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
Language:	English
Published:	Princeton Princeton University Press 2011
Edition:	1
Series:	Princeton 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
ISBN:	9780691129938, 0691129932, 1400841100, 9781400841103
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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 -- CONTENTS -- PREFACE -- CHAPTER ONE: 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 TWO: 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 THREE: DANTZIG, FULKERSON, AND JOHNSON -- 3.1 THE 49-CITY PROBLEM -- 3.2 THE CUTTING-PLANE METHOD -- 3.3 PRIMAL APPROACH -- CHAPTER FOUR: 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 FIVE: 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 SIX: 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 SEVEN: CUTS FROM BLOSSOMS AND BLOCKS -- 7.1 FAST BLOSSOMS -- 7.2 BLOCKS OF… -- 7.3 EXACT SEPARATION OF BLOSSOMS -- 7.4 SHRINKING -- CHAPTER EIGHT: COMBS FROM CONSECUTIVE ONES -- 8.1 IMPLEMENTATION OF PHASE 2 -- 8.2 PROOF OF THE CONSECUTIVE ONES THEOREM -- CHAPTER NINE: COMBS FROM DOMINOES -- 9.1 PULLING TEETH FROM PQ-TREES -- 9.2 NONREPRESENTABLE SOLUTIONS ALSO YIELD CUTS -- 9.3 DOMINO-PARITY INEQUALITIES -- CHAPTER TEN: CUT METAMORPHOSES
10.1 TIGHTEN -- 10.2 TEETHING -- 10.3 NADDEF-THIENEL SEPARATION ALGORITHMS -- 10.4 GLUING -- CHAPTER ELEVEN: LOCAL CUTS -- 11.1 AN OVERVIEW -- 11.2 MAKING CHOICES OF … AND σ -- 11.3 REVISIONIST POLICIES -- 11.4 DOES φ(X*) LIE OUTSIDE THE CONVEX HULL OF T? -- 11.5 SEPARATING φ(X*) FROM 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 TWELVE: MANAGING THE LINEAR PROGRAMMING PROBLEMS -- 12.1 THE CORE LP -- 12.2 CUT STORAGE -- 12.3 EDGE PRICING -- 12.4 THE MECHANICS -- CHAPTER THIRTEEN: 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 FOURTEEN: BRANCHING -- 14.1 PREVIOUS WORK -- 14.2 IMPLEMENTING BRANCH AND CUT -- 14.3 STRONG BRANCHING -- 14.4 TENTATIVE BRANCHING -- CHAPTER FIFTEEN: 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 SIXTEEN: 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 SEVENTEEN: 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
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Chapter 4. History of TSP Computation
Chapter 11. Local Cuts
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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