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    Introduction to optimum design / Jasbir S. Arora.

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    • Title:Introduction to optimum design / Jasbir S. Arora.
    •    
    • Author/Creator:Arora, Jasbir S.
    • Published/Created:Waltham, MA : Academic Press, ©2012.

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    • Library of Congress Subjects:Engineering design--Mathematical models.
    • Edition:3rd ed.
    • Description:xvi, 880 p. : ill. ; 25 cm.
    • 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.
    • ISBN:9780123813756 (hardback)
      0123813751 (hardback)
    • 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.
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