The Traveling Salesman Problem A Computational Study

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 rou...

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Bibliographic Details
Main Authors Applegate, David L, Bixby, Robert E, Chvátal, Vašek, Cook, William J
Format eBook Book
LanguageEnglish
Published Princeton Princeton University Press 2011
Edition1
SeriesPrinceton series in applied mathematics
Subjects
Abstract data type
Algorithm
AND gate
Assignment problem
Asymptotic analysis
Authoritarianism
Combinatorial optimization
Commodity
Computation
Computing
Confidence interval
Control zone
Convex hull
Cost
Cramer's rule
Cray Y-MP
Cutting-plane method
Data structure
Decomposition method (constraint satisfaction)
Default rule
Division of labour
Do while loop
Estimator
Factorization
Foreign direct investment
Foreign national
General Topics for Engineers
George Dantzig
Greedy algorithm
Heuristic
Heuristic argument
Icosian game
Implementation
Insider
Instance (computer science)
Iteration
Knight's tour
Likelihood function
Limit of a sequence
Linear programming
Margin of error
MATHEMATICS
MATHEMATICS / Applied
Minimum-cost flow problem
Nationalism
Opportunism
Opposition to immigration
Order by
Preference (economics)
Preprocessor
Pricing
Pricing strategies
Priority queue
Quadratic assignment problem
Quantity
Regional variation
Resentment
Result
Sampling bias
Solver
Standard deviation
Subsidy
Tailings
Theft
Time complexity
Trade-off
Transition point
Traveling-salesman problem
Travelling salesman problem
Ubuntu (philosophy)
Unrest
User expectations
Variance
Vehicle routing problem
Wheelbarrow
Nationalism
Resentment
Regional variation
Default rule
Heuristic argument
Division of labour
Result
Theft
Margin of error
Sampling bias
Decomposition method (constraint satisfaction)
Minimum-cost flow problem
Data structure
Likelihood function
Estimator
Trade-off
Quadratic assignment problem
Algorithm
Tailings
Wheelbarrow
Convex hull
Computation
Control zone
Insider
Time complexity
Heuristic
Transition point
Cray Y-MP
Cutting-plane method
Unrest
Solver
User expectations
George Dantzig
Vehicle routing problem
Travelling salesman problem
Iteration
Computing
Cost
Implementation
Variance
Opposition to immigration
Knight's tour
Commodity
Ubuntu (philosophy)
Pricing
Foreign direct investment
Standard deviation
AND gate
Asymptotic analysis
Abstract data type
Preference (economics)
Order by
Assignment problem
Linear programming
Cramer's rule
Quantity
Opportunism
Subsidy
Priority queue
Factorization
Authoritarianism
Instance (computer science)
Confidence interval
Do while loop
Limit of a sequence
Icosian game
Greedy algorithm
Pricing strategies
Preprocessor
Foreign national
Online AccessGet full text
ISBN9780691129938
0691129932
1400841100
9781400841103
DOI10.1515/9781400841103

Cover

Table of Contents:
  • The traveling salesman problem : a computational study -- CONTENTS -- PREFACE -- CHAPTER ONE: THE PROBLEM -- CHAPTER TWO: APPLICATIONS -- CHAPTER THREE: DANTZIG, FULKERSON, AND JOHNSON -- CHAPTER FOUR: HISTORY OF TSP COMPUTATION -- CHAPTER FIVE: LP BOUNDS AND CUTTING PLANES -- CHAPTER SIX: SUBTOUR CUTS AND PQ-TREES -- CHAPTER SEVEN: CUTS FROM BLOSSOMS AND BLOCKS -- CHAPTER EIGHT: COMBS FROM CONSECUTIVE ONES -- CHAPTER NINE: COMBS FROM DOMINOES -- CHAPTER TEN: CUT METAMORPHOSES -- CHAPTER ELEVEN: LOCAL CUTS -- CHAPTER TWELVE: MANAGING THE LINEAR PROGRAMMING PROBLEMS -- CHAPTER THIRTEEN: THE LINEAR PROGRAMMING SOLVER -- CHAPTER FOURTEEN: BRANCHING -- CHAPTER FIFTEEN: TOUR FINDING -- CHAPTER SIXTEEN: COMPUTATION -- CHAPTER SEVENTEEN: THE ROAD GOES ON -- BIBLIOGRAPHY -- INDEX
  • Front Matter Table of Contents Preface Chapter One: The Problem Chapter Two: Applications Chapter Three: Dantzig, Fulkerson, and Johnson Chapter Four: History of TSP Computation Chapter Five: LP Bounds and Cutting Planes Chapter Six: Subtour Cuts and PQ-Trees Chapter Seven: Cuts from Blossoms and Blocks Chapter Eight: Combs from Consecutive Ones Chapter Nine: Combs from Dominoes Chapter Ten: Cut Metamorphoses Chapter Eleven: Local Cuts Chapter Twelve: Managing the Linear Programming Problems Chapter Thirteen: The Linear Programming Solver Chapter Fourteen: Branching Chapter Fifteen: Tour Finding Chapter Sixteen: Computation Chapter Seventeen: The Road Goes On Bibliography Index
  • Cover -- Half title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Chapter 1. The Problem -- 1.1 Traveling Salesman -- 1.2 Other Travelers -- 1.3 Geometry -- 1.4 Human Solution of the TSP -- 1.5 Engine of Discovery -- 1.6 Is the TSP Hard? -- 1.7 Milestones in TSP Computation -- 1.8 Outline of the Book -- Chapter 2. Applications -- 2.1 Logistics -- 2.2 Genome Sequencing -- 2.3 Scan Chains -- 2.4 Drilling Problems -- 2.5 Aiming Telescopes and X-Rays -- 2.6 Data Clustering -- 2.7 Various Applications -- Chapter 3. Dantzig, Fulkerson, and Johnson -- 3.1 The 49-City Problem -- 3.2 The Cutting-Plane Method -- 3.3 Primal Approach -- Chapter 4. History of TSP Computation -- 4.1 Branch-and-Bound Method -- 4.2 Dynamic Programming -- 4.3 Gomory Cuts -- 4.4 The Lin-Kernighan Heuristic -- 4.5 TSP Cuts -- 4.6 Branch-and-Cut Method -- 4.7 Notes -- Chapter 5. LP Bounds and Cutting Planes -- 5.1 Graphs and Vectors -- 5.2 Linear Programming -- 5.3 Outline of the Cutting-Plane Method -- 5.4 Valid LP Bounds -- 5.5 Facet-Inducing Inequalities -- 5.6 The Template Paradigm for Finding Cuts -- 5.7 Branch-and-Cut Method -- 5.8 Hypergraph Inequalities -- 5.9 Safe Shrinking -- 5.10 Alternative Calls to Separation Routines -- Chapter 6. Subtour Cuts and PQ-Trees -- 6.1 Parametric Connectivity -- 6.2 Shrinking Heuristic -- 6.3 Subtour Cuts from Tour Intervals -- 6.4 Padberg-Rinaldi Exact Separation Procedure -- 6.5 Storing Tight Sets in PQ-trees -- Chapter 7. Cuts from Blossoms and Blocks -- 7.1 Fast Blossoms -- 7.2 Blocks of G* -- 7.3 Exact Separation of Blossoms -- 7.4 Shrinking -- Chapter 8. Combs from Consecutive Ones -- 8.1 Implementation of Phase 2 -- 8.2 Proof of the Consecutive Ones Theorem -- Chapter 9. Combs from Dominoes -- 9.1 Pulling Teeth from PQ-trees -- 9.2 Nonrepresentable Solutions also Yield Cuts -- 9.3 Domino-Parity Inequalities
  • Chapter 10. Cut Metamorphoses -- 10.1 Tighten -- 10.2 Teething -- 10.3 Naddef-Thienel Separation Algorithms -- 10.4 Gluing -- Chapter 11. Local Cuts -- 11.1 An Overview -- 11.2 Making Choices of V and σ -- 11.3 Revisionist Policies -- 11.4 Does (x*) Lie Outside the Convex Hull of T? -- 11.5 Separating (x*) from T T: The Three Phases -- 11.6 Phase 1: From T* to T -- 11.7 Phase 2: From T to T -- 11.8 Implementing Oracle -- 11.9 Phase 3: From T to T -- 11.10 Generalizations -- Chapter 12. Managing the Linear Programming Problems -- 12.1 The Core LP -- 12.2 Cut Storage -- 12.3 Edge Pricing -- 12.4 The Mechanics -- Chapter 13. The Linear Programming Solver -- 13.1 History -- 13.2 The Primal Simplex Algorithm -- 13.3 The Dual Simplex Algorithm -- 13.4 Computational Results: The LP Test Sets -- 13.5 Pricing -- Chapter 14. Branching -- 14.1 Previous Work -- 14.2 Implementing Branch and Cut -- 14.3 Strong Branching -- 14.4 Tentative Branching -- Chapter 15. Tour Finding -- 15.1 Lin-Kernighan -- 15.2 Flipper Routines -- 15.3 Engineering Lin-Kernighan -- 15.4 Chained Lin-Kernighan on TSPLIB Instances -- 15.5 Helsgaun's LKH Algorithm -- 15.6 Tour Merging -- Chapter 16. Computation -- 16.1 The Concorde Code -- 16.2 Random Euclidean Instances -- 16.3 The TSPLIB -- 16.4 Very Large Instances -- 16.5 The World TSP -- Chapter 17. The Road Goes On -- 17.1 Cutting Planes -- 17.2 Tour Heuristics -- 17.3 Decomposition Methods -- Bibliography -- Index
  • Chapter 1. The Problem
  • Chapter 8. Combs from Consecutive Ones
  • Chapter 5. LP Bounds and Cutting Planes
  • Chapter 10. Cut Metamorphoses
  • Chapter 17. The Road Goes On
  • Chapter 2. Applications
  • Index
  • Chapter 3. Dantzig, Fulkerson, and Johnson
  • -
  • Chapter 4. History of TSP Computation
  • Chapter 11. Local Cuts
  • /
  • Chapter 15. Tour Finding
  • Chapter 9. Combs from Dominoes
  • Contents
  • Chapter 7. Cuts from Blossoms and Blocks
  • Chapter 13. The Linear Programming Solver Chapter 14. Branching
  • Chapter 16. Computation
  • Chapter 14. Branching
  • Chapter 12. Managing the Linear Programming Problems
  • Frontmatter --
  • Chapter 6. Subtour Cuts and PQ-Trees
  • Preface
  • Bibliography