Über die Autorin bzw. den Autor

David L. Applegate, Robert E. Bixby, Va?ek Chvátal & William J. Cook

Von der hinteren Coverseite

"This book addresses one of the most famous and important combinatorial-optimization problems--the traveling salesman problem. It is very well written, with a vivid style that captures the reader's attention. Many examples are provided that are very useful to motivate and help the reader to better understand the results presented in the book."--Matteo Fischetti, University of Padova

"This is a fantastic book. Ever since the early days of discrete optimization, the traveling salesman problem has served as the model for computationally hard problems. The authors are main players in this area who forged a team in 1988 to push the frontiers on how good we are in solving hard and large traveling salesman problems. Now they lay out their views, experience, and findings in this book."--Bert Gerards, Centrum voor Wiskunde en Informatica

Aus dem Klappentext

"This book addresses one of the most famous and important combinatorial-optimization problems--the traveling salesman problem. It is very well written, with a vivid style that captures the reader's attention. Many examples are provided that are very useful to motivate and help the reader to better understand the results presented in the book."--Matteo Fischetti, University of Padova

"This is a fantastic book. Ever since the early days of discrete optimization, the traveling salesman problem has served as the model for computationally hard problems. The authors are main players in this area who forged a team in 1988 to push the frontiers on how good we are in solving hard and large traveling salesman problems. Now they lay out their views, experience, and findings in this book."--Bert Gerards, Centrum voor Wiskunde en Informatica

Auszug. © Genehmigter Nachdruck. Alle Rechte vorbehalten.

The Traveling Salesman Problem

Princeton University Press

Chapter One

Given a set of cities along with the cost of travel between each pair of them, the traveling salesman problem, or TSP for short, is to find the cheapest way of visiting all the cities and returning to the starting point. The "way of visiting all the cities" is simply the order in which the cities are visited; the ordering is called a tour or circuit through the cities.

This modest-sounding exercise is in fact one of the most intensely investigated problems in computational mathematics. It has inspired studies by mathematicians, computer scientists, chemists, physicists, psychologists, and a host of nonprofessional researchers. Educators use the TSP to introduce discrete mathematics in elementary, middle, and high schools, as well as in universities and professional schools. The TSP has seen applications in the areas of logistics, genetics, manufacturing, telecommunications, and neuroscience, to name just a few.

The appeal of the TSP has lifted it to one of the few contemporary problems in mathematics to become part of the popular culture. Its snappy name has surely played a role, but the primary reason for the wide interest is the fact that this easily understood model still eludes a general solution. The simplicity of the TSP, coupled with its apparent intractability, makes it an ideal platform for developing ideas and techniques to attack computational problems in general.

Our primary concern in this book is to describe a method and computer code that have succeeded in solving a wide range of large-scale instances of the TSP. Along the way we cover the interplay of applied mathematics and increasingly more powerful computing platforms, using the solution of the TSP as a general model in computational science.

A companion to the book is the computer code itself, called Concorde. The theory and algorithms behind Concorde will be described in detail in the book, along with computational tests of the code. The software is freely available at www.tsp.gatech.edu together with supporting documentation. This is jumping ahead in our presentation, however. Before studying Concorde we take a look at the history of the TSP and discuss some of the factors driving the continued interest in solution methods for the problem.

1.1 TRAVELING SALESMAN

The origin of the name "traveling salesman problem" is a bit of a mystery. There does not appear to be any authoritative documentation pointing out the creator of the name, and we have no good guesses as to when it first came into use. One of the most influential early TSP researchers was Merrill Flood of Princeton University and the RAND Corporation. In an interview covering the Princeton mathematics community, Flood [183] made the following comment.

Developments that started in the 1930s at Princeton have interesting consequences later. For example, Koopmans first became interested in the "48 States Problem" of Hassler Whitney when he was with me in the Princeton Surveys, as I tried to solve the problem in connection with the work of Bob Singleton and me on school bus routing for the State of West Virginia. I don't know who coined the peppier name "Traveling Salesman Problem" for Whitney's problem, but that name certainly caught on, and the problem has turned out to be of very fundamental importance.

This interview of Flood took place in 1984 with Albert Tucker posing the questions. Tucker himself was on the scene of the early TSP work at Princeton, and he made the following comment in a 1983 letter to David Shmoys [527].

The name of the TSP is clearly colloquial American. It may have been invented by Whitney. I have no alternative suggestion.

Except for small variations in spelling and punctuation, "traveling" versus "travelling," "salesman" versus "salesman's," etc., by the mid-1950s the TSP name was in wide use. The first reference containing the term appears to be the 1949 report by Julia Robinson, "On the Hamiltonian game (a traveling salesman problem)" [483], but it seems clear from the writing that she was not introducing the name. All we can conclude is that sometime during the 1930s or 1940s, most likely at Princeton, the TSP took on its name, and mathematicians began to study the problem in earnest.

Although we cannot identify the originator of the TSP name, it is easy to make an argument that it is a fitting identifier for the problem of finding the shortest route through cities in a given region. The traveling salesman has long captured our imagination, being a leading figure in stories, books, plays, and songs. A beautiful historical account of the growth and influence of traveling salesmen can be found in Timothy Spears' book 100 Years on the Road: The Traveling Salesman in American Culture [506]. Spears cites an 1883 estimate by Commercial Travelers Magazine of 200,000 traveling salesmen working in the United States and a further estimate of 350,000 by the turn of the century. This number continued to grow through the early 1900s, and at the time of the Princeton research the salesman was a familiar site in most American towns and villages.

The 1832 Handbook by the alten Commis-Voyageur

The numerous salesmen on the road were indeed interested in the planning of economical routes through their customer areas. An important reference in this context is the 1832 German handbook Der Handlungsreisende-wie er sein soll und was er zu thun hat, um Auftrge zu erhalten und eines glcklichen Erfolgs in seinen Geschften gewiss zu sein-Von einem alten Commis-Voyageur, first brought to the attention of the TSP research community in 1983 by Heiner Mller- Merbach [410]. The title page of this small book is shown in Figure 1.1.

The Commis-Voyageur [132] explicitly described the need for good tours in the following passage, translated from the German original by Linda Cook.

Business leads the traveling salesman here and there, and there is not a good tour for all occurring cases; but through an expedient choice and division of the tour so much time can be won that we feel compelled to give guidelines about this. Everyone should use as much of the advice as he thinks useful for his application. We believe we can ensure as much that it will not be possible to plan the tours through Germany in consideration of the distances and the traveling back and fourth, which deserves the traveler's special attention, with more economy. The main thing to remember is always to visit as many localities as possible without having to touch them twice.

This is an explicit description of the TSP, made by a traveling salesman himself!

The book includes five routes through regions of Germany and Switzerland. Four of these routes include return visits to an earlier city that serves as a base for that part of the trip. The fifth route, however, is indeed a traveling salesman tour, as described in Alexander Schrijver's [495] book on the field of combinatorial optimization. An illustration of the tour is given in Figure 1.2. The cities, in tour order, are listed in Table 1.1, and a picture locating the tour within Germany is given in Figure 1.3. One can see from the drawings that...