Table Of ContentGlobal Optimization in Engineering Design
Nonconvex Optimization and Its Applications
Volume 9
Managing Editors:
Panos Pardalos
University ofF lorida, U.S.A.
Reiner Horst
University of Trier, Germany
Advisory Board:
Ding-ZhuDu
University ofM innesota, U.S.A.
C. A. Floudas
Princeton University, U.S.A.
G.lnfanger
Stariford University, U.S.A.
J. Mockus
Lithuanian Academy of Sciences, Lithuania
H. D. Sherali
Virginia Polytechnic Institute and State University, U.S.A.
I. E. Grossmann
Carnegie Mellon University
The titles published in this series are listed at the end oft his volume.
Global Optimization in
Engineering Design
Edited by
Ignacio E. Grossmann
Carnegie Mellon University
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
Library of Congress Cataloging-in-Publication Data
Global optimization in engineering design 1 edited by Ignacio E.
Grossmann.
p. cm. -- <Nonconvex optimization and its applications v.
9>
ISBN 978-1-4419-4754-3 ISBN 978-1-4757-5331-8 (eBook)
DOI 10.1007/978-1-4757-5331-8
1. Chemical engineering--Mathematics. 2. Mathematical
optimization. 3. Nonlinear programming. I. Grossmann, Ignacio E.
II. Series.
TP149.G55 1996
620' .0042'015197--dc20 95-48887
ISBN 978-1-4419-4754-3
Printed on acid-free paper
AU Rights Reserved
© 1996 Springer Science+Business Media Dordrecht
Originally published by Kluwer Academic Publishers in 1996
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.
TABLE OF CONTENTS
Preface ..................................................... vii
1. Branch and Bound for Global NLP: New Bounding LP
T. G. W. Epperly and R. E. Swaney ....................................... 1
2. Branch and Bound for Global NLP: Iterative LP Algorithm Be
Results
T. G. W. Epperly and R. E. Swaney ..................................... 37
3. New Formulations and Branching Strategies for the GOP Algo
rithm
V. Visweswaran and C. A. Floudas ....................................... 75
4. Computational Results for an Efficient Implementation of the
GOP Algorithm and Its Variants
V. Visweswaran and C. A. Floudas ...................................... Ul
5. Solving Nonconvex Process Optimisation Problems Using Interval
Subdivision Algorithms
R. P. Byrne and I. D. L. Bogle .......................................... 155
6. Global Optimization of Nonconvex MINLP's by Interval Analysis
R. Vaidyanathan and M. EI-Halwagi .................................... 175
7. Planning of Chemical Process Networks via Global Concave Min-
imization
M.-L. Liu, N. V. Sahinidis and J. Parker Shecttnan ...•.................... 195
8. Global Optimization for Stochastic Planning, Scheduling and De
sign Problems
M. G. Ierapetritou and E. N. Pistikopoulos .............................. 231
9. Global Optimization of Heat Exchanger Networks with Fixed
Configuration for Multiperiod Design
R. R. Iyer and I. E. Grossmann ......................................... 289
10. Alternative Bounding Approximations for the Global Optimiza
tion of Various Engineering Design Problems
I. Quesada and I. E. Grossmann ........................................ 309
vi TABLE OF CONTENTS
11. A Pipe Reliability and Cost Model for an Integrated Approach
Toward Designing Water Distribution Systems
H. D. Sherali, E. P. Smith and S. Kim ................................... 333
12. Global Optimisation of General Process Models
E. M. B. Smith and C. C. Pantelides .................................... 355
PREFACE
Mathematical Programming has been of significant interest and relevance in
engineering, an area that is very rich in challenging optimization problems.
In particular, many design and operational problems give rise to nonlinear
and mixed-integer nonlinear optimization problems whose modeling and solu
tion is often nontrivial. Furthermore, with the increased computational power
and development of advanced analysis (e.g., process simulators, finite element
packages) and modeling systems (e.g., GAMS, AMPL, SPEEDUP, ASCEND,
gPROMS), the size and complexity of engineering optimization models is rapidly
increasing. While the application of efficient local solvers (nonlinear program
ming algorithms) has become widespread, a major limitation is that there is
often no guarantee that the solutions that are generated correspond to global
optima. In some cases finding a local solution might be adequate, but in others
it might mean incurring a significant cost penalty, or even worse, getting an
incorrect solution to a physical problem. Thus, the need for finding global optima
in engineering is a very real one.
It is the purpose of this monograph to present recent developments of tech
niques and applications of deterministic approaches to global optimization in
engineering. The present monograph is heavily represented by chemical engi
neers; and to a large extent this is no accident. The reason is that mathematical
programming is an active and vibrant area of research in chemical engineering.
This trend has existed for about 15 years. Currently the trend even appears to be
increasing! In contrast, the interest in other engineering disciplines is generally not
equally strong. Part of the reason can be attributed to those areas where there is
greater use of heuristics and non-traditional optimization tools such as simulated
annealing and genetic algorithms which are claimed to provide satisfactory answers
in selected applications.
To see how the need for global optimization has been motivated in chemical
engineering, it is instructive to briefly follow the development of nonlinear
optimization over the last 20 years in this engineering discipline. In the
70's, pioneering research on nonlinear programming algorithms, which were
applied to process design and optimal control problems, was performed at Imperial
College. Subsequently the advent of the successive quadratic programming
algorithm spurred a great deal of interest and was first applied to chemical process
simulators at Wisconsin in the late 70's. This algorithm was also adapted to
problems with many equations and few degrees of freedom (a common case in
engineering) with decomposition approaches developed in the early 80's at
Carnegie Mellon. New techniques for mixed-integer nonlinear programming
vii
viii PREFACE
emerged also at Carnegie Mellon in the mid to late 80's and were applied for
the first time to chemical process synthesis problems. Nonlinear programming
techniques, especially successive quadratic programming algorithms, continue
to be of active interest at Carnegie Mellon, Clarkson and Imperial College, par
ticularly for large scale applications, such as real time optimization. Likewise,
mixed-integer nonlinear programming algorithms continue to be of interest at
Abo Akademi, Carnegie Mellon, Dundee, Maribor and Imperial College. Ini
tial work in global optimization was performed at Stanford in the early 70's,
while the study of implications of nonconvexities in design and their handling
in decomposition strategies were developed at Florida in the mid-70's. Inter
est in global optimization resurfaced in the late 80's with the development of
Benders type of algorithms at Princeton. Since that time global optimization
has attracted increased attention, and work is being pursued at a number of
universities (largely represented in this monograph). It is this level of research
activity that has motivated the creation of this monograph.
The chapters of this monograph are roughly divided into two major parts: chap
ters 1 to 6 emphasize algorithms, and chapters 7 to 12 emphasize applications.
Chapters 1 and 2 describe a novel and elegant LP-based branch and bound
approach by Epperly and Swaney for solving nonlinear programs that are ex
pressed in factorable form. Computational experience is reported on a set of
50 test problems. Chapters 3 and 4 describe several recent enhancements and
improvements to the GOP algorithm by Visweswaran and Floudas. Details of
the implementation of the algorithm are described, as well as results of process
design and general test problems. Chapters 5 and 6 describe implementations
of methods based on interval analysis. Chapter 5 emphasizes implementations
of existing methods and the effect of inclusion functions, while chapter 6 em
phasizes strategies for accelerating the search and quickly identifying infeasible
solutions.
As for the applications, chapter 7 presents an exact and finite branch and bound
solution approach to the planning of process networks with separable concave
costs. Chapter 8 by Ierapetritou and Pistikopoulos deals with a number of
stochastic planning and scheduling models which are shown to obey convexity
properties when discretization and decomposition schemes are used on two
stage programming formulations. Chapter 9 by Iyer and Grossmann presents
the extension of the global optimization method for heat exchanger networks by
Quesada and Grossmann to the case of multiperiod design problems. Chapter
10 by Quesada and Grossmann explores alternative bounding approximations
for their algorithm for linear fractional and bilinear functions which is applied
to problems in layout design, design of truss structures, and multiproduct batch
design. Chapter 11 by Sherali, Smith and Kim outlines a comprehensive solu-
PREFACE ix
tion approach to the design of reliable water distribution systems in which a
number of nonconvex optimization subproblems are identified. Finally, Chap
ter 12 by Smith and Pantelides presents a symbolic manipulation algorithm
for the systematic reformulation of large structured models, and its implemen
tation in gPROMS for solution with branch and bound algorithms for global
optimization.
We believe that this monograph provides a good overview of the current state
of-the-art of deterministic global optimization techniques for engineering de
sign.
Ignacio E. Grossmann
Carnegie Mellon University
Description:Mathematical Programming has been of significant interest and relevance in engineering, an area that is very rich in challenging optimization problems. In particular, many design and operational problems give rise to nonlinear and mixed-integer nonlinear optimization problems whose modeling and solu
