Multicriteria Design: Optimization and Identification

218 Pages·1999·8.288 MB·English

by  Roman B. Statnikov (auth.)

Multicriteria Design
Applied Optimization
Volume 26
Series Editors:
Panos M. Pardalos
University ofF lorida, U.SA.
Donald Hearn
University ofF lorida, U.SA.
The titles published in this series are listed at the end of this volume.
Multicriteria Design
Optimization and Identification
by
Roman B. Statnikov
Mechmlical Engineering Research Institute,
RussUm Academy ofS ciences,
Moscow, Russia
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-5165-3 ISBN 978-94-017-2363-3 (eBook)
DOI 10.1007/978-94-017-2363-3
Printed on acid-free paper
All Rights Reserved
©1999 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1999
No part of the material protected by this copyright notice may be reproduced or
utilized in any form or by any means, electronic or mechanical,
including photocopying, recording or by any information storage and
retrieval system, without written permission from the copyright owner
Contents
PREFACE. ...................................................................................................... "VII
INTRODUCTION. WHAT IS THIS BOOK NEEDED FOR? ..................... IX
ION A HIGHLY WIDESPREAD CLASS OF ENGINEERING
OPTIMIZATION PROBLEMS ......................................................................... 1
1.1 ON Two PROBLEMS WHICH ARE NOT STATED ................................................ 1
1.1.1 Example: Oscillatory System ................................................................... 1
1.1.2 Example: The Rear Axle Housingfor a Truck ......................................... 3
1.2 GENERALIZED FORMULATION OF MULTICRITERIA OPTIMIZATION
PROBLEMS ............................................................................................................. 6
2 HOW TO HELP THE DESIGNER FORMULATE A MULTICRITERIA
OPTIMIZATION PROBLEM ......................................................................... 1 5
2.1 SEARCHING THE DESIGN VARIABLE SPACE .................................................... 15
2.2 PARAMETER SPACE INVESTIGATION METHOD IS A TOOL FOR FORMULATING
AND SOLVING ENGINEERING OPTIMIZATION PROBLEMS ...................................... 23
2.3 ON SOME POSSIBILITIES OF THE PSI METHOD ............................................... 30
3 MULTICRITERIA ANALYSIS IN OPTIMAL DESIGN. ......................... 37
3.1 STATEMENT AND SOLUTION OF MULTICRITERIA OPTIMIZATION PROBLEMS.
DISCUSSION ......................................................................................................... 37
3.1.1 Example: The Choice oft he Optimal Design Variables for an
Osc illatory System .......................................................................................... 37
3.1.2 Example: Optimal Design oft he Rear Axle Housingfor a Truck.. ....... 45
3.2 ON SOME ARGUMENTS OF EXPERTS ONCE AGAIN ......................................... 53
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vi Contents
4 MULTICRITERIA APPROACHES IN MECHANICAL
ENGINEERING ................................................................................................ 57
4.1 ESSAyS .......................................................................................................... 58
4.1.1 Machine Tools ....................................................................................... 58
4.1.2 Aircraft Gas Turbine Engine ................................................................. 63
4.1.3 Nuclear Reactor .................................................................................... 67
4.2 EXAMPLES ..................................................................................................... 73
4.2.1 Unmanned Vehicle Configuration ......................................................... 73
4.2.2 A Parallel Manipulator for Extremal Media ......................................... 80
4.2.3 Pumping Assemblies ofI nvolute Internal Gear Pumps ......................... 84
4.2.4 Improving the Truck Frame Prototype .................................................. 87
4.2.5 The Improvement of Vehicle Handling and Stability ............................. 91
4.2.6 Metal Cutting Machine Tools and Their Units ...................................... 96
4.2.7 Arrangement oft he Transmission ofa Four Wheel Drive Car ............ 104
5 MULTICRITERIA OPTIMIZATION OF LARGE-SCALE
SYSTEMS ........................................................................................................ 111
5.1 ESSAYS ........................................................................................................ III
5.1.1 Automobile .......................................................................................... 111
5.1.2 Aircraft ................................................................................................ 116
5.1.3 Multipurpose Aerospace Systems ........................................................ 122
5.2 THE CONSTRUCTION OF CONSISTENT SOLUTIONS ........................................ 132
5.2.1 Example: Design ofa Car for Shock Protection ................................. 134
6 MULTICRITERIA IDENTIFICATION ................................................... 143
6.1 ADEQUACY OF MATHEMATICAL MODELS. Two ESSAYS ............................. 143
6.2 MULTICRITERIA IDENTIFICA nON AND OPERATIONAL DEVELOPMENT.
ARGUMENTS ...................................................................................................... 149
6.2.1 Example: Multicriteria Identification oft he Parameters of
a Siotter ........................................................................................................ 153
6.2.2 Example: Multicriteria Identification ofC haracteristics of
a Spindle Unit and its Operational Development ........................................ 161
7 OPTIMAL DESIGN AND MULTICRITERIA CONTROL ................... 173
7.1 NEW ApPROACH TO SOLVING THE PROBLEM ............................................... 174
7.2 EXAMPLE: MULTI-STAGE AXIAL FLOW COMPRESSOR FOR THE
AIRCRAFT ENGINE ............................................................................................. 178
INSTEAD OF EPILOGUE. WHAT NEXT? ................................................ 190
ADDENDUM ................................................................................................... 191
REFERENCES ................................................................................................ 197
INDEX ............................................................................................................. 201
Preface
This book is devoted to the PSI method. Its appearance was a reaction to
the unsatisfactory situation in applications of optimization methods in
engineering. After comprehensive testing of the PSI method in various fields
of machine engineering it has become obvious that this method substantially
surpasses all other available techniques in many respects. It has now become
known that the PSI method is successfully used not only in machine design,
at which it was initially aimed, but also in polymer chemistry, pharmacy,
nuclear energy, biology, geophysics, and many other fields of human
activity. To all appearances this method has become so popular for its
potential of taking into account the specific features of applied optimization
better than other methods, being, at the same time, comparatively simple and
friendly, and because, unlike traditional optimization methods which are
intended only for searching for optimal solutions, the PSI method is also
aimed at correctly formulating engineering optimization problems. One
well-known aircraft designer once said, "To solve an optimization problem
in engineering means, first of all, to be able to state this problem properly".
In this sense the PSI method has no competitors. Although this method has
been presented in Russia in numerous papers and books, Western readers
have had the opportunity to familiarize themselves with this method only
recently (Ozernoy 1988; Lieberman 1991; Stadler and Dauer 1992; Dyer,
Fishburn, Steuer, Wallenius, and Zionts 1992; Steuer and Sun 1995, etc.). In
Russia there have been published two popular scientific books devoted to
the PSI method (Sobol' and Statnikov 1982; Statnikov and Matusov 1989).
One of the aims that I pursue in this book is to expound the PSI method
in simple terms with many illustrative examples, so as to make this novel
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viii Preface
approach to searching for optimal solutions in engineering accessible and
comprehensible to the general Western reader.
The PSI method is implemented in the software package MOVI
(Multicriteria Optimization and Vector Identification). With the use of the
MOVI package hundreds of problems have been solved, including the
problems presented in this book.
In a sense, any engineering optimization problem can be compared to a
novel with a thriller plot. This novel tells us how and why the problem
changes its form during the solution process, what kind of information
induces the designer to correct the problem statement, what motivates the
designer's behavior when analyzing the feasible solutions and selecting the
optimal design, and many other exciting things. You will be provided with
all this information if you apply the PSI method. The PSI method is not
rigidly formalized. It invites a designer to a dialog, provides himlher with
information for thinking and searching for alternative solutions, and
facilitates making a substantiated decision on the optimal design in
multicriteria situations.
In this book, by way of numerous examples, the efficiency of the PSI
method for the statement and solution of engineering problems of
identification and optimization, including optimization of a large-scale
system and optimization of control, is shown. I am sure that the PSI method
will greatly help the reader in solving engineering problems. My experience
of solving a great number of such problems over many years has made me
convinced of this.
Moscow, July 1998
R. Statnikov
Introduction
What is This Book Needed for?
The majority of engineering problems are essentially multicriteria problems.
In designing machine tools, airplanes, automobiles, ships, and locomotives
we do our best to increase their productivity, strength, reliability, longevity,
efficiency, and utilization factor. At the same time we try to decrease
vibration and noise, production and maintenance costs, the number of
failures, material and fuel consumption, overall dimensions, etc ..
To solve the optimization problem and to extract useful information from
the solution the designer must be able to answer the following three
questions:
WHAT TO SEARCH FOR? In response to this question we should
indicate all major objective functions (performance criteria).
WHERE TO SEARCH? In response to this question we should correctly
define all constraints to be imposed on the object. These constraints specify
the set of feasible solutions.
HOW TO SEARCH? In response to this question we should indicate the
optimization technique which is the best in taking into account the specific
features of the problems being solved.
In the remote fifties to seventies a great number of single-criterion
optimization techniques, together with the corresponding software, were
developed when computers began to be widely used in engineering practice,
see, e.g., Fiacco and McCormick (1968) and Himmelblau (1972).
The criteria used for evaluating the efficiency of algorithms involved:
- the time required for implementing the computational procedure (the
number of operations and the time needed for their execution);
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x Introduction
- the complicatedness of the problem (the number of design variables and
performance criteria and the number of equality and inequality
constraints);
the solution accuracy and other characteristics.
How many hopes and expectations there were at that time! Once you had
chosen a suitable method of optimization, you would be a winner!
Unfortunately, things appeared to be rather more complicated than had been
assumed. Many of the efficient methods which were the winners in the
corresponding classes of test functions did not give the anticipated results
when applied to practical problems. Nothing followed from the fact that we
can find an extremum of some test function in 2 min when using one method
and in 5 min when using another method. In many cases it turned out that
the optimal solutions obtained were of no applied interest. All this
stimulated works indicating the low efficiency of using optimization
methods in engineering. One of these works is the profound analytical
survey by H. Ashley (1982) in which he shows the low efficiency of using
optimization methods in the aircraft industry.
Doubts arose as to whether it was only optimization methods that
predetermined failure in using the optimization approach in engineering.
It is well known that to cure a sick person the physician must know the
diagnosis of hislher disease. In our case the diagnosis can be compared to
the adequate, correct statement of the optimization problem. Otherwise even
the best medicine (in our case, the method of optimization) can turn out to
have low efficiency. This is just the situation we often encounter in
engineering: the available optimization methods in practice cannot help
engineers in solving their problems.
Though a great number of publications are devoted to optimization
methods, there are virtually no works in which the specific features of
engineering optimization problems are considered and different statements
ofthese problems are discussed.
In engineering we deal with multicriteria optimization and, furthermore,
with performance criteria usually competing with each other (contradictory,
antagonistic): improving a system in terms of some of the criteria we make it
worse in some other criteria. In such a situation it is very difficult (if
possible at all) for a designer to formulate the optimization problem
correctly. In this sense such optimization problems are ill posed.
Very often by solving ill-posed problems we obtain an 'optimal' solution
which is of no practical interest.
Let us ask ourselves how many design solutions of a machining center,
an automobile, or a ship are considered before choosing the single one that
is to be put into quantity production? The answer is: not many. As a result
we have to seek the optimal solution among a few candidates that are often