THE TRAVELING SALESMAN PROBLEM: A SURVEYt

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.

[1]  Eugene L. Lawler,et al.  A solvable case of the traveling salesman problem , 1971, Math. Program..

[2]  L. L. Barachet.  Letter to the Editor---Graphic Solution of the Traveling-Salesman Problem , 1957 .

[3]  W. W. Hardgrave,et al.  On the Relation Between the Traveling-Salesman and the Longest-Path Problems , 1962 .

[4]  William J. Cook,et al.  Solution of a Large-Scale Traveling-Salesman Problem , 1954, 50 Years of Integer Programming.

[5]  Richard Bellman,et al.  Dynamic Programming Treatment of the Travelling Salesman Problem , 1962, JACM.

[6]  S. M. Roberts,et al.  An Engineering Approach to the Traveling Salesman Problem , 1966 .

[7]  E. Lawler.  The Quadratic Assignment Problem , 1963 .

[8]  S. S. Sengupta,et al.  The traveling salesman problem , 1961 .

[9]  M. Held,et al.  A dynamic programming approach to sequencing problems , 1962, ACM National Meeting.

[10]  M. M. Flood.  The Traveling-Salesman Problem , 1956 .

[11]  E. L. Lawler,et al.  Branch-and-Bound Methods: A Survey , 1966, Oper. Res..

[12]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  G. Croes.  A Method for Solving Traveling-Salesman Problems , 1958 .

[14]  M. Dacey.  Letter to the Editor---Selection of an Initial Solution for the Traveling-Salesman Problem , 1960 .

[15]  R. Gomory,et al.  Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem , 1964 .

[16]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[17]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[18]  Cyrus Derman,et al.  SURVEILLANCE OF MULTI-COMPONENT SYSTEMS: A STOCHASTIC TRAVELING SALESMAN'S PROBLEM. , 1966 .

[19]  Selmer M. Johnson,et al.  On a Linear-Programming, Combinatorial Approach to the Traveling-Salesman Problem , 1959 .

[20]  Michael Rothkopf,et al.  Letter to the Editor - The Traveling Salesman Problem: On the Reduction of Certain Large Problems to Smaller Ones , 1966, Operational Research.

[21]  R. A. Zemlin,et al.  Integer Programming Formulation of Traveling Salesman Problems , 1960, JACM.

[22]  Ralph E. Gomory,et al.  An algorithm for integer solutions to linear programs , 1958 .