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# Introduction to Optimum Design

- 2nd Edition - May 5, 2004
- Author: Jasbir Singh Arora
- Language: English
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 4 7 0 2 5 - 2

Optimization is a mathematical tool developed in the early 1960's used to find the most efficient and feasible solutions to an engineering problem. It can be used to find ideal sh… Read more

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Request a sales quoteOptimization is a mathematical tool developed in the early 1960's used to find the most efficient and feasible solutions to an engineering problem. It can be used to find ideal shapes and physical configurations, ideal structural designs, maximum energy efficiency, and many other desired goals of engineering.

This book is intended for use in a first course on engineering design and optimization. Material for the text has evolved over a period of several years and is based on classroom presentations for an undergraduate core course on the principles of design. Virtually any problem for which certain parameters need to be determined to satisfy constraints can be formulated as a design optimization problem. The concepts and methods described in the text are quite general and applicable to all such formulations. Inasmuch, the range of application of the optimum design methodology is almost limitless, constrained only by the imagination and ingenuity of the user. The book describes the basic concepts and techniques with only a few simple applications. Once they are clearly understood, they can be applied to many other advanced applications that are discussed in the text.

- Allows engineers involved in the design process to adapt optimum design concepts in their work using the material in the text
- Basic concepts of optimality conditions and numerical methods are described with simple examples, making the material high teachable and learnable
- Classroom-tested for many years to attain optimum pedagogical effectiveness

Jasbir S. Arora

Dedication

Preface

Chapter 1: Introduction to Design

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: Saw Mill 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

Exercises for Chapter 2

Chapter 3: Graphical Optimization

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 Minimum Weight Tubular Column

3.8: Graphical Solution for a Beam Design Problem

Exercises for Chapter 3

Chapter 4: Optimum Design Concepts

4.1: Definitions of Global and Local Minima

4.2: Review of Some Basic Calculus Concepts

4.3: Unconstrained Optimum Design Problems

4.4: Constrained Optimum Design Problems

4.5: Postoptimality Analysis: Physical Meaning of Lagrange Multipliers

4.6: Global Optimality

4.7: Engineering Design Examples

Exercises for Chapter 4

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: Sufficiency Check for Rectangular Beam Design Problem

Exercises for Chapter 5

Chapter 6: Linear Programming Methods for Optimum Design

6.1: Definition of a Standard Linear Programming Problem

6.2: Basic Concepts Related to Linear Programming Problems

6.3: Basic Ideas and Steps of the Simplex Method

6.4: Two-Phase Simplex Method-Artificial Variables

6.5: Postoptimality Analysis

6.6: Solution of LP Problems Using Excel Solver

Exercises for Chapter 6

Chapter 7: More on Linear Programming Methods for Optimum Design

7.1: 7.1 Derivation of the Simplex Method

7.2: Alternate Simplex Method

7.3: Duality in Linear Programming

Chapter 8: Numerical Methods for Unconstrained Optimum Design

8.1: General Concepts Related to Numerical Algorithms

8.2: Basic Ideas and Algorithms for Step Size Determination

8.3: Search Direction Determination: Steepest Descent Method

8.4: Search Direction Determination: Conjugate Gradient Method

Exercises for Chapter 8

Chapter 9: More on Numerical Methods for Unconstrained Optimum Design

9.1: More on Step Size Determination

9.2: More on Steepest Descent Method

9.3: Scaling of Design Variables

9.4: Search Direction Determination: Newton’s Method

9.5: Search Direction Determination: Quasi-Newton Methods

9.6: Engineering Applications of Unconstrained Methods

9.7: Solution of Constrained Problems Using Unconstrained Optimization Methods

Exercises for Chapter 9^{*}

Chapter 10: Numerical Methods for Constrained Optimum Design

10.1: Basic Concepts and Ideas

10.2: Linearization of Constrained Problem

10.3: Sequential Linear Programming Algorithm

10.4: Quadratic Programming Subproblem

10.5: Constrained Steepest Descent Method

10.6: Engineering Design Optimization Using Excel Solver

Exercises for Chapter 10

Chapter 11: More on Numerical Methods for Constrained Optimum Design

11.1: Potential Constraint Strategy

11.2: Quadratic Programming Problem

11.2.1: Definition of QP Problem

11.2.2: KKT Necessary Conditions for the QP Problem

11.2.3: Transformation of KKT Conditions

11.2.4: Simplex Method for Solving QP Problem

11.3: Approximate Step Size Determination

11.4: Constrained Quasi-Newton Methods

11.4.1: Derivation of Quadratic Programming Subproblem

11.4.2: Quasi-Newton Hessian Approximation

11.4.3: Modified Constrained Steepest Descent Algorithm

11.4.4: Observations on the Constrained Quasi-Newton Methods

11.4.5: Descent Functions

11.5: Other Numerical Optimization Methods

Chapter 12: Introduction to Optimum Design with MATLAB

12.1: Introduction to Optimization Toolbox

12.2: Unconstrained Optimum Design Problems

12.3: Constrained Optimum Design Problems

12.4: Optimum Design Examples with MATLAB

Chapter 13: Interactive Design Optimization

13.1: Role of Interaction in Design Optimization

13.2: Interactive Design Optimization Algorithms

13.3: Desired Interactive Capabilities

13.4: Interactive Design Optimization Software

13.5: Examples of Interactive Design Optimization

Exercises for Chapter 13

Chapter 14: Design Optimization Applications with Implicit Functions

14.1: Formulation of Practical Design Optimization Problems

14.2 Gradient Evaluation for 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: Discrete Variable Optimum Design

14.8: Optimal Control of Systems by Nonlinear Programming

Chapter 15: Discrete Variable Optimum Design Concepts and Methods

15.1: Basic Concepts and Definitions

15.2: Branch and Bound Methods (BBM)

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

Exercises for Chapter 15^{*}

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

Exercises for Chapter 16^{*}

Chapter 17: Multiobjective Optimum Design Concepts and Methods

17.1: Problem Definition

17.2: Terminology and Basic Concepts

17.3: Multiobjective 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

Chapter 18: Global Optimization Concepts and Methods for Optimum Design

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^{*}

Appendix A: Economic Analysis

A.1: Time Value of Money

A.2: Economic Bases for Comparison

Exercises for Appendix A

Appendix B: Vector and Matrix Algebra

B.1: Definition of Matrices

B.2: Type of Matrices and Their Operations

B.3: Solution of *n* Linear Equations in *n* Unknowns

B.4: Solution of *m* Linear Equations in *n* Unknowns

B.5: Concepts Related to a Set of Vectors

B.6: Eigenvalues and Eigenvectors

B.7*: Norm and Condition Number of a Matrix

Exercises for Appendix B

Appendix C: A Numerical Method for Solution of Nonlinear Equations

C.1: Single Nonlinear Equation

C.2: Multiple Nonlinear Equations

Exercises for Appendix C

Appendix D: Sample Computer Programs

D.1: Equal Interval Search

D.2: Golden Section Search

D.3: Steepest Descent Method

D.4: Modified Newton’s Method

References

Bibliography

Answers to Selected Problems

Chapter 4: Optimum Design Concepts

Chapter 5: More on Optimum Design Concepts

Chapter 6: Linear Programming Methods for Optimum Design

Chapter 7: More on Linear Programming Methods for Optimum Design

Chapter 8: Numerical Methods for Unconstrained Optimum Design

Chapter 9: More on Numerical Methods for Unconstrained Optimum Design 9.1

Chapter 10: Numerical Methods for Constrained Optimum Design

Chapter 12: Introduction to Optimum Design with MATLAB

Chapter 13: Interactive Design Optimization

Chapter 14: Design Optimization Applications with Implicit Functions

Chapter 18: Global Optimization Concepts and Methods for Optimum Design 18.1

Appendix A: Economic Analysis

Appendix B: Vector and Matrix Algebra

Appendix C: A Numerical Method for Solution of Nonlinear Equations

Index

- No. of pages: 728
- Language: English
- Edition: 2
- Published: May 5, 2004
- Imprint: Academic Press
- eBook ISBN: 9780080470252

JA

### Jasbir Singh Arora

*Introduction to Optimum Design*on ScienceDirect