Introduction to Optimum Design book cover

Introduction to Optimum Design

Hardbound, 896 Pages

Published: August 2011

Imprint: Academic Press

ISBN: 978-0-12-381375-6


  • "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. Arora’s 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 "Arora’s 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 appeal…among some of the distinguishing characteristics of Arora’s 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 engineer…In 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, Arora’s 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. Arora’s Introduction to Optimum Design, 2nd Ed…The 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



    1 Introduction to Design Optimization
    1.1 The Design Process
    1.2 Engineering Design versus EngineeringAnalysis
    1.3 Conventional versus Optimum Design Process
    1.4 Optimum Design versus Optimal Control
    1.5 Basic Terminology and Notation

    2 Optimum Design Problem Formulation
    2.1 The Problem Formulation Process
    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 SymmetricmThree-Bar Truss
    2.11 A General Mathematical Model for Optimum Design
    Exercises for Chapter 2

    3 Graphical Optimization and Basic Concepts
    3.1 Graphical Solution Process
    3.2 Use of Mathematica for Graphical Optimization
    3.3 Use of MATLAB for Graphical Optimization
    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 83

    4 Optimum Design Concepts: Optimality Conditions
    4.1 Definitions of Global and Local Minima
    4.2 Review of Some Basic Calculus Concepts
    4.3 Concept of Necessary and Sufficient Conditions
    4.4 Optimality Conditions: Unconstrained Problem
    4.5 Necessary Conditions: Equality-Constrained Problem
    4.6 Necessary Conditions for a General Constrained Problem
    4.7 Postoptimality Analysis: The Physical Meaning of Lagrange Multipliers
    4.8 Global Optimality
    4.9 Engineering Design Examples

    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
    Exercises for Chapter 5


    6 Optimum Design with Excel Solver
    6.1 Introduction to Numerical Methods for Optimum Design
    6.2 Excel Solver: An Introduction
    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
    6.9 Optimum Design of Members for Flexure
    6.10 Optimum Design of Telecommunication Poles
    Exercises for Chapter 6

    7 Optimum Design with MATLAB
    7.1 Introduction to the Optimization Toolbox
    7.2 Unconstrained Optimum Design Problems
    7.3 Constrained Optimum Design Problems
    7.4 Optimum Design Examples with MATLAB
    Exercises for Chapter 7

    8 Linear Programming Methods for Optimum Design
    8.1 Linear Functions
    8.2 Definition of a Standard Linear Programming Problem
    8.3 Basic Concepts Related to Linear Programming Problems
    8.4 Calculation of Basic Solutions
    8.5 The Simplex Method
    8.6 The Two-Phase Simplex Method-Artificial Variables
    8.7 Postoptimality Analysis
    Exercises for Chapter 8

    9 More on Linear Programming Methods
    for Optimum Design 377
    9.1 Derivation of the Simplex Method
    9.2 An Alternate Simplex Method
    9.3 Duality in Linear Programming
    9.4 KKT Conditions for the LP Problem
    9.5 Quadratic Programming Problems
    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
    10.3 Descent Direction and Convergence of Algorithms
    10.4 Step Size Determination: Basic Ideas
    10.5 Numerical Methods to Compute Step Size
    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
    11.2 More on the Steepest-Descent Method
    11.3 Scaling of Design Variables
    11.4 Search Direction Determination: Newton’s Method
    11.5 Search Direction Determination: Quasi-Newton Methods
    11.6 Engineering Applications of Unconstrained Methods
    11.7 Solutions to Constrained Problems Using Unconstrained Optimization Methods
    11.8 Rate of Convergence of Algorithms
    11.9 Direct Search Methods
    Exercises for Chapter 11

    12 Numerical Methods for Constrained Optimum Design
    12.1 Basic Concepts Related to Numerical Methods
    12.2 Linearization of the Constrained Problem
    12.3 The Sequential Linear Programming Algorithm
    12.4 Sequential Quadratic Programming
    12.5 Search Direction Calculation: The QP Subproblem
    12.6 The Step Size Calculation Subproblem
    12.7 The Constrained Steepest-Descent Method
    Exercises for Chapter 12

    13 More on Numerical Methods for Constrained Optimum Design
    13.1 Potential Constraint Strategy
    13.2 Inexact Step Size Calculation
    13.3 Bound-Constrained Optimization
    13.4 Sequential Quadratic Programming: SQP Methods
    13.5 Other Numerical Optimization Methods
    13.6 Solution to the Quadratic Programming Subproblem
    Exercises for Chapter 13

    14 Practical Applications of Optimization
    14.1 Formulation of Practical Design Optimization Problems
    14.2 Gradient Evaluation of Implicit Functions
    14.3 Issues in Practical Design Optimization
    14.4 Use of 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
    14.7 Optimal Control of Systems by Nonlinear Programming
    14.8 Alternative Formulations for Structural Optimization Problems
    14.9 Alternative Formulations for Time-Dependent Problems
    Exercises for Chapter 14


    15 Discrete Variable Optimum Design Concepts and Methods
    15.1 Basic Concepts and Definitions
    15.2 Branch-and-Bound Methods
    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
    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 653
    Exercises for Chapter 16

    17 Multi-objective Optimum Design Concepts and Methods
    17.1 Problem Definition
    17.2 Terminology and Basic Concepts
    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
    18.2 Overview of Deterministic Methods
    18.3 Overview of Stochastic Methods
    18.4 Two Local-Global Stochastic Methods
    18.5 Numerical Performance of Methods
    Exercises for Chapter 18

    19 Nature-Inspired Search Methods
    19.1 Differential Evolution Algorithm
    19.2 Ant Colony Optimization
    19.3 Particle Swarm Optimization
    Exercises for Chapter 19

    20 Additional Topics on Optimum Design
    20.1 Meta-Models for Design Optimization
    20.2 Design of Experiments for Response Surface Generation
    20.3 Discrete Design with Orthogonal Arrays
    20.4 Robust Design Approach
    20.5 Reliability-Based Design Optimization-Design under Uncertainty

    Appendix A: Vector and Matrix Algebra
    A.1 Definition of Matrices
    A.2 Types of Matrices and Their Operations
    A.3 Solving n Linear Equations in n Unknowns
    A.4 Solution to m Linear Equations in n Unknowns
    A.5 Concepts Related to a Set of Vectors
    A.6 Eigenvalues and Eigenvectors
    A.7 Norm and 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


    Answers to Selected Exercises



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