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文库首页课程资源讲义网络优化：连续和离散模型（英文文字版）【Dimitri P. Bertsekas】

网络优化：连续和离散模型（英文文字版）【Dimitri P. Bertsekas】

网络优化

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网络优化：连续和离散模型英文文字版 Dimitri P. Bertsekas

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Network Optimization:

Continuous and Discrete Models

Dimitri P. Bertsekas

Massachusetts Institute of Technology

WWW site for book information and orders

http://www.athenasc.com

Athena Scientiﬁc, Belmont, Massachusetts

Athena Scientiﬁc

Post Oﬃce Box 391

Belmont, Mass. 02178-9998

U.S.A.

Email: info@athenasc.com

WWW: http://www.athenasc.com

Cover Design: Ann Gallager

 1998 Dimitri P. Bertsekas

by any electronic or mechanical means (including photocopying, recording,

or information storage and retrieval) without permission in writing from

the publisher.

Publisher’s Cataloging-in-Publication Data

Bertsekas, Dimitri P.

Network Optimization: Continuous and Discrete Models

Includes bibliographical references and index

1. Network analysis (Planning). 2. Mathematical Optimization. I. Title.

T57.85.B44 1998 658.4’032-dc20 98-70298

ISBN 1-886529-02-7

ABOUT THE AUTHOR

Dimitri Bertsekas studied Mechanical and Electrical Engineering at

the National Technical University of Athens, Greece, and obtained his

Ph.D. in system science from the Massachusetts Institute of Technology.

He has held faculty positions at Stanford University and the Uni-

versity of Illinois. Since 1979 he has been teaching at the Massachusetts

Institute of Technology (M.I.T.), where he is currently McAfee Professor

of Engineering. He consults regularly with private industry and has held

editorial positions in several journals. His research spans several ﬁelds,

including optimization, control, large-scale computation, and data commu-

nication networks. He has written many research papers and he is the

author or coauthor of thirteen textbooks and research monographs.

Professor Bertsekas was awarded the INFORMS 1997 Prize for Re-

search Excellence in the Interface Between Operations Research and Com-

puter Science for his book ”Neuro-Dynamic Programming” (co-authored

with John Tsitsiklis), the 2000 Greek National Award for Operations Re-

search, and the 2001 ACC John R. Ragazzini Education Award. In 2001,

he was elected to the United States National Academy of Engineering.

iii

ATHENA SCIENTIFIC

OPTIMIZATION AND COMPUTATION SERIES

1. Convex Analysis and Optimization, by Dimitri P. Bertsekas, with

Angelia Nedi´c and Asuman E. Ozdaglar, 2003, ISBN 1-886529-

45-0, 560 pages

2. Introduction to Probability by Dimitri P. Bertsekas and John

Tsitsiklis, 2002, ISBN 1-886529-40-X, 430 pages

3. Dynamic Programming and Optimal Control, Vols. I and II, 2nd

Edition, by Dimitri P. Bertsekas, 2001, ISBN 1-886529-08-6, 704

pages

4. Nonlinear Programming, 2nd Edition, by Dimitri P. Bertsekas,

1999, ISBN 1-886529-00-0, 800 pages

5. Network Optimization: Continuous and Discrete Models by Dim-

itri P. Bertsekas, 1998, ISBN 1-886529-02-7, 608 pages

6. Network Flows and Monotropic Optimization by R. Tyrrell Rock-

afellar, 1998, ISBN 1-886529-06-X, 634 pages

7. Introduction to Linear Optimization by Dimitris Bertsimas and

John N. Tsitsiklis, 1997, ISBN 1-886529-19-1, 608 pages

8. Parallel and Distributed Computation: Numerical Methods by

Dimitri P. Bertsekas and John N. Tsitsiklis, 1997, ISBN 1-886529-

01-9, 718 pages

9. Neuro-Dynamic Programming, by Dimitri P. Bertsekas and John

N. Tsitsiklis, 1996, ISBN 1-886529-10-8, 512 pages

10. Constrained Optimization and Lagrange Multiplier Methods, by

Dimitri P. Bertsekas, 1996, ISBN 1-886529-04-3, 410 pages

11. Stochastic Optimal Control: The Discrete-Time Case by Dimitri

P. Bertsekas and Steven E. Shreve, 1996, ISBN 1-886529-03-5,

330 pages

Contents

1. Introduction .................... p.1

1.1. Graphs and Flows .................... p.3

1.1.1. Paths and Cycles .................. p.4

1.1.2. Flow and Divergence ................ p.6

1.1.3. Path Flows and Conformal Decomposition ....... p.7

1.2. Network Flow Models – Examples ............. p.8

1.2.1. The Minimum Cost Flow Problem . ......... p.9

1.2.2. Network Flow Problems with Convex Cost .......p.16

1.2.3. Multicommodity Flow Problems . . .........p.17

1.2.4. Discrete Network Optimization Problems .......p.19

1.3. Network Flow Algorithms – An Overview .........p.20

1.3.1. Primal Cost Improvement ..............p.21

1.3.2. Dual Cost Improvement ...............p.24

1.3.3. Auction ......................p.27

1.3.4. Good, Bad, and Polynomial Algorithms ........p.35

1.4. Notes, Sources, and Exercises ...............p.37

2. Shortest Path Problems ...............p.51

2.1. Problem Formulation and Applications . .........p.52

2.2. A Generic Shortest Path Algorithm . . . .........p.57

2.3. Label Setting (Dijkstra) Methods .............p.65

2.3.1. Performance of Label Setting Methods .........p.68

2.3.2. The Binary Heap Method ..............p.69

2.3.3. Dial’s Algorithm ..................p.70

2.4. Label Correcting Methods ................p.73

2.4.1. The Bellman-Ford Method ..............p.73

2.4.2. The D’Esopo-Pape Algorithm . . . .........p.75

2.4.3. The SLF and LLL Algorithms . . . .........p.76

2.4.4. The Threshold Algorithm ..............p.78

2.4.5. Comparison of Label Setting and Label Correcting . . . p. 80

2.5. Single Origin/Single Destination Methods .........p.81

2.5.1. Label Setting ....................p.81

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