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E-grāmata: Introduction to Optimum Design

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(Department of Civil and Environmental Engineering & Department of Mechanical Engineering, University of Iowa)
  • Formāts: PDF+DRM
  • Izdošanas datums: 02-Jun-2004
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780080470252
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  • Formāts: PDF+DRM
  • Izdošanas datums: 02-Jun-2004
  • Izdevniecība: Academic Press Inc
  • Valoda: eng
  • ISBN-13: 9780080470252
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The primary purpose of the text is to describe an organized approach to engineering design and its optimization in a rigorous and yet simplified manner. Major emphasis is on the correct formulation of the problem and basic concepts of optimum design. Only a few robust numerical procedures that bring out basic concepts and ideas are presented. It is not the purpose of this text to describe derivations of all the methods and discuss their advantages and disadvantages. References are cited for this purpose. A few modern methods that work well are described and illustrated. The necessary results from optimization theory are stated and their implications are studied through application to engineering design problems. Theory and concepts of optimum design are explained only through examples and simple engineering applications. Proofs of most theorems are omitted. Throughout the text, simple design problems involving two to three design variables and three to four constraints are solved in detail to illustrate fundamental concepts and basic ideas. Several of the numerical procedures and concepts described in the text are useful in many other engineering courses and applications.

- Provides a self-contained exposition to the subject of design optimization.

- Gives examples and exercises from several fields in order to make the subject appealing to all engineering disciplines.

- Allows pengineers involved in the design process to adapt optimum design concepts in their work using the material of the text.

Recenzijas

"I feel that Dr. Arora presented significant amounts of material in a clear and straightforward manner. The book is definitely a reference that practitioners would like to have and depend upon, especially with the plethora of examples and applications. As an educator, Dr. Aroras book also has a tremendous number of problems at the end of the chapters and examples that I would try to use in class...the book is a solid introduction to optimization algorithms." --Georges Fadel, Associate Editor, Journal of Mechanical Design

"Aroras introduction of a much-anticipated second edition of Introduction to Optimum Design will not only satisfy established users of his well-received first edition, but moreover, significant updates, supplementary material, and fine-tuning of the pedagogical aspects of the presentation will certainly broaden its appealamong some of the distinguishing characteristics of Aroras book are its adaptability to audiences with diverse backgrounds, as well as the extent to which it makes the topic clear and approachable...The book would also be excellent as a self-study reference for the practicing engineerIn summary, when considering the pedagogical refinements of the book, the expanded and updated software examples, as well as the extended survey of emerging computational methods, Aroras Introduction to Optimum Design, 2nd Ed., furthers its goal of describing engineering design optimization in a rigorous yet simplified manner which is both highly accessible to and useful for a wide audience." --David F. Thompson, Graduate Program Director, University of Cincinnati

"I have used several optmization books over the past 10 years to support my various graduate optimization courses. Of all the books that I have used, I prefer Dr. Aroras Introduction to Optimum Design, 2nd EdThe strength of this book lies in his attention to detail using numeric exercises to demonstrate the numerical processes used in the various optimization methods. I particularly like his choice of nomenclature throughout the book, as it conforms to the standard symbols and function names used in classical optimization literature. The application exercises presented cover a broad range in technologies, which makes it a good textbook for any engineering discipline." --Tom R. Mincer, California State University

"...this book is well written and covers just about every topic that one needs to know about the optimum design process. It includes a good balance of theory and application. The book will therefore be appealing to all users." --Practice Periodical On Structural Design and Construction - ASCE, Nov. 2005

Papildus informācija

- Provides a self-contained exposition to the subject of design optimization. - Gives examples and exercises from several fields in order to make the subject appealing to all engineering disciplines. - Allows pengineers involved in the design process to adapt optimum design concepts in their work using the material of the text.
Preface ix
Introduction to Design
1(14)
The Design Process
2(2)
Engineering Design versus Engineering Analysis
4(1)
Conventional versus Optimum Design Process
4(2)
Optimum Design versus Optimal Control
6(1)
Basic Terminology and Notation
7(8)
Sets and Points
7(2)
Notation for Constraints
9(1)
Superscripts/Subscripts and Summation Notation
9(2)
Norm/Length of a Vector
11(1)
Functions
11(1)
U.S.-British versus SI Units
12(3)
Optimum Design Problem Formulation
15(40)
The Problem Formulation Process
16(2)
Step 1: Project/Problem Statement
16(1)
Step 2: Data and Information Collection
16(1)
Step 3: Identification/Definition of Design Variables
16(1)
Step 4: Identification of a Criterion to Be Optimized
17(1)
Step 5: Identification of Constraints
17(1)
Design of a Can
18(2)
Insulated Spherical Tank Design
20(2)
Saw Mill Operation
22(2)
Design of a Two-Bar Bracket
24(6)
Design of a Cabinet
30(2)
Formulation 1 for Cabinet Design
30(1)
Formulation 2 for Cabinet Design
31(1)
Formulation 3 for Cabinet Design
31(1)
Minimum Weight Tubular Column Design
32(3)
Formulation 1 for Column Design
33(1)
Formulation 2 for Column Design
34(1)
Minimum Cost Cylindrical Tank Design
35(1)
Design of Coil Springs
36(2)
Minimum Weight Design of a Symmetric Three-Bar Truss
38(3)
A General Mathematical Model for Optimum Design
41(14)
Standard Design Optimization Model
42(1)
Maximization Problem Treatment
43(1)
Treatment of ``Greater Than Type'' Constraints
43(1)
Discrete and Integer Design Variables
44(1)
Feasible Set
45(1)
Active/Inactive/Violated Constraints
45(1)
Exercises for
Chapter 2
46(9)
Graphical Optimization
55(28)
Graphical Solution Process
55(5)
Profit Maximization Problem
55(1)
Step-by-Step Graphical Solution Procedure
56(4)
Use of Mathematica for Graphical Optimization
60(4)
Plotting Functions
61(1)
Identification and Hatching of Infeasible Region for an Inequality
62(1)
Identification of Feasible Region
62(1)
Plotting of Objective Function Contours
63(1)
Identification of Optimum Solution
63(1)
Use of MATLAB for Graphical Optimization
64(2)
Plotting of Function Contours
64(1)
Editing of Graph
64(2)
Design Problem with Multiple Solutions
66(1)
Problem with Unbounded Solution
66(1)
Infeasible Problem
67(2)
Graphical Solution for Minimum Weight Tubular Column
69(1)
Graphical Solution for a Beam Design Problem
69(14)
Exercises for
Chapter 3
72(11)
Optimum Design Concepts
83(92)
Definitions of Global and Local Minima
84(5)
Minimum
84(5)
Existence of Minimum
89(1)
Review of Some Basic Calculus Concepts
89(14)
Gradient Vector
90(2)
Hessian Matrix
92(1)
Taylor's Expansion
93(3)
Quadratic Forms and Definite Matrices
96(6)
Concept of Necessary and Sufficient Conditions
102(1)
Unconstrained Optimum Design Problems
103(16)
Concepts Related to Optimality Conditions
103(1)
Optimality Conditions for Functions of Single Variable
104(5)
Optimality Conditions for Functions of Several Variables
109(7)
Roots of Nonlinear Equations Using Excel
116(3)
Constrained Optimum Design Problems
119(24)
Role of Constraints
119(2)
Necessary Conditions: Equality Constraints
121(7)
Necessary Conditions: Inequality Constraints---Karush-Kuhn-Tucker (KKT) Conditions
128(12)
Solution of KKT Conditions Using Excel
140(1)
Solution of KKT Conditions Using MATLAB
141(2)
Postoptimality Analysis: Physical Meaning of Lagrange Multipliers
143(6)
Effect of Changing Constraint Limits
143(3)
Effect of Cost Function Scaling on Lagrange Multipliers
146(1)
Effect of Scaling a Constraint on Its Lagrange Multiplier
147(1)
Generalization of Constraint Variation Sensitivity Result
148(1)
Global Optimality
149(9)
Convex Sets
149(2)
Convex Functions
151(2)
Convex Programming Problem
153(3)
Transformation of a Constraint
156(1)
Sufficient Conditions for Convex Programming Problems
157(1)
Engineering Design Examples
158(17)
Design of a Wall Bracket
158(4)
Design of a Rectangular Beam
162(4)
Exercises for
Chapter 4
166(9)
More on Optimum Design Concepts
175(16)
Alternate Form of KKT Necessary Conditions
175(3)
Irregular Points
178(1)
Second-Order Conditions for Constrained Optimization
179(5)
Sufficiency Check for Rectangular Beam Design Problem
184(7)
Exercises for
Chapter 5
185(6)
Linear Programming Methods for Optimum Design
191(68)
Definition of a Standard Linear Programming Problem
192(3)
Linear Constraints
192(1)
Unrestricted Variables
193(1)
Standard LP Definition
193(2)
Basic Concepts Related to Linear Programming Problems
195(6)
Basic Concepts
195(3)
LP Terminology
198(3)
Optimum Solution for LP Problems
201(1)
Basic Ideas and Steps of the Simplex Method
201(17)
The Simplex
202(1)
Canonical Form/General Solution of Ax = b
202(1)
Tableau
203(2)
The Pivot Step
205(1)
Basic Steps of the Simplex Method
206(5)
Simplex Algorithm
211(7)
Two-Phase Simplex Method--Artificial Variables
218(10)
Artificial Variables
219(1)
Artificial Cost Function
219(1)
Definition of Phase I Problem
220(1)
Phase I Algorithm
220(1)
Phase II Algorithm
221(5)
Degenerate Basic Feasible Solution
226(2)
Postoptimality Analysis
228(15)
Changes in Resource Limits
229(6)
Ranging Right Side Parameters
235(4)
Ranging Cost Coefficients
239(2)
Changes in the Coefficient Matrix
241(2)
Solution of LP Problems Using Excel Solver
243(16)
Exercises for
Chapter 6
246(13)
More on Linear Programming Methods for Optimum Design
259(18)
Derivation of the Simplex Method
259(3)
Selection of a Basic Variable That Should Become Nonbasic
259(1)
Selection of a Nonbasic Variable That Should Become Basic
260(2)
Alternate Simplex Method
262(1)
Duality in Linear Programming
263(14)
Standard Primal LP
263(1)
Dual LP Problem
264(1)
Treatment of Equality Constraints
265(1)
Alternate Treatment of Equality Constraints
266(1)
Determination of Primal Solution from Dual Solution
267(4)
Use of Dual Tableau to Recover Primal Solution
271(2)
Dual Variables as Lagrange Multipliers
273(2)
Exercises for
Chapter 7
275(2)
Numerical Methods for Unconstrained Optimum Design
277(28)
General Concepts Related to Numerical Algorithms
278(4)
A General Algorithm
279(1)
Descent Direction and Descent Step
280(2)
Convergence of Algorithms
282(1)
Rate of Convergence
282(1)
Basic Ideas and Algorithms for Step Size Determination
282(11)
Definition of One-Dimensional Minimization Subproblem
282(1)
Analytical Method to Compute Step Size
283(2)
Concepts Related to Numerical Methods to Compute Step Size
285(1)
Equal Interval Search
286(2)
Alternate Equal Interval Search
288(1)
Golden Section Search
289(4)
Search Direction Determination: Steepest Descent Method
293(3)
Search Direction Determination: Conjugate Gradient Method
296(9)
Exercises for
Chapter 8
300(5)
More on Numerical Methods for Unconstrained Optimum Design
305(34)
More on Step Size Determination
305(5)
Polynomial Interpolation
306(3)
Inaccurate Line Search
309(1)
More on Steepest Descent Method
310(5)
Properties of the Gradient Vector
310(4)
Orthogonality of Steepest Descent Directions
314(1)
Scaling of Design Variables
315(3)
Search Direction Determination: Newton's Method
318(6)
Classical Newton's Method
318(1)
Modified Newton's Method
319(4)
Marquardt Modification
323(1)
Search Direction Determination: Quasi-Newton Methods
324(5)
Inverse Hessian Updating: DFP Method
324(3)
Direct Hessian Updating: BFGS Method
327(2)
Engineering Applications of Unconstrained Methods
329(3)
Minimization of Total Potential Energy
329(2)
Solution of Nonlinear Equations
331(1)
Solution of Constrained Problems Using Unconstrained Optimization Methods
332(7)
Sequential Unconstrained Minimization Techniques
333(1)
Multiplier (Augmented Lagrangian) Methods
334(1)
Exercises for
Chapter 9
335(4)
Numerical Methods for Constrained Optimum Design
339(40)
Basic Concepts and Ideas
340(6)
Basic Concepts Related to Algorithms for Constrained Problems
340(2)
Constraint Status at a Design Point
342(1)
Constraint Normalization
343(2)
Descent Function
345(1)
Convergence of an Algorithm
345(1)
Linearization of Constrained Problem
346(6)
Sequential Linear Programming Algorithm
352(6)
The Basic Idea---Move Limits
352(1)
An SLP Algorithm
353(4)
SLP Algorithm: Some Observations
357(1)
Quadratic Programming Subproblem
358(5)
Definition of QP Subproblem
358(3)
Solution of QP Subproblem
361(2)
Constrained Steepest Descent Method
363(6)
Descent Function
364(2)
Step Size Determination
366(2)
CSD Algorithm
368(1)
CSD Algorithm: Some Observations
368(1)
Engineering Design Optimization Using Excel Solver
369(10)
Exercises for
Chapter 10
373(6)
More on Numerical Methods for Constrained Optimum Design
379(34)
Potential Constraint Strategy
379(4)
Quadratic Programming Problem
383(5)
Definition of QP Problem
383(1)
KKT Necessary Conditions for the QP Problem
384(1)
Transformation of KKT Conditions
384(1)
Simplex Method for Solving QP Problem
385(3)
Approximate Step Size Determination
388(12)
The Basic Idea
388(1)
Descent Condition
389(4)
CSD Algorithm with Approximate Step Size
393(7)
Constrained Quasi-Newton Methods
400(7)
Derivation of Quadratic Programming Subproblem
400(3)
Quasi-Newton Hessian Approximation
403(1)
Modified Constrained Steepest Descent Algorithm
404(2)
Observations on the Constrained Quasi-Newton Methods
406(1)
Descent Functions
406(1)
Other Numerical Optimization Methods
407(6)
Method of Feasible Directions
407(2)
Gradient Projection Method
409(1)
Generalized Reduced Gradient Method
410(1)
Exercises for
Chapter 11
411(2)
Introduction to Optimum Design with MATLAB
413(20)
Introduction to Optimization Toolbox
413(2)
Variables and Expressions
413(1)
Scalar, Array, and Matrix Operations
414(1)
Optimization Toolbox
414(1)
Unconstrained Optimum Design Problems
415(3)
Constrained Optimum Design Problems
418(2)
Optimum Design Examples with MATLAB
420(13)
Location of Maximum Shear Stress for Two Spherical Bodies in Contact
420(1)
Column Design for Minimum Mass
421(4)
Flywheel Design for Minimum Mass
425(4)
Exercises for
Chapter 12
429(4)
Interactive Design Optimization
433(32)
Role of Interaction in Design Optimization
434(2)
What Is Interactive Design Optimization?
434(1)
Role of Computers in Interactive Design Optimization
434(1)
Why Interactive Design Optimization?
435(1)
Interactive Design Optimization Algorithms
436(12)
Cost Reduction Algorithm
436(4)
Constraint Correction Algorithm
440(2)
Algorithm for Constraint Correction at Constant Cost
442(3)
Algorithm for Constraint Correction at Specified Increase in Cost
445(1)
Constraint Correction with Minimum Increase in Cost
446(1)
Observations on Interactive Algorithms
447(1)
Desired Interactive Capabilities
448(2)
Interactive Data Preparation
448(1)
Interactive Capabilities
448(1)
Interactive Decision Making
449(1)
Interactive Graphics
450(1)
Interactive Design Optimization Software
450(4)
User Interface for IDESIGN
451(2)
Capabilities of IDESIGN
453(1)
Examples of Interactive Design Optimization
454(11)
Formulation of Spring Design Problem
454(1)
Optimum Solution for the Spring Design Problem
455(1)
Interactive Solution for Spring Design Problem
455(2)
Use of Interactive Graphics
457(5)
Exercises for
Chapter 13
462(3)
Design Optimization Applications with Implicit Functions
465(48)
Formulation of Practical Design Optimization Problems
466(7)
General Guidelines
466(1)
Example of a Practical Design Optimization Problem
467(6)
Gradient Evaluation for Implicit Functions
473(5)
Issues in Practical Design Optimization
478(1)
Selection of an Algorithm
478(1)
Attributes of a Good Optimization Algorithm
478(1)
Use of General-Purpose Software
479(2)
Software Selection
480(1)
Integration of an Application into General-Purpose Software
480(1)
Optimum Design of Two-Member Frame with Out-of-Plane Loads
481(2)
Optimum Design of a Three-Bar Structure for Multiple Performance Requirements
483(8)
Symmetric Three-Bar Structure
483(1)
Asymmetric Three-Bar Structure
484(6)
Comparison of Solutions
490(1)
Discrete Variable Optimum Design
491(2)
Continuous Variable Optimization
492(1)
Discrete Variable Optimization
492(1)
Optimal Control of Systems by Nonlinear Programming
493(20)
A Prototype Optimal Control Problem
493(4)
Minimization of Error in State Variable
497(6)
Minimum Control Effort Problem
503(2)
Minimum Time Control Problem
505(3)
Comparison of Three Formulations for Optimal Control of System Motion
508(1)
Exercises for
Chapter 14
508(5)
Discrete Variable Optimum Design Concepts and Methods
513(18)
Basic Concepts and Definitions
514(2)
Definition of Mixed Variable Optimum Design Problem: MV-OPT
514(1)
Classification of Mixed Variable Optimum Design Problems
514(1)
Overview of Solution Concepts
515(1)
Branch and Bound Methods (BBM)
516(5)
Basic BBM
517(2)
BBM with Local Minimization
519(1)
BBM for General MV-OPT
520(1)
Integer Programming
521(1)
Sequential Linearization Methods
522(1)
Simulated Annealing
522(2)
Dynamic Rounding-off Method
524(1)
Neighborhood Search Method
525(1)
Methods for Linked Discrete Variables
525(1)
Selection of a Method
526(5)
Exercises for
Chapter 15
527(4)
Genetic Algorithms for Optimum Design
531(12)
Basic Concepts and Definitions
532(2)
Fundamentals of Genetic Algorithms
534(4)
Genetic Algorithm for Sequencing-Type Problems
538(1)
Applications
539(4)
Exercises for
Chapter 16
540(3)
Multiobjective Optimum Design Concepts and Methods
543(22)
Problem Definition
543(3)
Terminology and Basic Concepts
546(6)
Criterion Space and Design Space
546(2)
Solution Concepts
548(3)
Preferences and Utility Functions
551(1)
Vector Methods and Scalarization Methods
551(1)
Generation of Pareto Optimal Set
551(1)
Normalization of Objective Functions
552(1)
Optimization Engine
552(1)
Multiobjective Genetic Algorithms
552(3)
Weighted Sum Method
555(1)
Weighted Min-Max Method
556(1)
Weighted Global Criterion Method
556(2)
Lexicographic Method
558(1)
Bounded Objective Function Method
558(1)
Goal Programming
559(1)
Selection of Methods
559(6)
Exercises for
Chapter 17
560(5)
Global Optimization Concepts and Methods for Optimum Design
565(28)
Basic Concepts of Solution Methods
565(2)
Basic Concepts
565(2)
Overview of Methods
567(1)
Overview of Deterministic Methods
567(5)
Covering Methods
568(1)
Zooming Method
568(1)
Methods of Generalized Descent
569(2)
Tunneling Method
571(1)
Overview of Stochastic Methods
572(7)
Pure Random Search
573(1)
Multistart Method
573(1)
Clustering Methods
573(2)
Controlled Random Search
575(3)
Acceptance-Rejection Methods
578(1)
Stochastic Integration
579(1)
Two Local-Global Stochastic Methods
579(6)
A Conceptual Local-Global Algorithm
579(1)
Domain Elimination Method
580(2)
Stochastic Zooming Method
582(1)
Operations Analysis of the Methods
583(2)
Numerical Performance of Methods
585(8)
Summary of Features of Methods
585(1)
Performance of Some Methods Using Unconstrained Problems
586(1)
Performance of Stochastic Zooming and Domain Elimination Methods
586(1)
Global Optimization of Structural Design Problems
587(1)
Exercises for
Chapter 18
588(5)
Appendix A Economic Analysis
593(18)
A.1 Time Value of Money
593(5)
A.1.1 Cash Flow Diagrams
594(1)
A.1.2 Basic Economic Formulas
594(4)
A.2 Economic Bases for Comparison
598(13)
A.2.1 Annual Base Comparisons
599(2)
A.2.2 Present Worth Comparisons
601(3)
Exercises for Appendix A
604(7)
Appendix B Vector and Matrix Algebra
611(36)
B.1 Definition of Matrices
611(2)
B.2 Type of Matrices and Their Operations
613(5)
B.2.1 Null Matrix
613(1)
B.2.2 Vector
613(1)
B.2.3 Addition of Matrices
613(1)
B.2.4 Multiplication of Matrices
613(2)
B.2.5 Transpose of a Matrix
615(1)
B.2.6 Elementary Row--Column Operations
616(1)
B.2.7 Equivalence of Matrices
616(1)
B.2.8 Scalar Product--Dot Product of Vectors
616(1)
B.2.9 Square Matrices
616(1)
B.2.10 Partitioning of Matrices
617(1)
B.3 Solution of n Linear Equations in n Unknowns
618(10)
B.3.1 Linear Systems
618(1)
B.3.2 Determinants
619(2)
B.3.3 Gaussian Elimination Procedure
621(4)
B.3.4 Inverse of a Matrix: Gauss-Jordan Elimination
625(3)
B.4 Solution of m Linear Equations in n Unknowns
628(7)
B.4.1 Rank of a Matrix
628(1)
B.4.2 General Solution of m x n Linear Equations
629(6)
B.5 Concepts Related to a Set of Vectors
635(7)
B.5.1 Linear Independence of a Set of Vectors
635(4)
B.5.2 Vector Spaces
639(3)
B.6 Eigenvalues and Eigenvectors
642(1)
B.7 Norm and Condition Number of a Matrix
643(4)
B.7.1 Norm of Vectors and Matrices
643(1)
B.7.2 Condition Number of a Matrix
644(1)
Exercises for Appendix B
645(2)
Appendix C A Numerical Method for Solution of Nonlinear Equations
647(10)
C.1 Single Nonlinear Equation
647(3)
C.2 Multiple Nonlinear Equations
650(7)
Exercises for Appendix C
655(2)
Appendix D Sample Computer Programs
657(18)
D.1 Equal Interval Search
657(3)
D.2 Golden Section Search
660(1)
D.3 Steepest Descent Method
660(9)
D.4 Modified Newton's Method
669(6)
References 675(8)
Bibliography 683(4)
Answers to Selected Problems 687(8)
Index 695


Dr. Arora is the F. Wendell Miller Distinguished Professor, Emeritus, of Civil, Environmental and Mechanical Engineering at the University of Iowa. He was also Director of the Optimal Design Laboratory and Associate Director of the Center for Computer Aided Design. He is an internationally recognized expert in the fields of optimization, numerical analysis, and real-time implementation. His research interests include optimization-based digital human modeling, dynamic response optimization, optimal control of systems, design sensitivity analysis and optimization of nonlinear systems, and parallel optimization algorithms. Dr. Arora has authored two books, co-authored or edited five others, written 160 journal articles, 27 book chapters, 130 conference papers, and more than 300 technical reports.