Traveling Salesman Problem A Computational Study

ISBN-10: 0691129932

ISBN-13: 9780691129938

Edition: 2007

List price: $82.50 Buy it from $49.99
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Description: This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.The authors of this book are the same pioneers who for nearly two decades have led the investigation into the traveling salesman problem. They have derived solutions to almost eighty-six thousand cities, yet a general solution to the problem has yet to be discovered. Here they describe the method and computer code they used to solve a broad range of large-scale problems, and along the way they demonstrate the interplay of applied mathematics with increasingly powerful computing platforms. They also give the fascinating history of the problem--how it developed, and why it continues to intrigue us.

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Book details

List price: $82.50
Copyright year: 2007
Publisher: Princeton University Press
Publication date: 2/4/2007
Binding: Hardcover
Pages: 608
Size: 6.50" wide x 9.25" long x 1.75" tall
Weight: 2.134
Language: English

William J. Cook is professor of combinatorics and optimization at the University of Waterloo. He is the coauthor of "The Traveling Salesman Problem: A Computational Study" (Princeton).

Preface
The Problem
Traveling Salesman
Other Travelers
Geometry
Human Solution of the TSP
Engine of Discovery
Is the TSP Hard?
Milestones in TSP Computation
Outline of the Book
Applications
Logistics
Genome Sequencing
Scan Chains
Drilling Problems
Aiming Telescopes and X-Rays
Data Clustering
Various Applications
Dantzig, Fulkerson, and Johnson
The 49-City Problem
The Cutting-Plane Method
Primal Approach
History of TSP Computation
Branch-and-Bound Method
Dynamic Programming
Gomory Cuts
The Lin-Kernighan Heuristic
TSP Cuts
Branch-and-Cut Method
Notes
LP Bounds and Cutting Planes
Graphs and Vectors
Linear Programming
Outline of the Cutting-Plane Method
Valid LP Bounds
Facet-Inducing Inequalities
The Template Paradigm for Finding Cuts
Branch-and-Cut Method
Hypergraph Inequalities
Safe Shrinking
Alternative Calls to Separation Routines
Subtour Cuts and PQ-Trees
Parametric Connectivity
Shrinking Heuristic
Subtour Cuts from Tour Intervals
Padberg-Rinaldi Exact Separation Procedure
Storing Tight Sets in PQ-trees
Cuts from Blossoms and Blocks
Fast Blossoms
Blocks of G
Exact Separation of Blossoms
Shrinking
Combs from Consecutive Ones
Implementation of Phase 2
Proof of the Consecutive Ones Theorem
Combs from Dominoes
Pulling Teeth from PQ-trees
Nonrepresentable Solutions also Yield Cuts
Domino-Parity Inequalities
Cut Metamorphoses
Tighten
Teething
Naddef-Thienel Separation Algorithms
Gluing
Local Cuts
An Overview
Making Choices of V and sigma;
Revisionist Policies
Does phi;(chi;*) Lie Outside the Convex Hull ofT?
Separating phi;(chi;*) fromT: The Three Phases
PHASE 1: FromT* toT"
PHASE 2: FromT" toT'
Implementing ORACLE
PHASE 3: FromT' toT
Generalizations
Managing the Linear Programming Problems
The Core LP
Cut Storage
Edge Pricing
The Mechanics
The Linear Programming Solver
History
The Primal Simplex Algorithm
The Dual Simplex Algorithm
Computational Results: The LP Test Sets
Pricing
Branching
Previous Work
Implementing Branch and Cut
Strong Branching
Tentative Branching
Tour Finding
Lin-Kernighan
Flipper Routines
Engineering Lin-Kernighan
Chained Lin-Kernighan on TSPLIB Instances
Helsgaun's LKH Algorithm
Tour Merging
Computation
The Concorde Code
Random Euclidean Instances
The TSPLIB
Very Large Instances
The World TSP
The Road Goes On
Cutting Planes
Tour Heuristics
Decomposition Methods
Bibliography
Index
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