 # Introduction to Optimum Design

3rd Edition - August 12, 2011

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• Author: Jasbir Arora
• eBook ISBN: 9780123813763

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## Description

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.

• Dedication

Preface to Third Edition

Acknowledgments

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

Bibliography

Answers to Selected Exercises

Index

## Product details

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

## About the Author

### 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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