Interactive Decision Maps: Approximation and Visualization of Pareto Frontier

310 Pages·2004·1.14 MB·English

by  Alexander V. Lotov

INTERACTIVE DECISION MAPS
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
Applied Optimization
Volume 89
Series Editors:
Panos M. Pardalos
University ofF lorida, U.SA.
Donald W. Hearn
University ofF lorida, U.SA.
INTERACTIVE DECISION MAPS
Approximation and Visualization of
Pareto Frontier
by
Alexander V. Lotov
State University-Higher School ofE conomics, Russia,
Dorodnicyn Computing Centre ofR ussian Academy ofS ciences, Russia,
Lomonosov Moscow State University, Russia
Vladimir A. Bushenkov
University ofEvora, Portugal
Georgy K. Kamenev
Dorodnicyn Computing Centre ofR ussian Academy ofS ciences, Russia
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
• Electronic Services <http://www.wkap.nl>
Library of Congress Cataloging-in-Publication
Lotov, Alexander V./ Bushenkov, Vladimir A./ Kamenev, Georgy K.
Interactive Decision Maps: Approximation and Visualization of Pareto Frontier
ISBN 978-1-4613-4690-6 ISBN 978-1-4419-8851-5 (eBook)
DOI 10.1007/978-1-4419-8851-5
Copyright© 2004 by Springer Science+ Business Media New York
Originally published by Kluwer Academic Publishers in 2004
Softcover reprint of the hardcover 1st edition 2004
All rights reserved. No part oft his publication may be reproduced, stored in a retrieval system or
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recording, or otherwise, without the prior written permission ofthe publisher, with the exception
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Printed on acid-free paper.
To our Teachers
Contents
Foreword xi
Preface xiii
Acknowledgments xxi
Part I Environmental, Business and Other Applications of
Interactive Decision Maps
1. INTRODUCTION TO INTERACTIVE DECISION MAPS 3
1 Visualization in decision screening 3
2 Visualization of the Pareto frontier in a regional
environmental problem 7
3 Interactive Decision Maps 16
4 The FGM/IDM technique 21
5 Computational aspects of the IDM technique 29
2. ACADEMIC APPLICATIONS 35
1 Ocean waste management decisions 36
2 Search for efficient water-related strategies of regional
agricultural development 40
3 Analysis of long-term development of a national economy 48
4 Searching for trans-boundary air pollution control
strategies 53
5 Searching for smart strategies for abatement of global
climate change 60
3. REAL-LIFE APPLICATIONS 69
1 On the real-life application of decision support techniques:
identification of national goals 69
2 DSS for water quality planning in river basins 74
3 DSS for screening of water quality improvement plans 81
viii INTERACTIVE DECISION MAPS
4. REASONABLE GOALS METHOD AND ITS
APPLICATIONS 99
1 Introduction to the Reasonable Goals Method 100
2 RGM in water quality planning 109
3 Screening of national energy production strategies 111
4 Selection of a location for rural health practice 115
5 RGM on the Web: application server for e-commerce 119
6 Several other applications 124
7 RGM as a tool for database visualization, data mining
and cost-benefit analysis 126
5. NON-LINEAR SYSTEMS AND OTHER NEW
DEVELOPMENTS 129
1 Feasible Goals Method for non-linear models 129
2 FGM/IDM technique for non-linear models 140
3 RGM/IDM technique for non-linear models 146
4 Visualization of risk-related decision problems 147
5 Visualization in Data Envelopment Analysis 154
Part II Computational Methods of the IDM Technique
6. COMPUTATIONAL METHODS FOR STATIC MODELS 165
1 Methods based on convolution of linear inequalities 170
2 Methods for polyhedral approximation of convex bodies 182
3 Approximating the Edgeworth-Pareto Hull in the convex
case 199
4 Approximating the FCS for non-linear models 201
5 Approximating the EPH in the non-linear case 210
7. COMPUTATIONAL METHODS FOR DYNAMIC SYSTEMS 219
1 Approximation of FCSs and EPHs for dynamic systems 220
2 Approximation of reachable sets for convex systems 223
3 Reduction-based methods for constructing reachable sets 225
4 Approximating and estimating reachable sets for non-
convex systems 230
5 Approximating the FCS for systems in partial derivatives 231
Contents ix
Part III Several Topics Related to Mathematical Basis of IDM
8. THEORY OF ITERATIVE METHODS FOR POLYHEDRAL
APPROXIMATION OF CONVEX BODIES 237
1 Polyhedral approximation of compact convex bodies 237
2 Asymptotic theory of polyhedral approximation of
compact convex bodies 239
3 Augmentation and cutting schemes 244
4 H -classes of adaptive methods 246
5 Optimality and efficiency of H-methods 249
6 Optimality and efficiency of H1-methods 250
7 Several optimal methods for polyhedral approximation of
CCB 257
8 Related topics 260
9. PERTURBATIONS OF SOLUTION SETS OF LINEAR
SYSTEMS 263
1 Perturbations of convex bodies given by linear mappings 264
2 Perturbations of solution sets of linear systems in Banach
space 266
3 Perturbations of solution sets of finite-dimensional linear
inequality systems 269
4 Perturbations of solution sets of linear systems of equalities
and inequalities 273
5 Perturbations of solution sets of linear equality systems 275
6 Condition number for finite-dimensional systems and its
application 276
Epilogue: New applications of IDM technique in Web 279
References 289
Author Index 303
Index 307
Foreword
Multiple criteria optimization (MCO) is an important problem area
which has challenged researchers and practitioners for several decades.
Its importance derives from the prevalence of multiple criteria problems
in virtually every sphere of policy and decision making. Its challenge
results from computational complexity, as well as the inherent difficulty
of making decisions and crafting policy when there is a large number of
choices and many conflicting objectives.
Now, with the publication of this book, we have a welcome addition to
the MCO literature and to the toolkit of the MCO practitioners. Alexan
der Lotov, whose work I have followed and admired for thirty years, is a
leader in MCO and multiple criteria decision making (of which MCO is
an important branch) - leadership which has been recognized with the
prestigious Edgeworth-Pareto Prize awarded by the International Multi
ple Criteria Decision Making Society. Dr. Lotov and his colleagues, Dr.
Bushenkov and Dr. Kamenev, have recorded here the major methods
that they have developed and applied over several years.
It is especially noteworthy that the book and its original methods
cover all of the major aspects of MCO problems. We have a method
for approximating the Pareto frontier - the first and fundamentally
important problem in MCO. Though many techniques and treatments
would stop at this point, this book continues on to the crucial (but
often ignored) problem of visualizing the Pareto frontier. This more
comprehensive approach makes the methods covered in the book all the
more valuable, but Lotov and his colleagues do not stop there. They also
explore ways to use their methodology to support the decision maker's
search for a preferred solution from among the many (likely infinite)
Pareto solutions.
This book also presents many applications of the techniques. This
is important, for MCO is a field that has developed and evolved in