Introduction to Optimum Design
- 3rd Edition - August 12, 2011
- Author: Jasbir Singh Arora
- Language: English
Introduction to Optimum Design, Third Edition describes an organized approach to engineering design optimization in a rigorous yet simplified manner. It illustrates various concep… Read more
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.
- 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
- Edition: 3
- Published: August 12, 2011
- Language: English
JA
Jasbir Singh 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 IowaRead Introduction to Optimum Design on ScienceDirect