The Traveling Salesman Problem: A Computational Study (Princeton Series in Applied Mathematics)

This book covers almost all techniques and approaches to solve the TSP. The authors were the greater contributors to the construction of exact and heuristic solutions we know about. The salesman problem still is challenger to the students and still has a strong appeal. We can look around to other interesting problems, but sometimes we look again to TSP to check for improvements. The TSP is one of the simplest ones to enunciate but it is NP hard.Probably it is hard also to find another book as complete like this one.

I've just read the first chapter .. it seems intresting.I guess this book is not as general as I hoped .. though it is amazing but it keep referencing a code package.

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 ([...] 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 [...].

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.