# Solution of a Large-Scale Traveling-Salesman Problem

@article{Dantzig1954SolutionOA, title={Solution of a Large-Scale Traveling-Salesman Problem}, author={George B. Dantzig and Delbert Ray Fulkerson and Selmer M. Johnson}, journal={Oper. Res.}, year={1954}, volume={2}, pages={393-410} }

The RAND Corporation in the early 1950s contained “what may have been the most remarkable group of mathematicians working on optimization ever assembled” [6]: Arrow, Bellman, Dantzig, Flood, Ford, Fulkerson, Gale, Johnson, Nash, Orchard-Hays, Robinson, Shapley, Simon, Wagner, and other household names. Groups like this need their challenges. One of them appears to have been the traveling salesman problem (TSP) and particularly its instance of finding a shortest route through Washington, DC, and…

## 701 Citations

Symmetric traveling salesman problem and flows in hypergraphs: New algorithmic possibilities

- Computer Science
- 2019

This work focuses on one compact formulation for the symmetric TSP, known as the “multistage insertion” formulation, and shows that its linear programming (LP) relaxation can be viewed as a minimum-cost flow problem in a hypergraph.

The Traveling Salesman Problem: Deceptivley Easy to State; Notoriously Hard to Solve

- Computer Science
- 2006

The purpose of this thesis is to give an overview of the history of the Traveling Salesman Problem and to show how it has been an integral part of the development of the fields of Integer…

Geometric and LP-based heuristics for the quadratic travelling salesman problem

- Computer ScienceComput. Oper. Res.
- 2019

Approximation Algorithms for Traveling Salesman Problems Based on Linear Programming Relaxations

- Computer Science
- 2012

This thesis presents the first nontrivial approximation algorithm for this problem by giving a novel algorithmic technique to shortcut Eulerian circuits while bounding the lengths of the shortcuts needed, and achieves an O(log n/ log log n)-approximation algorithm.

Using the TSP Solution for Optimal Route Scheduling in Construction Management

- Computer Science
- 2011

First descriptive formulation of the TSP can be found in a famous German handbook for traveling salesman from 1832 (Voigt, 1832) and the proposed 1832 German route might even be optimal.

Solution of a Min-Max Vehicle Routing Problem

- Computer ScienceINFORMS Journal on Computing
- 2002

This algorithmic framework combines the LP-based traveling salesman code of Applegate, Bixby, ChvAital, and Cook, with specialized cutting planes and a distributed search algorithm, permitting the use of a computing network located across Rice, Princeton, AT&T, and Bonn.

A Survey on Travelling Salesman Problem

- Business, Computer Science
- 2010

The paper relates the Travelling Salesman problem with the hamiltonian circuit problem in order to demonstrate the existing property of reducibility between the two problems and the its advantages in providing a solution to the TSP.

THE PRECEDENCE CONSTRAINED TRAVELING SALESMAN PROBLEM

- Computer Science
- 1991

The lower bounding procedure is a generalization of t he restricted Lagrangean method that has been successfully adapted to the TSP by Balas and Christofides (2), and the branch and bound algorithm also incorporates several heuristics and variable reduction tests.

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

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

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