# The Traveling Salesman Problem: A Survey

@article{Bellmore1968TheTS, title={The Traveling Salesman Problem: A Survey}, author={Mandell Bellmore and George L. Nemhauser}, journal={Oper. Res.}, year={1968}, volume={16}, pages={538-558} }

A survey and synthesis of research on the traveling salesman problem is given. We begin by defining the problem and presenting several theorems. This is followed by a general classification of the solution techniques and a detailed description of some of the proven methods. Finally a summary of computational results is given.

## 511 Citations

The Traveling Salesman Problem and its Implications

- Computer Science
- 1975

The aim of this review is to outline the main exact and approximate approaches to the traveling salesman problem (TSP), the various problems arisen from recent work on this subject, the particular…

A continuous variable representation of the traveling salesman problem

- Computer ScienceMath. Program.
- 1978

It is shown that every solution to the network problem is a hamiltonian circuit.

A Preference Order Dynamic Program for a Stochastic Traveling Salesman Problem

- Computer Science, BusinessOper. Res.
- 1978

This paper presents a preference order dynamic program for solving the traveling salesman problem with stochastic travel times, and introduces a branch-and-bound strategy in the solution procedure.

An efficient procedure for obtaining feasible solutions to the n-city traveling salesman problem

- Business
- 1990

The traveling salesman problem: An update of research

- Computer Science
- 1983

This article presents a review of attacks on the traveling salesman problem for problems defined on weighted and unweighted graphs and includes some aspects of nonexact algorithms with major interest confined to the establishment of worst-case bounds.

Improved lower bounds to the travelling salesman problem

- Mathematics, Computer Science
- 1978

The dual of the Travelling Salesman Problem is studied as a source of lower bounds for the primai problem and a gênerai itérative procedure in the space of the multipliers, i.e. dual variables is designed, which also provides new simple bounds.

Some Simple Applications of the Travelling Salesman Problem

- Business, Computer Science
- 1974

This paper reports on typical applications in computer wiring, vehicle routing, clustering and job-shop scheduling that originated from real world problems and thus seem to be of particular interest.

The adjacency relation on the traveling salesman polytope is NP-Complete

- Computer ScienceMath. Program.
- 1978

This problem of determining whether two traveling salesman tours correspond to non-adjacent vertices of the convex polytope associated with the traveling salesman problem is shown to be NP-Complete for both the symmetric and nonsymmetric traveled salesman problem.

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