Introduction to Optimum Design

Introduction to Optimum Design

3rd Edition - August 12, 2011

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  • Author: Jasbir Arora
  • eBook ISBN: 9780123813763

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Introduction to Optimum Design, Third Edition describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It 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. Excel and MATLAB® are featured as learning and teaching aids.

Key Features

  • Basic concepts of optimality conditions and numerical methods are described with simple and practical examples, making the material highly teachable and learnable
  • Includes applications of optimization methods for structural, mechanical, aerospace, and industrial engineering problems
  • Introduction to MATLAB Optimization Toolbox
  • Practical design examples introduce students to the use of optimization methods early in the book
  • New example problems throughout the text are enhanced with detailed illustrations
  • Optimum design with Excel Solver has been expanded into a full chapter
  • New chapter on several advanced optimum design topics serves the needs of instructors who teach more advanced courses


Upper level undergraduate and graduate engineering students and practitioners studying optimization and engineering design.

Table of Contents

  • Dedication

    Preface to Third Edition


    Key Symbols and Abbreviations

    Chapter 1. Introduction to Design Optimization

    1.1. The 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

    Chapter 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

    2.7. Minimum-Weight Tubular 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. A General Mathematical Model for Optimum Design

    Chapter 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 Solutions

    3.6. Infeasible Problem

    3.7. Graphical Solution for the Minimum-Weight Tubular Column

    3.8. Graphical Solution for a Beam Design Problem

    Chapter 4. Optimum Design Concepts

    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

    Chapter 5. More on Optimum Design Concepts

    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 the Rectangular Beam Design Problem

    5.5. Duality in Nonlinear Programming

    Chapter 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

    Chapter 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

    Chapter 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

    Chapter 9. More on Linear Programming Methods for Optimum Design

    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

    Chapter 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

    Chapter 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

    Chapter 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

    Chapter 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

    Chapter 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 a 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

    Chapter 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

    Chapter 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

    Chapter 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

    Chapter 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

    Chapter 19. Nature-Inspired Search Methods

    19.1. Differential Evolution Algorithm

    19.2. Ant Colony Optimization

    19.3. Particle Swarm Optimization

    Chapter 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

    Appendix B. Sample Computer Programs


    Answers to Selected Exercises


Product details

  • No. of pages: 896
  • Language: English
  • Copyright: © Academic Press 2011
  • Published: August 12, 2011
  • Imprint: Academic Press
  • eBook ISBN: 9780123813763

About the Author

Jasbir Arora

Jasbir Arora
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.

Affiliations and Expertise

Department of Civil and Environmental Engineering & Department of Mechanical Engineering, University of Iowa, iowa City, IA, USA

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