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A brilliant treatment of a knotty problem in computing. This volume contains chapters written by reputable researchers and provides the state of the art in theory and algorithms for the traveling salesman problem (TSP). The book covers all important areas of study on TSP, including polyhedral theory for symmetric and asymmetric TSP, branch and bound, and branch and cut algorithms, probabilistic aspects of TSP, and includes a thorough computational analysis of heuristic and metaheuristic algorithms.

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Customer Reviews (2)

An Excellent Introduction to Algorithm Design for Combinatorial Optimisation
The latest book by Applegate, Bixby, Chvátal, and Cook provides an excellent survey of methods that kick-started the "engine of discovery in applied mathematics", known as the Travelling Salesman Problem (TSP). In more than 600 pages, the authors present a survey of methods used in their present-best TSP solver Concorde, almost to the exclusion of any other content. Chapters 1-4 describe the TSP and Chapters 5-6 provide a brief introduction to solving the TSP by using the branch and cut method. At the heart of the book are then Chapters 7-11, which survey various classes of cuts, in some cases first proposed by the authors themselves. Chapter 7 surveys cuts from blossoms and blocks, Chapter 8 presents cuts from combs and consecutive ones, and Chapter 9 introduces cuts from dominoes. Chapters 11 and 12 then describe in yet more detail separation and metamorphoses of strong valid inequalities. Other variants of the problem, such as the asymmetric TSP, and other solution approaches, including metaheuristics and approximation algorithms, are mentioned only in the passing. They are, however, well-covered elsewhere (Gutin & Punnen, 2002), and the seemingly narrow focus consequently enables the authors to provide an outstandingly in-depth treatment.

I cannot be stressed enough how much the treatment benefits from authors' extensive experience with development of Concorde (http://www.tsp.gatech.edu/). In many textbooks on combinatorial optimisation, primal heuristics are mentioned only in passing and cuts are presented in the very mathematical style of definition - proof of validity - proof of dimensionality. Not here. Chapter 6-11 suggest separation routines, exact or heuristic, alongside the description of strong valid inequalities, Chapter 12 is devoted to management of cuts and instances of linear programming, Chapter 13 describes pricing routines for column generation, and last but not least, Chapter 15 is devoted to primal (tour-finding) heuristics. "Implementation details", such as the choice of suitable data structures and trade-offs between heuristic and exact separation, are thoroughly discussed. This makes the book a wonderful introduction to the design of branch-and-cut/price in general.

Although narrow in scope, the book can be recommended to a surprisingly wide audience -- most likely to any researcher working in combinatorial optimisation, and anyone else with a keen interest in algorithm design for combinatorial optimisation.

For the full review, see DOI [...].

Twenty years in the making
The coauthors have been working at solving large scale traveling saleman problem instances for more than 20 years. This book, along with the publicly available Concorde code, is the culmination of that twenty years of work.

The first four chapters of the book (130 pages or so) are an extremely readable description of the use and history of the traveling salesman problem.For our field, the traveling salesman problem has been an exemplar of a hard combinatorial problem, commonly used to test new ideas in problem solving.It is no coincidence that the first papers on simulated annealing, DNA computing, and other approaches for combinatorial problems describe their methods in the context of the TSP:it is the most well known of all the problems in operations research.

The authors' primary emphasis is on computation:how can optimal tours be found?The history of TSP computation is very much the history of computational combinatorial optimization.From the fundamental work of Dantzig, Fulkerson, and Johnson in solving the famous 42-city example, through Held and Karp's relaxations andLin-Kernighan's improvement heuristics, to modern-day branch-and-cut, the TSP has been at the forefront of computational methods in our field.The description of this history is outstanding, and appropriately nontechnical, suitable for reading by beginners in operations research.

The main part of the book is on the computational approaches needed to solve large TSPs.This part is well-written, though beyond a beginner level.Despite that, it has broad interest in the way it melds computational issues (like data structures and heuristic ordering) with the theory.

At the end, this book is an exemplar for how to do research in computational operations research.While not aimed at the non-specialist, it is perfectly readable by those who have gone through an introduction in optimization or operations research.
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Provides an in-depth treatment of the Traveling Salesman problem--the archetypical problem in combinatorial optimization. Each chapter deals with a different aspect of the problem, and has been written by an acknowledged expert in the field. Focusses on the essential ideas in a self-contained manner. Includes exercises and an extensive bibliography. ... Read more

Customer Reviews (1)

An excellent book for attempts to solve computationally intractable problems
The question of existence of polynomial-time algorithms for hard problems now classified to becomputationally intractable, is one of the most challenging open problems in Theoretical Computer Science. Even mathematicians has named it as one of the Millenium problems and have announced a 1 million dollar prize for one who solves it. This book with articles from several world-class experts who have tried to solve this problem or have obtained partial solutions, is an excellent reference book for someone who wants to enter this field or simply wants to gain some knowledge in this area. ... Read more

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Diplomarbeit, die am 01.07.1995 erfolgreich an einer Universität in Deutschland eingereicht wurde. Einleitung: Das Traveling Salesman Problem (TSP) wird mit heuristischen Verfahren näherungsweise gelöst. Man kann das TSP exakt lösen, aber der Zeitaufwand wächst exponentiell mit der Anzahl der Städte. Man ist daher bemüht, mit neuartigen Verfahren vorgegebene Probleme näherungsweise zu lösen. In der Praxis ist der Zeitaufwand deutlich geringer und die Güte dieser Lösungen ausreichend. Das bekannteste heuristische Verfahren ist Simulated Annealing. Es entstand durch Analogien aus der Feststoffphysik und liefert schnell gute Ergebnisse. In dieser Arbeit wird dieses Verfahren mit sowie weitere verwandte Methoden vergleichend angewendet. Dazu wurde in Turbo-Pascal ein Programm geschrieben, das diese Verfahren anwendet. Man kann Größe des Problems sowie das zu verwendende Verfahren eingeben und kann die Ergebnisfindung grafisch anschaulich dargestellt verfolgen.Inhaltsverzeichnis: 1.|Vorwort|1 2.|(Historische) Einführung|3 2.1|Das Traveling Salesman Problem|3 2.2|Problematik|4 2.3|Einige bekannte Verfahren zur Lösung des TSP|4 2.3.1|Exakte Verfahren|4 2.3.2|Heuristische Verfahren|5 3.|Physikalische und mathematische Grundlagen|9 3.1|Physikalische Grundlagen|9 3.2|Mathematische Grundlagen|12 4.|Simulated Annealing|15 4.1|Grundlagen|15 4.2|Implementation: Das Programm travel|17 4.2.1|Grundlegende Implementation|17 4.2.2|Die Benutzerführung des Programms|21 5.|Verwandte Verfahren|26 5.1|Threshold Accepting|26 5.1.1|Grundlagen|26 5.1.2|Implementation|27 5.2|Great-Deluge-Algorithmus|27 5.2.1|Grundlagen|27 5.2.2|Implementation|29 5.3|Record-to-record-Travel|30 5.4|Bekannte Fehler des Programms travel|31 6.|Bewertung und Vergleich der Ergebnisse|34 6.1|Berechnete Ergebnisse|34 6.2|Vergleich der Ergebnisse|41 7.|Erweiterungsmöglichkeiten und Ausblicke|55 8.|Anhang|58 8.1|Listing des Programms|58 8.1.1|Das ... Read more

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This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2007. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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The probabilistic traveling salesman problem is a well known problem that is quite challenging to solve. It involves finding the tour with the lowest expected cost for customers that will require a visit with a given probability. There are several proposed algorithms for the homogeneous version of the problem, where all customers have identical probability of being realized. From the literature, the most successful approaches involve local search procedures, with the most famous being the 2-p-opt and 1-shift procedures proposed by Bertsimas [D.J. Bertsimas, L. Howell, Further results on the probabilistic traveling salesman problem, European Journal of Operational Research 65 (1) (1993) 68-95]. Recently, however, evidence has emerged that indicates the equations offered for these procedures are not correct, and even when corrected, the translation to the heterogeneous version of the problem is not simple. In this paper we extend the analysis and correction to the heterogeneous case. We derive new expressions for computing the cost of 2-p-opt and 1-shift local search moves, and we show that the neighborhood of a solution may be explored in O(n^2) time, the same as for the homogeneous case, instead of O(n^3) as first reported in the literature. ... Read more

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This digital document is an article from Journal of Computer Science, published by Science Publications on October 1, 2008. The length of the article is 3563 words. The page length shown above is based on a typical 300-word page. The article is delivered in HTML format and is available immediately after purchase. You can view it with any web browser.

From the author: Key words: Genetic Algorithms (GAs), Traveling Salesman Problem (TSP), Symmetric TSP, Social-Based Genetic Algorithm (SBGA)

Citation Details
Title: The traveling salesman problem as a benchmark test for a Social-Based Genetic Algorithm.(Technical report)
Author: Nagham Azmi al- Madi
Publication: Journal of Computer Science (Magazine/Journal)
Date: October 1, 2008
Publisher: Science Publications
Volume: 4Issue: 10Page: 871(6)

Article Type: Technical report

Distributed by Gale, a part of Cengage Learning ... Read more

Product Description
This digital document is a journal article from Computers and Operations Research, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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In the probabilistic traveling salesman problem (PTSP), customers require a visit with a given probability, and the best solution is the tour through all customers with the lowest expected final tour cost. The PTSP is an important problem, both operationally and strategically, but is quite difficult to solve with realistically sized problem instances. One alternative is to aggregate customers into regions and solve the PTSP on the reduced problem. This approach raises questions such as how to best divide customers into regions and what scale is necessary to represent the full objective. This paper addresses these questions and presents computational results from experiments with both uniformly distributed and clustered data sets. The focus is on large problem instances where customers have a low probability of requiring a visit and the CPU time available is quite limited. For this class of instances, aggregation can yield very tight estimates of the full objective very quickly, and solving an aggregated form of the problem first can often lead to full solutions with lower expected costs. ... Read more

Product Description
This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2005. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The probabilistic traveling salesman problem concerns the best way to visit a set of customers located in some metric space, where each customer requires a visit only with some known probability. A solution to this problem is an a priori tour which visits all customers, and the objective is to minimize the expected length of the a priori tour over all customer subsets, assuming that customers in any given subset must be visited in the same order as they appear in the a priori tour. This problem belongs to the class of stochastic vehicle routing problems, a class which has received increasing attention in recent years, and which is of major importance in real world applications. Several heuristics have been proposed and tested for the probabilistic traveling salesman problem, many of which are a straightforward adaptation of heuristics for the classical traveling salesman problem. In particular, two local search algorithms (2-p-opt and 1-shift) were introduced by Bertsimas. In a previous report we have shown that the expressions for the cost evaluation of 2-p-opt and 1-shift moves, as proposed by Bertsimas, are not correct. In this paper we derive the correct versions of these expressions, and we show that the local search algorithms based on these expressions perform significantly better than those exploiting the incorrect expressions. ... Read more

Product Description
This digital document is a journal article from European Journal of Operational Research, published by Elsevier in 2005. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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Data structures play a crucial role in the efficient implementation of local search algorithms for problems that require circuit optimization in graphs. The traveling salesman problem (TSP) is the benchmark problem used in this study where two implementations of the stem-and-cycle (S&C) ejection chain algorithm are compared. The first implementation uses an Array data structure organized as a doubly linked list to represent TSP tours as well as the S&C reference structure. The second implementation considers a two-level tree structure. The motivation for this study comes from the fact that the S&C neighborhood structure usually requires subpaths to be reversed in order to preserve a feasible orientation for the resulting tour. The traditional Array structure proves to be inefficient for large-scale problems since to accomplish a path reversal it is necessary to update the predecessor and the successor of each node on the path to be reversed. Computational results performed on a set of benchmark problems up to 316,228 nodes clearly demonstrate the relative efficiency of the two-level tree data structure. ... Read more

Product Description
This digital document is a journal article from Computers and Operations Research, published by Elsevier in 2007. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The probabilistic traveling salesman problem (PTSP) is an important theoretical and practical topic in the study of stochastic network problems. It provides researchers with a modeling framework for exploring the stochastic effects in routing problems. This paper focuses on developing the hybrid scatter search (HSS) by incorporating the nearest neighbor rule (NNR), threshold accepting (TA) and edge recombination (ER) crossover into a scatter search conceptual framework to solve the PTSP. A set of numerical experiments were conducted to test the validity of the HSS based on the test problems from Tang and Miller-Hooks' study. The numerical results showed that the HSS can effectively solve the PTSP in most of the tested cases in terms of objective function value. Moreover, the results also indicated that incorporating threshold accepting into the scatter search framework can further increase the computation efficiency while maintaining solution quality. These findings show the potential of the proposed HSS in solving the large-scale PTSP. ... Read more

Product Description
This digital document is a journal article from Computers and Operations Research, published by Elsevier in 2006. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

Description:
The state-of-the-art of local search heuristics for the traveling salesman problem (TSP) is chiefly based on algorithms using the classical Lin-Kernighan (LK) procedure and the stem-and-cycle (S&C) ejection chain method. Critical aspects of implementing these algorithms efficiently and effectively rely on taking advantage of special data structures and on maintaining appropriate candidate lists to store and update potentially available moves. We report the outcomes of an extensive series of tests on problems ranging from 1000 to 1,000,000 nodes, showing that by intelligently exploiting elements of data structures and candidate lists routinely included in state-of-the-art TSP solution software, the S&C algorithm clearly outperforms all implementations of the LK procedure. Moreover, these outcomes are achieved without the use of special tuning and implementation tricks that are incorporated into the leading versions of the LK procedure to enhance their computational efficiency. y. ... Read more

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This digital document is a journal article from Transportation Research Part E, published by Elsevier in 2005. The article is delivered in HTML format and is available in your Amazon.com Media Library immediately after purchase. You can view it with any web browser.

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This paper investigates the development and application of a general meta-heuristic, Meta-RaPS (meta-heuristic for randomized priority search), to the traveling salesman problem (TSP). The Meta-RaPS approach is tested on several established test sets. The Meta-RaPS approach outperformed most other solution methodologies in terms of percent difference from optimal. Additionally, an industry case study that incorporates Meta-RaPS TSP in a large truck route assignment model is presented. The company estimates a more than 50% reduction in engineering time and over $2.5 million annual savings in transportation costs using the automated Meta-RaPS TSP tool compared to their current method. ... Read more

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The Traveling Salesman Problem (TSP) has already been solved in the semi-optimal manners using the numbers of different methods. Among them, genetic algorithms (GA) are pre-dominating. This paper presents a new approach to solve this problem using the Simplified Bi-directional Associative Memory (sBAM), a type of Artificial Neural Network. To get a comparative idea of its performance, the same problem has been solved using a genetic algorithm. In this paper, performance has been analyzed of a TSP by Genetic Algorithm (GA) and sBAM. Finally we proved that sBAM provide real time highly faster nearly optimal solutions than the genetic algorithm. ... Read more

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This is a AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING AND MANAGEMENT report procured by the Pentagon and made available for public release. It has been reproduced in the best form available to the Pentagon. It is not spiral-bound, but rather assembled with Velobinding in a soft, white linen cover. The Storming Media report number is A100293. The abstract provided by the Pentagon follows: The surveillance mission requires aircraft to fly from a starting point through defended terrain to targets and return to a safe destination (usually the starting point). The process of selecting such a flight path is known as the Mission Route Planning (MRP) Problem and is a three-dimensional, multi-criteria (fuel expenditure, time required, risk taken, priority targeting, goals met, etc.) path search. Planning aircraft routes involves an elaborate search through numerous possibilities, which can severely task the resources of the system being used to compute the routes. Operational systems can take up to a day to arrive at a solution due to the combinatoric nature of the problem. This delay is not acceptable because timeliness of obtaining surveillance information is critical in many surveillance missions. Also, the information that the software uses to solve the MRP may become invalid during computation. An effective and efficient way of solving the MRP with multiple aircraft and multiple targets is desired. One approach to finding solutions is to simplify and view the problem as a two-dimensional, minimum path problem. This approach also minimizes fuel expenditure, time required, and even risk taken. The simplified problem is then the Traveling Salesman Problem (TSP). ... Read more