Introduction to Optimum Design, Fourth Edition

933 Pages·2016·49.4 MB·English

by  Arora

INTRODUCTION
TO OPTIMUM
DESIGN
FOURTH EDITION
Jasbir singh arora
The University of Iowa,
College of Engineering,
Iowa City, Iowa
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Dedications
To
Rita
Ruhee
Matthew
and
in memory of my parents
Balwant Kaur
Wazir Singh
Preface to Fourth Edition
Introduction to Optimum Design, Fourth Edi- basis for a first course on optimum design.
tion presents an organized approach to opti- More detailed calculations are included in
mizing the design of engineering systems. examples to illustrate procedures. Key ideas
Basic concepts and procedures of optimiza- of various concepts are highlighted for easy
tion are illustrated with examples to show reference.
their applicability to engineering design Practical applications of optimization
problems. The crucial step of formulating techniques are expanding rapidly, and to
a design optimization problem is detailed. illustrate this, engineering design exam-
The numerical process of refining an initial ples are presented throughout the text.
formulation of the optimization problem Chapters: Optimum Design: Numerical
is illustrated and how to correct the initial Solution Process and Excel Solver, Opti-
formulation if it fails to produce a solution mum Design with MATLAB®, and Practical
or does not produce an acceptable solution. Applications of Optimization also address
This as well as other numerical aspects of various aspects of practical applications of
the solution process for optimum design are optimization with example problems. Many
consolidated in chapter: Optimum Design: projects (identified with a *) based on prac-
Numerical Solution Process and Excel Solver. tical applications are included as exercises
The pedagogical aspects of the material at the end of c hapters: Optimum Design
are addressed from student as well as teach- Problem Formulation, Graphical Solution
er’s point of view. This is particularly true Method and Basic Optimization Concepts,
for the material of chapters: Introduction Optimum Design: Numerical Solution Pro-
to Design Optimization, Optimum Design cess and Excel Solver, Optimum Design
Problem Formulation, Graphical Solution with MATLAB®, Practical Applications of
Method and Basic Optimization Concepts, Optimization, Discrete Variable Optimum
Optimum Design Concepts: Optimality Con- Design Concepts and Methods, and Nature-
ditions, More on Optimum Design Concepts: Inspired Search Methods.
Optimality Conditions, Optimum Design: Direct search methods that do not use any
Numerical Solution Process and Excel Solver, stochastic ideas in their search are presented
Optimum Design with MATLAB®, Linear in chapter: More on Numerical Methods for
Programming Methods for Optimum Design, Unconstrained Optimum Design and those
More on Linear Programming Methods for that do are presented in chapter: Nature-
Optimum Design, Numerical Methods for Inspired Search Methods. These methods do
Unconstrained Optimum Design, More on not require derivatives of the problem func-
Numerical Methods for Unconstrained Opti- tions, therefore they are broadly applicable
mum Design, and Numerical Methods for for practical applications and they are rela-
Constrained Optimum Design that forms the tively easy to program and use.
xv
xvi PrEFacE to Fourth Edition
The instructor’s manual that accompanies for students. Three courses are suggested,
the text is comprehensive and user-friendly. although several variations are possible.
The original problem statement for each
exercise is included in the solution page for Undergraduate/First-Year Graduate
easy reference. Many MATLAB and Excel
Level Course
files for the problems are also included.
The text is broadly divided into three Topics for an undergraduate and/or first-
parts. Part I presents the basic concepts year graduate course include:
related to optimum design and optimal-
• Formulation of optimization problems
ity conditions in chapters: Introduction to
(see chapters: Introduction to Design
Design Optimization 2 Optimum Design
Optimization and Optimum Design
Problem Formulation, Graphical Solution
Problem Formulation)
Method and Basic Optimization Concepts,
• Optimization concepts using the
Optimum Design Concepts: Optimality Con-
graphical method (see chapter: Graphical
ditions, and More on Optimum Design Con-
Solution Method and Basic Optimization
cepts: Optimality Conditions. Part II treats
Concepts)
numerical methods for continuous variable
• Optimality conditions for unconstrained
smooth optimization problems and their
and constrained problems (see chapter:
practical applications in chapters: Opti-
Optimum Design Concepts: Optimality
mum Design: Numerical Solution Process
Conditions)
and Excel Solver, Optimum Design with
• Use of Excel and MATLAB® illustrating
MATLAB®, Linear Programming Methods
optimum design of practical problems
for Optimum Design, More on Linear Pro-
(see chapters: Optimum Design:
gramming Methods for Optimum Design,
Numerical Solution Process and Excel
Numerical Methods for Unconstrained
Solver and Optimum Design with
Optimum Design, More on Numerical Meth-
MATLAB®)
ods for Unconstrained Optimum Design,
• Linear programming (see chapter: Linear
Numerical Methods for Constrained Opti-
Programming Methods for Optimum
mum Design, More on Numerical Methods
Design)
for Constrained Optimum Design, Practical
• Numerical methods for unconstrained
Applications of Optimization. Part III con-
and constrained problems (see chapters:
tains advanced topics of practical interest on
Numerical Methods for Unconstrained
optimum design, including nature-inspired
Optimum Design and Numerical
metaheuristic methods that do not require
Methods for Constrained Optimum
derivatives of the problem functions in
Design)
chapters: Discrete Variable Optimum Design
Concepts and Methods, Global Optimization The use of Excel and MATLAB should be
Concepts and Methods, Nature-Inspired introduced mid-semester so that students
Search Methods, Multi-objective Optimum have a chance to formulate and solve more
Design Concepts and Methods, and Addi- challenging projects by the semester’s end.
tional Topics on Optimum Design. Note that project exercises and sections with
Introduction to Optimum Design, Fourth advanced material are marked with an aster-
Edition can be used to design several types of isk (*) next to section headings, which means
courses depending on the learning objectives that they may be omitted for this course.
PrEFacE to Fourth Edition xvii
First Graduate-Level Course of iterative algorithms, derivation of
numerical methods, and direct search
Topics for a first graduate-level course
methods (see chapters: Introduction
include
to Design Optimization, Optimum
• Theory and numerical methods for Design Problem Formulation, Graphical
unconstrained optimization (see Solution Method and Basic Optimization
chapters: Introduction to Design Concepts, Optimum Design Concepts:
Optimization, Optimum Design Problem Optimality Conditions, More on
Formulation, Graphical Solution Method Optimum Design Concepts: Optimality
and Basic Optimization Concepts, Conditions, Optimum Design: Numerical
Optimum Design Concepts: Optimality Solution Process and Excel Solver,
Conditions, Numerical Methods for Optimum Design with MATLAB®, Linear
Unconstrained Optimum Design, Programming Methods for Optimum
and More on Numerical Methods for Design, More on Linear Programming
Unconstrained Optimum Design) Methods for Optimum Design,
• Theory and numerical methods for Numerical Methods for Unconstrained
constrained optimization (see chapters: Optimum Design, More on Numerical
Optimum Design Concepts: Optimality Methods for Unconstrained Optimum
Conditions, More on Optimum Design Design, and Numerical Methods for
Concepts: Optimality Conditions, Constrained Optimum Design, More
Numerical Methods for Constrained on Numerical Methods for Constrained
Optimum Design, and More on Optimum Design, and Practical
Numerical Methods for Constrained Applications of Optimization)
Optimum Design) • Methods for discrete variable problems
• Linear and quadratic programming (see (see chapter: Discrete Variable Optimum
chapters: Linear Programming Methods Design Concepts and Methods)
for Optimum Design and More on Linear • Global optimization (see chapter: Global
Programming Methods for Optimum Optimization Concepts and Methods)
Design) • Nature-inspired search methods
(see chapter: Nature-Inspired Search
The pace of material can be a bit faster
Methods)
for this course. Students should code some
• Multi-objective optimization (see chapter:
of the algorithms into computer programs
Multi-objective Optimum Design
and solve some projects based on practical
Concepts and Methods)
applications.
• Response surface methods, robust
design, and reliability-based design
optimization (see chapter: Additional
Second Graduate-Level Course
Topics on Optimum Design)
This course presents advanced topics on
In this course, students write computer
optimum design:
programs to implement some of the numeri-
• Duality theory in nonlinear cal methods to gain experience with their
programming, rate of convergence coding and to solve practical problems.
Acknowledgments
I would like to thank my colleague Pro- classroom instruction and provided me with
fessor Karim Abdel-Malek, Director of the their input.
Center for Computer-Aided Design and Pro- I acknowledge the input of my current
fessor of Biomedical Engineering at The Uni- and former colleagues at The University of
versity of Iowa, for his enthusiastic support Iowa who have used the book to teach an
for this book and for the exciting research on undergraduate course on optimum design:
optimization-based modeling, simulation Professors Karim Abdel-Malek, Asghar
and biomechanics of human motion. Bhatti, Kyung Choi, Vijay Goel, Ray Han,
I would like to thank the following col- Harry Kane, George Lance, and Emad
leagues for their contribution to some Tanbour.
chapters: Professor Tae Hee Lee – chapter: Thesis works of all of my current and for-
Optimum Design with MATLAB®; Dr Tim mer graduate students on various topics of
Marler – chapter: Multi-objective Optimum optimization have been invaluable in broad-
Design Concepts and Methods; Professor ening of my horizons on the subject.
G. J. Park – chapter: Additional Topics on I would like to thank reviewers of various
Optimum Design; and Dr Marcelo A. da parts of the book for their suggestions.
Silva and Dr. Qian Wang – chapter: Practical I would also like to thank Steve Merken,
Applications of Optimization. Peter Jardim, Kiruthika Govindaraju and
Dr Yujiang Xiang, Dr Rajan Bhatt, their team at Elsevier for their superb han-
Dr Hyun-Joon Chung, John Nicholson and dling of the manuscript and production of
Robert Lucente provided valuable input for the book.
some chapters. I value the support of the Department of
I appreciate the help given by Jun Choi, Civil and Environmental Engineering, Cen-
John Nicholson, Palani Permeswaran, Karlin ter for Computer-Aided Design, College of
Stutzman, Dr Hyun-Jung Kwon, Dr Hyun- Engineering, and The University of Iowa for
Joon Chung, and Dr Mohammad Bataineh this project.
with parts of the instructor’s manual. Finally, I highly appreciate the uncondi-
I would like to thank instructors at vari- tional love and support of my family and
ous universities who have used the book for friends.
xix
Key Symbols and Abbreviations
(a · b) Dot product of vectors a and b; aTb ILP Integer linear programming
c(x) Gradient of cost function, ∇f(x) KKT Karush–Kuhn–Tucker
f(x) Cost function to be minimized LP Linear programming
g(x) jth inequality constraint MV-OPT Mixed variable optimization problem
j
h(x) ith equality constraint NLP Nonlinear programming
i
m Number of inequality constraints PSO Particle swarm optimization
n Number of design variables QP Quadratic programming
p Number of equality constraints RBDO Reliability-based design optimization
x Design variable vector of dimension n SA Simulated annealing
x ith component of design variable vector x SLP Sequential linear programming
i
x(k) kth design variable vector SQP Sequential quadratic programming
ACO Ant colony optimization TS Traveling salesman (salesperson)
BBM Branch-and-bound method
CDF Cumulative distribution function
CSD Constrained steepest descent Note: A superscript “*” indicates (1) optimum value for a
DE Differential evolution; Domain elimination variable, (2) advanced material section, and (3) a project-
GA Genetic algorithm type exercise.
xxi
C H A P T E R
1
Introduction to Design Optimization
Upon completion of this chapter, you will be able to:
• Describe the overall process of designing • Distinguish between optimum design and
systems optimal control problems
• Distinguish between engineering design and • Understand the notations used for
engineering analysis activities operations with vectors, matrices, and
functions and their derivatives
• Distinguish between the conventional design
process and optimum design process
Engineering consists of a number of well-established activities, including analysis, design,
fabrication, sales, research, and development of systems. The subject of this text—the design
of systems—is a major field in the engineering profession. The process of designing and fab-
ricating systems has been developed over centuries. The existence of many complex systems,
such as buildings, bridges, highways, automobiles, airplanes, space vehicles, and others, is
an excellent testimonial to its long history. However, the evolution of such systems has been
slow and the entire process is both time-consuming and costly, requiring substantial human
and material resources. Therefore, the procedure is to design, fabricate, and use a system
regardless of whether it is the best one. Improved systems have been designed only after a
substantial investment has been recovered.
The preceding discussion indicates that several systems can usually accomplish the same
task, and that some systems are better than others. For example, the purpose of a bridge
is to provide continuity in traffic from one side of the river to the other. Several types of
bridges can serve this purpose. However, to analyze and design all possibilities can be time-
consuming and costly. Usually one type is selected based on some preliminary analyses and
is designed in detail.
The design of a system can be formulated as a problem of optimization in which a performance
measure is optimized while all other requirements are satisfied. Many numerical methods of
optimization have been developed and used to design better systems. This text describes the
basic concepts of optimization and numerical methods for the design of engineering systems.
Design process, rather than optimization theory, is emphasized. Various theorems are stated
Introduction to Optimum Design. http://dx.doi.org/10.1016/B978-0-12-800806-5.00001-9
Copyright © 2017 Elsevier Inc. All rights reserved.
3
4 1. INTrODuCTION TO DESIgN OPTImIzATION
as results without rigorous proofs. However, their implications from an engineering point of
view are discussed.
any problem in which certain parameters need to be determined to satisfy constraints
can be formulated as an optimization problem. once this has been done, optimization con-
cepts and methods described in this text can be used to solve it. optimization methods are
quite general, having a wide range of applicability in diverse fields. It is not possible to
discuss every application of optimization concepts and methods in this introductory text.
However, using simple applications, we discuss concepts, fundamental principles, and basic
techniques that are used in most applications. The student should understand them with-
out getting bogged down with notations, terminologies, and details on particular areas of
application.
1.1 THE DESIGN PROCESS
How Do I Begin to Design a System?
Designing engineering systems can be a complex process. assumptions must be made to
develop realistic models that can be subjected to mathematical analysis by the available meth-
ods. The models may need to be verified by experiments. Many possibilities and factors must
be considered during the optimization problem formulation phase. Economic considerations
play an important role in designing cost-effective systems. To complete the design of an en-
gineering system, designers from different fields of engineering must usually cooperate. For
example, the design of a high-rise building involves designers from architectural, structural,
mechanical, electrical, and environmental engineering, as well as construction management
experts. Design of a passenger car requires cooperation among structural, mechanical, auto-
motive, electrical, chemical, hydraulics design, and human factor engineers. Thus, in an inter-
disciplinary environment, considerable interaction is needed among design teams to complete
the project. For most applications, the entire design project must be broken down into several
subproblems, which are then treated somewhat independently. Each of the subproblems can
be posed as a problem of optimum design.
The design of a system begins with the analysis of various options. Subsystems and their
components are identified, designed, and tested. This process results in a set of drawings,
calculations, and reports with the help of which the system can be fabricated. We use a sys-
tems engineering model to describe the design process. although complete discussion of this
subject is beyond the scope of this text, some basic concepts are discussed using a simple
block diagram.
Design is an iterative process. Iterative implies analyzing several trial designs one after an-
other until an acceptable design is obtained. It is important to understand the concept of
a trial design. In the design process, the designer estimates a trial design of the system
based on experience, intuition, or some simple mathematical analyses. The trial design is
then analyzed to determine if it is acceptable. In case it gets accepted, the design process
is terminated. In the optimization process, the trial design is analyzed to determine if it is the
best. Depending on the specifications, “best” can have different connotations for different
systems. In general, it implies that a system is cost-effective, efficient, reliable, and durable.
I. THE BaSIc concEpTS