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E-raamat: Introduction to Optimum Design

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(Department of Civil and Environmental Engineering & Department of Mechanical Engineering, University of Iowa)
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  • Ilmumisaeg: 05-Apr-2016
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128009185
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Introduction to Optimum DesignSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 05-Apr-2016
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780128009185
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Introduction to Optimum Design, Fourth Edition, carries on the tradition of the most widely used textbook in engineering optimization and optimum design courses. It is intended for use in a first course on engineering design and optimization at the undergraduate or graduate level in engineering departments of all disciplines, with a primary focus on mechanical, aerospace, and civil engineering courses.

Through a basic and organized approach, the text describes engineering design optimization in a rigorous, yet simplified manner, illustrates various concepts and procedures with simple examples, and demonstrates their applicability to engineering design problems.

Formulation of a design problem as an optimization problem is emphasized and illustrated throughout the text using Excel and MATLAB as learning and teaching aids. This fourth edition has been reorganized, rewritten in parts, and enhanced with new material, making the book even more appealing to instructors regardless of course level.

  • Includes basic concepts of optimality conditions and numerical methods that are described with simple and practical examples, making the material highly teachable and learnable
  • Presents applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems
  • Provides practical design examples that introduce students to the use of optimization methods early in the book
  • Contains chapter on several advanced optimum design topics that serve the needs of instructors who teach more advanced courses

Muu info

By carrying on the tradition of the most widely used textbook in engineering optimization and optimum design courses, this book is ideal for undergraduate or graduate level courses in engineering departments of all disciplines, providing instructors with new methods for teaching optimization at any level in the engineering curriculum
Preface to Fourth Edition xv
Acknowledgments xix
Key Symbols and Abbreviations xxi
I The Basic Concepts
1 Introduction to Design Optimization
1.1 The Design Process
4(2)
1.2 Engineering Design Versus Engineering Analysis
6(1)
1.3 Conventional Versus Optimum Design Process
6(2)
1.4 Optimum Design Versus Optimal Control
8(1)
1.5 Basic Terminology and Notation
8(10)
1.5.1 Vectors and Points
8(1)
1.5.2 Sets
9(2)
1.5.3 Notation for Constraints
11(1)
1.5.4 Superscripts/Subscripts and Summation Notation
11(1)
1.5.5 Norm/Length of a Vector
12(1)
1.5.6 Functions of Several Variables
13(1)
1.5.7 Partial Derivatives of Functions
14(1)
1.5.8 US-British Versus SI Units
15(3)
Reference
18(2)
2 Optimum Design Problem Formulation
2.1 The Problem Formulation Process
20(8)
2.1.1 Step 1: Project/Problem Description
20(1)
2.1.2 Step 2: Data and Information Collection
21(1)
2.1.3 Step 3: Definition of Design Variables
22(2)
2.1.4 Step 4: Optimization Criterion
24(1)
2.1.5 Step 5: Formulation of Constraints
25(3)
2.2 Design of a Can
28(1)
2.3 Insulated Spherical Tank Design
29(3)
2.4 Sawmill Operation
32(1)
2.5 Design of a Two-bar Bracket
33(7)
2.6 Design of a Cabinet
40(3)
2.6.1 Formulation 1 for Cabinet Design
41(1)
2.6.2 Formulation 2 for Cabinet Design
41(1)
2.6.3 Formulation 3 for Cabinet Design
42(1)
2.7 Minimum-weight Tubular Column Design
43(3)
2.7.1 Formulation 1 for Column Design
44(1)
2.7.2 Formulation 2 for Column Design
45(1)
2.8 Minimum-cost Cylindrical Tank Design
46(1)
2.9 Design of Coil Springs
47(3)
2.10 Minimum-weight Design of a Symmetric Three-bar Truss
50(4)
2.11 A General Mathematical Model for Optimum Design
54(6)
2.11.1 Standard Design Optimization Model
54(1)
2.11.2 Maximization Problem Treatment
55(1)
2.11.3 Treatment of "Greater Than Type" Constraints
56(1)
2.11.4 Application to Different Engineering Fields
56(1)
2.11.5 Important Observations about the Standard Model
56(1)
2.11.6 Feasible Set
57(1)
2.11.7 Active/Inactive/Violated Constraints
57(1)
2.11.8 Discrete and Integer Design Variables
58(1)
2.11.9 Types of Optimization Problems
59(1)
2.12 Development of Problem Formulation for Practical Applications
60(1)
Exercises for
Chapter 2
61(9)
References
70(2)
3 Graphical Solution Method and Basic Optimization Concepts
3.1 Graphical Solution Process
72(5)
3.1.1 Profit Maximization Problem-Formulation
72(1)
3.1.2 Step-by-step Graphical Solution Procedure
73(4)
3.2 Use of Mathematica for Graphical Optimization
77(4)
3.2.1 Plotting Functions
78(1)
3.2.2 Identification and Shading of Infeasible Region for an Inequality
79(1)
3.2.3 Identification of Feasible Region
80(1)
3.2.4 Plotting of Objective Function Contours
80(1)
3.2.5 Identification of Optimum Solution
81(1)
3.3 Use of MATLAB for Graphical Optimization
81(4)
3.3.1 Plotting of Function Contours
82(3)
3.3.2 Editing of Graph
85(1)
3.4 Design Problem with Multiple Solutions
85(1)
3.5 Design Problem with Unbounded Solutions
86(1)
3.6 Infeasible Design Problem
87(1)
3.7 Graphical Solution for the Minimum-weight Tubular Column
88(2)
3.8 Graphical Solution for a Beam Design Problem
90(2)
Exercises for
Chapter 3
92(14)
4 Optimum Design Concepts: Optimality Conditions
4.1 Definitions of Global and Local Minima
106(7)
4.1.1 Minimum/Maximum
107(5)
4.1.2 Existence of a Minimum
112(1)
4.2 Review of Some Basic Calculus Concepts
113(14)
4.2.1 Gradient Vector: Partial Derivatives of a Function
114(1)
4.2.2 Hessian Matrix: Second-order Partial Derivatives
115(2)
4.2.3 Taylor's Expansion
117(3)
4.2.4 Quadratic Forms and Definite Matrices
120(7)
4.3 Concepts of Necessary and Sufficient Conditions
127(1)
4.4 Optimality Conditions: Unconstrained Problem
128(15)
4.4.1 Concepts Related to Optimality Conditions
128(1)
4.4.2 Optimality Conditions for Functions of a Single Variable
129(6)
4.4.3 Optimality Conditions for Functions of Several Variables
135(8)
4.5 Necessary Conditions: Equality-constrained Problem
143(9)
4.5.1 Lagrange Multipliers
144(5)
4.5.2 Lagrange Multiplier Theorem
149(3)
4.6 Necessary Conditions for a General Constrained Problem
152(19)
4.6.1 The Role of Inequalities
152(2)
4.6.2 Karush-Kuhn-Tucker Necessary Conditions
154(16)
4.6.3 Summary of the KKT Solution Approach
170(1)
4.7 Postoptimality Analysis: the Physical Meaning of Lagrange Multipliers
171(7)
4.7.1 Effect of Changing Constraint Limits
171(4)
4.7.2 Effect of Cost Function Scaling on Lagrange Multipliers
175(1)
4.7.3 Effect of Scaling a Constraint on its Lagrange Multiplier
176(1)
4.7.4 Generalization of the Constraint Variation Sensitivity Result
177(1)
4.8 Global Optimality
178(11)
4.8.1 Convex Sets
179(2)
4.8.2 Convex Functions
181(2)
4.8.3 Convex Programming Problem
183(4)
4.8.4 Transformation of a Constraint
187(1)
4.8.5 Sufficient Conditions for Convex Programming Problems
188(1)
4.9 Engineering Design Examples
189(8)
4.9.1 Design of a Wall Bracket
189(4)
4.9.2 Design of a Rectangular Beam
193(4)
Exercises for
Chapter 4
197(10)
5 More on Optimum Design Concepts: Optimality Conditions
5.1 Alternate form of KKT Necessary Conditions
207(3)
5.2 Irregular Points
210(2)
5.3 Second-order Conditions for Constrained Optimization
212(6)
5.4 Second-order Conditions for the Rectangular Beam Design Problem
218(2)
5.5 Duality in Nonlinear Programming
220(9)
5.5.1 Local Duality: Equality Constraints Case
220(6)
5.5.2 Local Duality: The Inequality Constraints Case
226(3)
Exercises for
Chapter 5
229(4)
References
233(5)
II Numerical Methods For Continuous Variable Optimization
6 Optimum Design: Numerical Solution Process and Excel Solver
6.1 Introduction to Numerical Search Methods
238(3)
6.1.1 Derivative-based Methods
238(1)
6.1.2 Direct Search Methods
239(1)
6.1.3 Derivative-free Methods
240(1)
6.1.4 Nature-inspired Search Methods
240(1)
6.1.5 Selection of a Method
241(1)
6.2 Optimum Design: Numerical Aspects of Problem Formulation
241(9)
6.2.1 General Guidelines
241(1)
6.2.2 Scaling of Constraints
242(4)
6.2.3 Scaling of Design Variables
246(2)
6.2.4 Iterative Process for Development of Problem Formulation
248(2)
6.3 Numerical Solution Process for Optimum Design
250(3)
6.3.1 Integration of an Application into General Purpose Software
250(1)
6.3.2 How to Find Feasible Points
251(1)
6.3.3 A Feasible Point Cannot Be Obtained
251(1)
6.3.4 Algorithm Does Not Converge
252(1)
6.4 Excel Sol ve r: an Introduction
253(7)
6.4.1 Excel Solver
253(1)
6.4.2 Roots of a Nonlinear Equation
253(4)
6.4.3 Roots of a Set of Nonlinear Equations
257(3)
6.5 Excel Solver for Unconstrained Optimization Problems
260(1)
6.6 Excel Solver for Linear Programming Problems
260(6)
6.7 Excel Solver for Nonlinear Programming: Optimum Design of Springs
266(2)
6.8 Optimum Design of Plate Girders using Excel Solver
268(8)
Exercises for
Chapter 6
276(2)
References
278(1)
7 Optimum Design with MATLAB®
7.1 Introduction to the Optimization Toolbox
279(3)
7.1.1 Variables and Expressions
279(1)
7.1.2 Scalar, Array, and Matrix Operations
280(1)
7.1.3 Optimization Toolbox
280(2)
7.2 Unconstrained Optimum Design Problems
282(3)
7.3 Constrained Optimum Design Problems
285(3)
7.4 Optimum Design Examples with MATLAB
288(12)
7.4.1 Location of Maximum Shear Stress for Two Spherical Bodies in Contact
288(2)
7.4.2 Column Design for Minimum Mass
290(3)
7.4.3 Flywheel Design for Minimum Mass
293(7)
Exercises for
Chapter 7
300(4)
References
304(4)
8 Linear Programming Methods for Optimum Design
8.1 Linear Functions
308(1)
8.2 Definition of a Standard LP Problem
308(5)
8.2.1 Standard LP Definition
308(2)
8.2.2 Transcription to Standard LP
310(3)
8.3 Basic Concepts Related to LP Problems
313(10)
8.3.1 Basic Concepts
314(5)
8.3.2 LP Terminology
319(2)
8.3.3 Optimum Solution to LP Problems
321(2)
8.4 Calculation of Basic Solutions
323(6)
8.4.1 The Tableau
323(1)
8.4.2 The Pivot Step
324(2)
8.4.3 Basic Solutions of Ax = b
326(3)
8.5 The Simplex Method
329(14)
8.5.1 The Simplex
329(1)
8.5.2 Basic Steps in the Simplex Method
330(5)
8.5.3 Basic Theorems of LP
335(8)
8.6 The Two-phase Simplex Method-Artificial Variables
343(13)
8.6.1 Artificial Variables
343(2)
8.6.2 Artificial Cost Function
345(1)
8.6.3 Definition of the Phase I Problem
345(1)
8.6.4 Phase I Algorithm
346(2)
8.6.5 Phase II Algorithm
348(7)
8.6.6 Degenerate Basic Feasible Solution
355(1)
8.7 Postoptimality Analysis
356(18)
8.7.1 Changes in Constraint Limits
358(7)
8.7.2 Ranging Right-side Parameters
365(4)
8.7.3 Ranging Cost Coefficients
369(3)
8.7.4 Changes in the Coefficient Matrix
372(2)
Exercises for
Chapter 8
374(13)
Reference
387(2)
9 More on Linear Programming Methods for Optimum Design
9.1 The Simplex Method: Derivation
389(8)
9.1.1 General Solution of Ax = b
389(2)
9.1.2 Selection of a Nonbasic Variable that Should Become Basic
391(2)
9.1.3 Selection of a Basic Variable that Should Become Nonbasic
393(1)
9.1.4 Artificial Cost Function
394(1)
9.1.5 The Pivot Step
395(1)
9.1.6 The Simplex Algorithm
396(1)
9.2 An Alternate Simplex method
397(2)
9.3 Duality in Linear Programming
399(12)
9.3.1 Standard Primal LP Problem
399(1)
9.3.2 Dual LP Problem
399(2)
9.3.3 Treatment of Equality Constraints
401(1)
9.3.4 Alternate Treatment of Equality Constraints
402(1)
9.3.5 Determination of the Primal Solution from the Dual Solution
403(4)
9.3.6 Use of the Dual Tableau to Recover the Primal Solution
407(3)
9.3.7 Dual Variables as Lagrange Multipliers
410(1)
9.4 Simplex Method and KKT Conditions for the LP Problem
411(3)
9.4.1 KKT Optimality Conditions
412(1)
9.4.2 Solution of the KKT Conditions
412(2)
9.5 Quadratic Programming Problems
414(6)
9.5.1 Definition of a QP Problem
414(1)
9.5.2 KKT Necessary Conditions for the QP Problem
415(1)
9.5.3 Transformation of KKT Conditions
415(1)
9.5.4 The Simplex Method for Solving QP Problem
416(4)
Exercises for
Chapter 9
420(1)
References
421(3)
10 Numerical Methods for Unconstrained Optimum Design
10.1 General Concepts
424(1)
10.2 A General Iterative Algorithm
425(1)
10.3 Descent Direction and Convergence of Algorithms
426(3)
10.3.1 Descent Direction and Descent Step
427(1)
10.3.2 Convergence of Algorithms
428(1)
10.3.3 Rate of Convergence
428(1)
10.4 Step Size Determination: Basic Ideas
429(3)
10.4.1 Definition of the Step Size Determination Subproblem
429(2)
10.4.2 Analytical Method to Compute Step Size
431(1)
10.5 Numerical Methods to Compute Step Size
432(10)
10.5.1 General Concepts
432(2)
10.5.2 Equal-interval Search
434(2)
10.5.3 Alternate Equal-interval Search
436(1)
10.5.4 Golden Section Search
437(5)
10.6 Search Direction Determination: The Steepest-descent Method
442(3)
10.7 Search Direction Determination: The Conjugate Gradient Method
445(3)
10.8 Other Conjugate Gradient Methods
448(1)
Exercises for
Chapter 10
449(4)
References
453(3)
11 More on Numerical Methods for Unconstrained Optimum Design
11.1 More on Step Size Determination
456(7)
11.1.1 Polynomial Interpolation
456(4)
11.1.2 Inexact Line Search: Armijo's Rule
460(2)
11.1.3 Inexact Line Search: Wolfe Conditions
462(1)
11.1.4 Inexact Line Search: Goldstein Test
462(1)
11.2 More on the Steepest-descent Method
463(6)
11.2.1 Properties of the Gradient Vector
463(5)
11.2.2 Orthogonality of Steepest-descent Directions
468(1)
11.3 Scaling of Design Variables
469(3)
11.4 Search Direction Determination: Newton Method
472(7)
11.4.1 Classical Newton Method
472(1)
11.4.2 Modified Newton Method
473(5)
11.4.3 Marquardt Modification
478(1)
11.5 Search Direction Determination: Quasi-Newton Methods
479(5)
11.5.1 Inverse Hessian Updating: The DFP Method
479(3)
11.5.2 Direct Hessian Updating: The BFGS Method
482(2)
11.6 Engineering Applications of Unconstrained Methods
484(5)
11.6.1 Data Interpolation
485(1)
11.6.2 Minimization of Total Potential Energy
486(2)
11.6.3 Solution of Nonlinear Equations
488(1)
11.7 Solution of Constrained Problem Using Unconstrained Optimization Methods
489(5)
11.7.1 Sequential Unconstrained Minimization Techniques
490(2)
11.7.2 Augmented Lagrangian (Multiplier) Methods
492(2)
11.8 Rate of Convergence of Algorithms
494(4)
11.8.1 Definitions
494(1)
11.8.2 Steepest-descent Method
495(1)
11.8.3 Newton Method
496(1)
11.8.4 Conjugate Gradient Method
497(1)
11.8.5 Quasi-Newton Methods
497(1)
11.9 Direct Search Methods
498(8)
11.9.1 Univariate Search
498(1)
11.9.2 Hooke-Jeeves Method
499(1)
11.9.3 Nelder-Mead Simplex Method
500(6)
Exercises for
Chapter 11
506(2)
References
508(4)
12 Numerical Methods for Constrained Optimum Design
12.1 Basic Concepts Related to Numerical Methods
512(5)
12.1.1 Basic Concepts Related to Algorithms for Constrained Problems
512(3)
12.1.2 Constraint Status at a Design Point
515(1)
12.1.3 The Descent Function
516(1)
12.1.4 Convergence of an Algorithm
516(1)
12.2 Linearization of the Constrained Problem
517(7)
12.3 The Sequential Linear Programming Algorithm
524(7)
12.3.1 Move Limits in SLP
524(2)
12.3.2 An SLP Algorithm
526(4)
12.3.3 The SLP Algorithm: Some Observations
530(1)
12.4 Sequential Quadratic Programming
531(1)
12.5 Search Direction Calculation: The QP Subproblem
532(7)
12.5.1 Definition of the QP Subproblem
532(5)
12.5.2 Solving the QP Subproblem
537(2)
12.6 The Step Size Calculation Subproblem
539(8)
12.6.1 The Descent Function
539(3)
12.6.2 Step Size Calculation: Line Search
542(5)
12.7 The Constrained Steepest-descent Method
547(2)
12.7.1 The CSD Algorithm
548(1)
12.7.2 The CSD Algorithm: Some Observations
548(1)
Exercises for
Chapter 12
549(4)
References
553(3)
13 More on Numerical Methods for Constrained Optimum Design
13.1 Potential Constraint Strategy
556(4)
13.2 Inexact Step Size Calculation
560(12)
13.2.1 Basic Concept
560(1)
13.2.2 Descent Condition
560(5)
13.2.3 CSD Algorithm with Inexact Step Size
565(7)
13.3 Bound-constrained Optimization
572(5)
13.3.1 Optimality Conditions
573(1)
13.3.2 Projection Methods
574(2)
13.3.3 Step Size Calculation
576(1)
13.4 Sequential Quadratic Programming: SQP Methods
577(11)
13.4.1 Derivation of the Quadratic Programming Subproblem
578(2)
13.4.2 Quasi-Newton Hessian Approximation
580(2)
13.4.3 SQP Algorithm
582(5)
13.4.4 Observations on SQP Methods
587(1)
13.4.5 Descent Functions
587(1)
13.5 Other Numerical Optimization Methods
588(5)
13.5.1 Method of Feasible Directions
588(3)
13.5.2 Gradient Projection Method
591(1)
13.5.3 Generalized Reduced Gradient Method
592(1)
13.6 Solution of the Quadratic Programming Subproblem
593(4)
13.6.1 KKT Necessary Conditions for QP
594(2)
13.6.2 Direct Solution of the QP Subproblem
596(1)
Exercises for
Chapter 13
597(1)
References
598(4)
14 Practical Applications of Optimization
14.1 Formulation of Practical Design Optimization Problems
602(7)
14.1.1 General Guidelines
602(1)
14.1.2 Example of a Practical Design Optimization Problem
603(6)
14.2 Gradient Evaluation of Implicit Functions
609(5)
14.3 Issues in Practical Design Optimization
614(1)
14.3.1 Selection of an Algorithm
614(1)
14.3.2 Attributes of a Good Optimization Algorithm
614(1)
14.4 Use of General-purpose Software
615(2)
14.4.1 Software Selection
616(1)
14.4.2 Integration of an Application into General-purpose Software
616(1)
14.5 Optimum Design: Two-member Frame with Out-of-plane Loads
617(2)
14.6 Optimum Design: Three-bar Structure for Multiple Performance Requirements
619(6)
14.6.1 Symmetric Three-bar Structure
619(2)
14.6.2 Asymmetric Three-bar Structure
621(4)
14.6.3 Comparison of Solutions
625(1)
14.7 Optimal Control of Systems by Nonlinear Programming
625(14)
14.7.1 A Prototype Optimal Control Problem
625(4)
14.7.2 Minimization of Error in the State Variable
629(6)
14.7.3 Minimum Control Effort Problem
635(2)
14.7.4 Minimum Time Control Problem
637(2)
14.7.5 Comparison of Three Formulations for the Optimal Control of System Motion
639(1)
14.8 Optimum Design of Tension Members
639(5)
14.9 Optimum Design of Compression Members
644(8)
14.9.1 Formulation of the Problem
644(5)
14.9.2 Formulation of the Problem for Inelastic Buckling
649(2)
14.9.3 Formulation of the Problem for Elastic Buckling
651(1)
14.10 Optimum Design of Members for Flexure
652(12)
14.11 Optimum Design of Telecommunication Poles
664(8)
14.12 Alternative Formulations for Structural Optimization Problems
672(2)
14.13 Alternative Formulations for Time-dependent Problems
674(1)
Exercises for
Chapter 14
675(4)
References
679(5)
III Advanced And Modern Topics On Optimum Design
15 Discrete Variable Optimum Design Concepts and Methods
15.1 Basic Concepts and Definitions
684(3)
15.1.1 Definition of a Mixed Variable Optimum Design Problem: MV-OPT
684(1)
15.1.2 Classification of Mixed Variable Optimum Design Problems
685(1)
15.1.3 Overview of Solution Concepts
686(1)
15.2 Branch-and-bound Methods
687(5)
15.2.1 Basic BBM
687(2)
15.2.2 BBM with Local Minimization
689(2)
15.2.3 BBM for General MV-OPT
691(1)
15.3 Integer Programming
692(1)
15.4 Sequential Linearization Methods
693(1)
15.5 Simulated Annealing
693(3)
15.6 Dynamic Rounding-off Method
696(1)
15.7 Neighborhood Search Method
697(1)
15.8 Methods for Linked Discrete Variables
697(2)
15.9 Selection of a Method
699(1)
15.10 Adaptive Numerical Method for Discrete Variable Optimization
699(3)
15.10.1 Continuous Variable Optimization
701(1)
15.10.2 Discrete Variable Optimization
701(1)
Exercises for
Chapter 15
702(3)
References
705(3)
16 Global Optimization Concepts and Methods
16.1 Basic Concepts of Solution Methods
708(2)
16.1.1 Basic Solution Concepts
708(1)
16.1.2 Overview of Methods
709(1)
16.2 Overview of Deterministic Methods
710(6)
16.2.1 Covering Methods
711(1)
16.2.2 Zooming Method
712(1)
16.2.3 Methods of Generalized Descent
712(2)
16.2.4 Tunneling Method
714(2)
16.3 Overview of Stochastic Methods
716(7)
16.3.1 Pure Random Search Method
717(1)
16.3.2 Multistart Method
717(1)
16.3.3 Clustering Methods
718(2)
16.3.4 Controlled Random Search
720(1)
16.3.5 Acceptance-Rejection Methods
721(1)
16.3.6 Stochastic Integration
722(1)
16.4 Two Local-global Stochastic Methods
723(6)
16.4.1 Conceptual Local-global Algorithm
723(1)
16.4.2 Domain Elimination Method
724(2)
16.4.3 Stochastic Zooming Method
726(1)
16.4.4 Operations Analysis of Methods
727(2)
16.5 Numerical Performance of Methods
729(5)
16.5.1 Summary of Features of Methods
730(1)
16.5.2 Performance of Some Methods with Unconstrained Problems
731(1)
16.5.3 Performance of Stochastic Zooming and Domain Elimination Methods
731(1)
16.5.4 Global Optimization of Structural Design Problems
732(2)
Exercises for
Chapter 16
734(3)
References
737(4)
17 Nature-inspired Search Methods
17.1 Genetic Algorithms (GA) for Optimum Design
741(9)
17.1.1 Basic Concepts and Definitions Related to GA
741(2)
17.1.2 Fundamentals of Genetic Algorithms
743(5)
17.1.3 Genetic Algorithm for Sequencing-type Problems
748(1)
17.1.4 Applications of GA
749(1)
17.2 Differential Evolution Algorithm
750(5)
17.2.1 Generation of Initial Population for DEA
750(1)
17.2.2 Generation of a Donor Design for DEA
751(1)
17.2.3 Crossover Operation to Generate the Trial Design in DEA
752(1)
17.2.4 Acceptance/Rejection of the Trial Design in DEA
752(1)
17.2.5 Differential Evolution Algorithm
752(3)
17.3 Ant Colony Optimization
755(9)
17.3.1 Ant Behavior
755(2)
17.3.2 ACO Algorithm for the Traveling Salesman Problem
757(3)
17.3.3 ACO Algorithm for Design Optimization
760(4)
17.4 Particle Swarm Optimization
764(2)
17.4.1 Swarm Behavior and Terminology
764(1)
17.4.2 Particle Swarm Optimization Algorithm
765(1)
Exercises for
Chapter 17
766(3)
References
769(2)
18 Multi-objective Optimum Design Concepts and Methods
18.1 Problem Definition
771(2)
18.2 Terminology and Basic Concepts
773(8)
18.2.1 Criterion Space and Design Space
773(3)
18.2.2 Solution Concepts
776(3)
18.2.3 Preferences and Utility Functions
779(1)
18.2.4 Vector Methods and Scalarization Methods
780(1)
18.2.5 Generation of Pareto Optimal Set
780(1)
18.2.6 Normalization of Objective Functions
780(1)
18.2.7 Optimization Engine
781(1)
18.3 Multi-objective Genetic Algorithms
781(4)
18.4 Weighted Sum Method
785(1)
18.5 Weighted Min-max Method
785(1)
18.6 Weighted Global Criterion Method
786(2)
18.7 Lexicographic Method
788(1)
18.8 Bounded Objective Function Method
788(1)
18.9 Goal Programming
789(1)
18.10 Selection of Methods
790(1)
Exercises for
Chapter 18
790(3)
References
793(2)
19 Additional Topics on Optimum Design
19.1 Meta-models for Design Optimization
795(10)
19.1.1 Meta-model
795(2)
19.1.2 Response Surface Method
797(4)
19.1.3 Normalization of Variables
801(4)
19.2 Design of Experiments for Response Surface Generation
805(8)
19.3 Discrete Design with Orthogonal Arrays
813(4)
19.4 Robust Design Approach
817(16)
19.4.1 Robust Optimization
818(7)
19.4.2 The Taguchi Method
825(8)
19.5 Reliability-based Design Optimization-Design Under Uncertainty
833(16)
19.5.1 Review of Background Material for RBDO
833(5)
19.5.2 Calculation of the Reliability Index
838(10)
19.5.3 Formulation of Reliability-based Design Optimization
848(1)
References
849(2)
Appendix A Vector and Matrix Algebra
A.1 Definition of Matrices
851(2)
A.2 Types of Matrices and their Operations
853(5)
A.2.1 Null Matrix
853(1)
A.2.2 Vector
853(1)
A.2.3 Addition of Matrices
853(1)
A.2.4 Multiplication of Matrices
853(2)
A.2.5 Transpose of a Matrix
855(1)
A.2.6 Elementary Row-column Operations
856(1)
A.2.7 Equivalence of Matrices
856(1)
A.2.8 Scalar Product-Dot Product of Vectors
856(1)
A.2.9 Square Matrices
857(1)
A.2.10 Partitioning of Matrices
857(1)
A.3 Solving n Linear Equations in n Unknowns
858(11)
A.3.1 Linear Systems
858(1)
A.3.2 Determinants
859(3)
A.3.3 Gaussian Elimination Procedure
862(4)
A.3.4 Inverse of a Matrix: Gauss-Jordan Elimination
866(3)
A.4 Solution to m Linear Equations in n Unknowns
869(7)
A.4.1 Rank of a Matrix
869(1)
A.4.2 General Solution of in X n Linear Equations
870(6)
A.5 Concepts Related to a Set of Vectors
876(6)
A.5.1 Linear Independence of a Set of Vectors
876(4)
A.5.2 Vector Spaces
880(2)
A.6 Eigenvalues and Eigenvectors
882(2)
A.7 Norm and Condition Number of a Matrix
884(1)
A.7.1 Norm of Vectors and Matrices
884(1)
A.7.2 Condition Number of a Matrix
885(1)
A.8 Exercises for Appendix A
885(4)
References
889(2)
Appendix B Sample Computer Programs
B.1 Equal Interval Search
891(3)
B.2 Golden Section Search
894(3)
B.3 Steepest-descent Method
897(1)
B.4 Modified Newton's Method
897(12)
Bibliography 909(10)
Answers to Selected Exercises 919(10)
Subject Index 929
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.
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