on a tour elimination branching scheme, is presented.

Polyhedral results and exact algorithms for the asymmetric travelling salesman problem with replenishment arcs

- Business, Computer ScienceDiscret. Appl. Math.
- 2007

Tolerance-based Branch and Bound algorithms for the ATSP

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- 2008

Lower tolerance-based Branch and Bound algorithms for the ATSP

- Computer Science, BusinessComput. Oper. Res.
- 2012

The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests

- Computer ScienceALENEX
- 2001

A preliminary report on the first broad-based experimental comparison of modern heuristics for the asymmetric traveling salesmen problem (ATSP), finding that no single algorithm is dominant over all instance classes, although for each class the best tours are found by Zhang's algorithm or an iterated variant on Kanellakis-Papadimitriou.

Phase Transitions and Backbones of the Asymmetric Traveling Salesman Problem

- Computer ScienceJ. Artif. Intell. Res.
- 2004

This paper studies phase transitions of the asymmetric Traveling Salesman Problem, an NP-hard combinatorial optimization problem that has many real-world applications and empirically shows 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.

Asymmetric Traveling Salesman and Multi-Stopover Problem with Turn Restrictions-Exact Real-Time Computation for Stopovers ≤ 10

- Computer Science, Business
- 2010

An algorithm directly working on directed graphs observing turn restrictions indispensable for today’s civil and military navigation applications is given.

Models and algorithms for the Asymmetric Traveling Salesman Problem: an experimental comparison

- Computer ScienceEURO J. Transp. Logist.
- 2012

This paper surveys the most effective mathematical models and exact algorithms proposed for finding the optimal solution of the well-known Asymmetric Traveling Salesman Problem (ATSP). The…

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- Computer ScienceDiscret. Optim.
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