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Introduction to optimum design / Jasbir S. Arora.
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Title:Introduction to optimum design / Jasbir S. Arora.
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Author/Creator:Arora, Jasbir S.
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Published/Created:Waltham, MA : Academic Press, ©2012.
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Location:WOODWARD LIBRARY stacksWhere is this?
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Call Number: TA174 .A76 2012
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Number of Items:1
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Status:Available
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Links:Donor bookplate
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Location:WOODWARD LIBRARY stacksWhere is this?
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Library of Congress Subjects:Engineering design--Mathematical models.
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Edition:3rd ed.
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Description:xvi, 880 p. : ill. ; 25 cm.
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Notes:Machine generated contents note: Introduction to Design Optimization Optimum Design Problem Formulation Graphical Optimization and Basic Concepts Optimum Design Concepts: Optimality Conditions More on Optimum Design Concepts: Optimality Conditions Optimum Design with Excel Solver Optimum Design with MATLAB Linear Programming Methods for Optimum Design More on Linear Programming Methods for Optimum Design Numerical Methods for Unconstrained Optimum Design More on Numerical Methods for Unconstrained Optimum Design Numerical Methods for Constrained Optimum Design More on Numerical Methods for Constrained Optimum Design Practical Applications of Optimization Discrete Variable Optimum Design Concepts and Methods Genetic Algorithms for Optimum Design Multi-Objective Optimum Design Concepts and Methods Global Optimization Concepts and Methods Nature-Inspired Search Methods Additional Topics on Optimum Design Appendices.
Includes bibliographical references and index.
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ISBN:9780123813756 (hardback)
0123813751 (hardback)
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Contents:Machine generated contents note: I. BASIC CONCEPTS
1. Introduction to Design Optimization
1.1. Design Process
1.2. Engineering Design versus Engineering Analysis
1.3. Conventional versus Optimum Design Process
1.4. Optimum Design versus Optimal Control
1.5. Basic Terminology and Notation
1.5.1. Points and Sets
1.5.2. Notation for Constraints
1.5.3. Superscripts/Subscripts and Summation Notation
1.5.4. Norm/Length of a Vector
1.5.5. Functions
1.5.6. Derivatives of Functions
1.5.7. U.S.
British versus SI Units
2. Optimum Design Problem Formulation
2.1. Problem Formulation Process
2.1.1. Step 1: Project/Problem Description
2.1.2. Step 2: Data and Information Collection
2.1.3. Step 3: Definition of Design Variables
2.1.4. Step 4: Optimization Criterion
2.1.5. Step 5: Formulation of Constraints
2.2. Design of a Can
2.3. Insulated Spherical Tank Design
2.4. Sawmill Operation
2.5. Design of a Two-Bar Bracket
2.6. Design of a Cabinet
2.6.1. Formulation 1 for Cabinet Design
2.6.2. Formulation 2 for Cabinet Design
2.6.3. Formulation 3 for Cabinet Design
2.7. Minimum-Weight Tubular Column Design
2.7.1. Formulation 1 for Column Design
2.7.2. Formulation 2 for Column Design
2.8. Minimum-Cost Cylindrical Tank Design
2.9. Design of Coil Springs
2.10. Minimum-Weight Design of a Symmetric Three-Bar Truss
2.11. General Mathematical Model for Optimum Design
2.11.1. Standard Design Optimization Model
2.11.2. Maximization Problem Treatment
2.11.3. Treatment of "Greater Than Type" Constraints
2.11.4. Application to Different Engineering Fields
2.11.5. Important Observations about the Standard Model
2.11.6. Feasible Set
2.11.7. Active/Inactive/Violated Constraints
2.11.8. Discrete and Integer Design Variables
2.11.9. Types of Optimization Problems
Exercises for Chapter 2
3. Graphical Optimization and Basic Concepts
3.1. Graphical Solution Process
3.1.1. Profit Maximization Problem
3.1.2. Step-by-Step Graphical Solution Procedure
3.2. Use of Mathematica for Graphical Optimization
3.2.1. Plotting Functions
3.2.2. Identification and Shading of Infeasible Region for an Inequality
3.2.3. Identification of Feasible Region
3.2.4. Plotting of Objective Function Contours
3.2.5. Identification of Optimum Solution
3.3. Use of MATLAB for Graphical Optimization
3.3.1. Plotting of Function Contours
3.3.2. Editing of Graph
3.4. Design Problem with Multiple Solutions
3.5. Problem with Unbounded Solution
3.6. Infeasible Problem
3.7. Graphical Solution for the Minimum-Weight Tubular Column
3.8. Graphical Solution for a Beam Design Problem
Exercises for Chapter 3
4. Optimum Design Concepts: Optimality Conditions
4.1. Definitions of Global and Local Minima
4.1.1. Minimum
4.1.2. Existence of a Minimum
4.2. Review of Some Basic Calculus Concepts
4.2.1. Gradient Vector: Partial Derivatives of a Function
4.2.2. Hessian Matrix: Second-Order Partial Derivatives
4.2.3. Taylor's Expansion
4.2.4. Quadratic Forms and Definite Matrices
4.3. Concept of Necessary and Sufficient Conditions
4.4. Optimality Conditions: Unconstrained Problem
4.4.1. Concepts Related to Optimality Conditions
4.4.2. Optimality Conditions for Functions of a Single Variable
4.4.3. Optimality Conditions for Functions of Several Variables
4.5. Necessary Conditions: Equality-Constrained Problem
4.5.1. Lagrange Multipliers
4.5.2. Lagrange Multiplier Theorem
4.6. Necessary Conditions for a General Constrained Problem
4.6.1. Role of Inequalities
4.6.2. Karush-Kuhn-Tucker Necessary Conditions
4.6.3. Summary of the KKT Solution Approach
4.7. Postoptimality Analysis: The Physical Meaning of Lagrange Multipliers
4.7.1. Effect of Changing Constraint Limits
4.7.2. Effect of Cost Function Scaling on the Lagrange Multipliers
4.7.3. Effect of Scaling a Constraint on Its Lagrange Multiplier
4.7.4. Generalization of Constraint Variation Sensitivity Result
4.8. Global Optimality
4.8.1. Convex Sets
4.8.2. Convex Functions
4.8.3. Convex Programming Problem
4.8.4. Transformation of a Constraint
4.8.5. Sufficient Conditions for Convex Programming Problems
4.9. Engineering Design Examples
4.9.1. Design of a Wall Bracket
4.9.2. Design of a Rectangular Beam
Exercises for Chapter 4
5. More on Optimum Design Concepts: Optimality Conditions
5.1. Alternate Form of KKT Necessary Conditions
5.2. Irregular Points
5.3. Second-Order Conditions for Constrained Optimization
5.4. Second-Order Conditions for Rectangular Beam Design Problem
5.5. Duality in Nonlinear Programming
5.5.1. Local Duality: Equality Constraints Case
5.5.2. Local Duality: The Inequality Constraints Case
Exercises for Chapter 5
II. NUMERICAL METHODS FOR CONTINUOUS VARIABLE OPTIMIZATION
6. Optimum Design with Excel Solver
6.1. Introduction to Numerical Methods for Optimum Design
6.1.1. Classification of Search Methods
6.1.2. What to Do If the Solution Process Fails
6.1.3. Simple Scaling of Variables
6.2. Excel Solver: An Introduction
6.2.1. Excel Solver
6.2.2. Roots of a Nonlinear Equation
6.2.3. Roots of a Set of Nonlinear Equations
6.3. Excel Solver for Unconstrained Optimization Problems
6.4. Excel Solver for Linear Programming Problems
6.5. Excel Solver for Nonlinear Programming: Optimum Design of Springs
6.6. Optimum Design of Plate Girders Using Excel Solver
6.7. Optimum Design of Tension Members
6.8. Optimum Design of Compression Members
6.8.1. Formulation of the Problem
6.8.2. Formulation of the Problem for Inelastic Buckling
6.8.3. Formulation of the Problem for Elastic Buckling
6.9. Optimum Design of Members for Flexure
6.10. Optimum Design of Telecommunication Poles
7. Optimum Design with MATLAB
7.1. Introduction to the Optimization Toolbox
7.1.1. Variables and Expressions
7.1.2. Scalar, Array, and Matrix Operations
7.1.3. Optimization Toolbox
7.2. Unconstrained Optimum Design Problems
7.3. Constrained Optimum Design Problems
7.4. Optimum Design Examples with MATLAB
7.4.1. Location of Maximum Shear Stress for Two Spherical Bodies in Contact
7.4.2. Column Design for Minimum Mass
7.4.3. Flywheel Design for Minimum Mass
Exercises for Chapter 7
8. Linear Programming Methods for Optimum Design
8.1. Linear Functions
8.2. Definition of a Standard Linear Programming Problem
8.2.1. Standard LP Definition
8.2.2. Transcription to Standard LP
8.3. Basic Concepts Related to Linear Programming Problems
8.3.1. Basic Concepts
8.3.2. LP Terminology
8.3.3. Optimum Solution to LP Problems
8.4. Calculation of Basic Solutions
8.4.1. Tableau
8.4.2. Pivot Step
8.4.3. Basic Solutions to Ax = b
8.5. Simplex Method
8.5.1. Simplex
8.5.2. Basic Steps in the Simplex Method
8.5.3. Basic Theorems of Linear Programming
8.6. Two-Phase Simplex Method
-Artificial Variables
8.6.1. Artificial Variables
8.6.2. Artificial Cost Function
8.6.3. Definition of the Phase I Problem
8.6.4. Phase I Algorithm
8.6.5. Phase II Algorithm
8.6.6. Degenerate Basic Feasible Solution
8.7. Postoptimality Analysis
8.7.1. Changes in Constraint Limits
8.7.2. Ranging Right-Side Parameters
8.7.3. Ranging Cost Coefficients
8.7.4. Changes in the Coefficient Matrix
Exercises for Chapter 8
9. More on Linear Programming Methods for Optimum Design
9.1. Derivation of the Simplex Method
9.1.1. General Solution to Ax = b
9.1.2. Selection of a Nonbasic Variable that Should Become Basic
9.1.3. Selection of a Basic Variable that Should Become Nonbasic
9.1.4. Artificial Cost Function
9.1.5. Pivot Step
9.1.6. Simplex Algorithm
9.2. Alternate Simplex Method
9.3. Duality in Linear Programming
9.3.1. Standard Primal LP Problem
9.3.2. Dual LP Problem
9.3.3. Treatment of Equality Constraints
9.3.4. Alternate Treatment of Equality Constraints
9.3.5. Determination of the Primal Solution from the Dual Solution
9.3.6. Use of the Dual Tableau to Recover the Primal Solution
9.3.7. Dual Variables as Lagrange Multipliers
9.4. KKT Conditions for the LP Problem
9.4.1. KKT Optimality Conditions
9.4.2. Solution to the KKT Conditions
9.5. Quadratic Programming Problems
9.5.1. Definition of a QP Problem
9.5.2. KKT Necessary Conditions for the QP Problem
9.5.3. Transformation of KKT Conditions
9.5.4. Simplex Method for Solving QP Problem
Exercises for Chapter 9
10. Numerical Methods for Unconstrained Optimum Design
10.1. Gradient-Based and Direct Search Methods
10.2. General Concepts: Gradient-Based Methods
10.2.1. General Concepts
10.2.2. General Iterative Algorithm
10.3. Descent Direction and Convergence of Algorithms
10.3.1. Descent Direction and Descent Step
10.3.2. Convergence of Algorithms
10.3.3. Rate of Convergence
10.4. Step Size Determination: Basic Ideas
10.4.1. Definition of the Step Size Determination Subproblem
10.4.2. Analytical Method to Compute Step Size
10.5. Numerical Methods to Compute Step Size
10.5.1. General Concepts
10.5.2. Equal-Interval Search
Contents note continued: 10.5.3. Alternate Equal-Interval Search
10.5.4. Golden Section Search
10.6. Search Direction Determination: The Steepest-Descent Method
10.7. Search Direction Determination: The Conjugate Gradient Method
10.8. Other Conjugate Gradient Methods
Exercises for Chapter 10
11. More on Numerical Methods for Unconstrained Optimum Design
11.1. More on Step Size Determination
11.1.1. Polynomial Interpolation
11.1.2. Inexact Line Search: Armijo's Rule
11.1.3. Inexact Line Search: Wolfe Conditions
11.1.4. Inexact Line Search: Goldstein Test
11.2. More on the Steepest-Descent Method
11.2.1. Properties of the Gradient Vector
11.2.2. Orthogonality of Steepest-Descent Directions
11.3. Scaling of Design Variables
11.4. Search Direction Determination: Newton's Method
11.4.1. Classical Newton's Method
11.4.2. Modified Newton's Method
11.4.3. Marquardt Modification
11.5. Search Direction Determination: Quasi-Newton Methods
11.5.1. Inverse Hessian Updating: The DFP Method
11.5.2. Direct Hessian Updating: The BFGS Method
11.6. Engineering Applications of Unconstrained Methods
11.6.1. Data Interpolation
11.6.2. Minimization of Total Potential Energy
11.6.3. Solutions of Nonlinear Equations
11.7. Solutions to Constrained Problems Using Unconstrained Optimization Methods
11.7.1. Sequential Unconstrained Minimization Techniques
11.7.2. Augmented Lagrangian (Multiplier) Methods
11.8. Rate of Convergence of Algorithms
11.8.1. Definitions
11.8.2. Steepest-Descent Method
11.8.3. Newton's Method
11.8.4. Conjugate Gradient Method
11.8.5. Quasi-Newton Methods
11.9. Direct Search Methods
11.9.1. Univariate Search
11.9.2. Hooke-Jeeves Method
Exercises for Chapter 11
12. Numerical Methods for Constrained Optimum Design
12.1. Basic Concepts Related to Numerical Methods
12.1.1. Basic Concepts Related to Algorithms for Constrained Problems
12.1.2. Constraint Status at a Design Point
12.1.3. Constraint Normalization
12.1.4. Descent Function
12.1.5. Convergence of an Algorithm
12.2. Linearization of the Constrained Problem
12.3. Sequential Linear Programming Algorithm
12.3.1. Move Limits in SLP
12.3.2. SLP Algorithm
12.3.3. SLP Algorithm: Some Observations
12.4. Sequential Quadratic Programming
12.5. Search Direction Calculation: The QP Subproblem
12.5.1. Definition of the QP Subproblem
12.5.2. Solving of the QP Subproblem
12.6. Step Size Calculation Subproblem
12.6.1. Descent Function
12.6.2. Step Size Calculation: Line Search
12.7. Constrained Steepest-Descent Method
12.7.1. CSD Algorithm
12.7.2. CSD Algorithm: Some Observations
Exercises for Chapter 12
13. More on Numerical Methods for Constrained Optimum Design
13.1. Potential Constraint Strategy
13.2. Inexact Step Size Calculation
13.2.1. Basic Concept
13.2.2. Descent Condition
13.2.3. CSD Algorithm with Inexact Step Size
13.3. Bound-Constrained Optimization
13.3.1. Optimality Conditions
13.3.2. Projection Methods
13.3.3. Step Size Calculation
13.4. Sequential Quadratic Programming: SQP Methods
13.4.1. Derivation of the Quadratic Programming Subproblem
13.4.2. Quasi-Newton Hessian Approximation
13.4.3. SQP Algorithm
13.4.4. Observations on SQP Methods
13.4.5. Descent Functions
13.5. Other Numerical Optimization Methods
13.5.1. Method of Feasible Directions
13.5.2. Gradient Projection Method
13.5.3. Generalized Reduced Gradient Method
13.6. Solution to the Quadratic Programming Subproblem
13.6.1. Solving the KKT Necessary Conditions
13.6.2. Direct Solution to the QP Subproblem
Exercises for Chapter 13
14. Practical Applications of Optimization
14.1. Formulation of Practical Design Optimization Problems
14.1.1. General Guidelines
14.1.2. Example of a Practical Design Optimization Problem
14.2. Gradient Evaluation of Implicit Functions
14.3. Issues in Practical Design Optimization
14.3.1. Selection of an Algorithm
14.3.2. Attributes of a Good Optimization Algorithm
14.4. Use of General-Purpose Software
14.4.1. Software Selection
14.4.2. Integration of an Application into General-Purpose Software
14.5. Optimum Design of Two-Member Frame with Out-of-Plane Loads
14.6. Optimum Design of a Three-Bar Structure for Multiple Performance Requirements
14.6.1. Symmetric Three-Bar Structure
14.6.2. Asymmetric Three-Bar Structure
14.6.3. Comparison of Solutions
14.7. Optimal Control of Systems by Nonlinear Programming
14.7.1. Prototype Optimal Control Problem
14.7.2. Minimization of Error in State Variable
14.7.3. Minimum Control Effort Problem
14.7.4. Minimum Time Control Problem
14.7.5. Comparison of Three Formulations for the Optimal Control of System Motion
14.8. Alternative Formulations for Structural Optimization Problems
14.9. Alternative Formulations for Time-Dependent Problems
Exercises for Chapter 14
III. ADVANCED AND MODERN TOPICS ON OPTIMUM DESIGN
15. Discrete Variable Optimum Design Concepts and Methods
15.1. Basic Concepts and Definitions
15.1.1. Definition of Mixed Variable Optimum Design Problem: MV-OPT
15.1.2. Classification of Mixed Variable Optimum Design Problems
15.1.3. Overview of Solution Concepts
15.2. Branch-and-Bound Methods
15.2.1. Basic BBM
15.2.2. BBM with Local Minimization
15.2.3. BBM for General MV-OPT
15.3. Integer Programming
15.4. Sequential Linearization Methods
15.5. Simulated Annealing
15.6. Dynamic Rounding-Off Method
15.7. Neighborhood Search Method
15.8. Methods for Linked Discrete Variables
15.9. Selection of a Method
15.10. Adaptive Numerical Method for Discrete Variable Optimization
15.10.1. Continuous Variable Optimization
15.10.2. Discrete Variable Optimization
Exercises for Chapter 15
16. Genetic Algorithms for Optimum Design
16.1. Basic Concepts and Definitions
16.2. Fundamentals of Genetic Algorithms
16.3. Genetic Algorithm for Sequencing-Type Problems
16.4. Applications
Exercises for Chapter 16
17. Multi-objective Optimum Design Concepts and Methods
17.1. Problem Definition
17.2. Terminology and Basic Concepts
17.2.1. Criterion Space and Design Space
17.2.2. Solution Concepts
17.2.3. Preferences and Utility Functions
17.2.4. Vector Methods and Scalarization Methods
17.2.5. Generation of Pareto Optimal Set
17.2.6. Normalization of Objective Functions
17.2.7. Optimization Engine
17.3. Multi-objective Genetic Algorithms
17.4. Weighted Sum Method
17.5. Weighted Min-Max Method
17.6. Weighted Global Criterion Method
17.7. Lexicographic Method
17.8. Bounded Objective Function Method
17.9. Goal Programming
17.10. Selection of Methods
Exercises for Chapter 17
18. Global Optimization Concepts and Methods
18.1. Basic Concepts of Solution Methods
18.1.1. Basic Solution Concepts
18.1.2. Overview of Methods
18.2. Overview of Deterministic Methods
18.2.1. Covering Methods
18.2.2. Zooming Method
18.2.3. Methods of Generalized Descent
18.2.4. Tunneling Method
18.3. Overview of Stochastic Methods
18.3.1. Pure Random Search Method
18.3.2. Multistart Method
18.3.3. Clustering Methods
18.3.4. Controlled Random Search: Nelder-Mead Method
18.3.5. Acceptance-Rejection Methods
18.3.6. Stochastic Integration
18.4. Two Local-Global Stochastic Methods
18.4.1. Conceptual Local-Global Algorithm
18.4.2. Domain Elimination Method
18.4.3. Stochastic Zooming Method
18.4.4. Operations Analysis of Methods
18.5. Numerical Performance of Methods
18.5.1. Summary of Features of Methods
18.5.2. Performance of Some Methods with Unconstrained Problems
18.5.3. Performance of Stochastic Zooming and Domain Elimination Methods
18.5.4. Global Optimization of Structural Design Problems
Exercises for Chapter 18
19. Nature-Inspired Search Methods
19.1. Differential Evolution Algorithm
19.1.1. Generation of an Initial Population
19.1.2. Generation of a Donor Design
19.1.3. Crossover Operation to Generate the Trial Design
19.1.4. Acceptance/Rejection of the Trial Design
19.1.5. DE Algorithm
19.2. Ant Colony Optimization
19.2.1. Ant Behavior
19.2.2. ACO Algorithm for the Traveling Salesman Problem
19.2.3. ACO Algorithm for Design Optimization
19.3. Particle Swarm Optimization
19.3.1. Swarm Behavior and Terminology
19.3.2. Particle Swarm Optimization Algorithm
Exercises for Chapter 19
20. Additional Topics on Optimum Design
20.1. Meta-Models for Design Optimization
20.1.1. Meta-Model
20.1.2. Response Surface Method
20.1.3. Normalization of Variables
20.2. Design of Experiments for Response Surface Generation
20.3. Discrete Design with Orthogonal Arrays
20.4. Robust Design Approach
20.4.1. Robust Optimization
20.4.2. Taguchi Method
20.5. Reliability-Based Design Optimization
-Design under Uncertainty
20.5.1. Review of Background Material for RBDO
20.5.2. Calculation of the Reliability Index
20.5.3. Formulation of Reliability-Based Design Optimization
Appendix A Vector and Matrix Algebra
A.1. Definition of Matrices
Contents note continued: A.2. Types of Matrices and Their Operations
A.2.1. Null Matrix
A.2.2. Vector
A.2.3. Addition of Matrices
A.2.4. Multiplication of Matrices
A.2.5. Transpose of a Matrix
A.2.6. Elementary Row
-Column Operations
A.2.7. Equivalence of Matrices
A.2.8. Scalar Product
-Dot Product of Vectors
A.2.9. Square Matrices
A.2.10. Partitioning of Matrices
A.3. Solving n Linear Equations in n Unknowns
A.3.1. Linear Systems
A.3.2. Determinants
A.3.3. Gaussian Elimination Procedure
A.3.4. Inverse of a Matrix: Gauss-Jordan Elimination
A.4. Solution to m Linear Equations in n Unknowns
A.4.1. Rank of a Matrix
A.4.2. General Solution of m X n Linear Equations
A.5. Concepts Related to a Set of Vectors
A.5.1. Linear Independence of a Set of Vectors
A.5.2. Vector Spaces
A.6. Eigenvalues and Eigenvectors
A.7. Norm and Condition Number of a Matrix
A.7.1. Norm of Vectors and Matrices
A.7.2. Condition Number of a Matrix
Exercises for Appendix A
Appendix B Sample Computer Programs
B.1. Equal Interval Search
B.2. Golden Section Search
B.3. Steepest-Descent Method
B.4. Modified Newton's Method.