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Introduction to Optimum Design
2nd Edition - May 5, 2004
Author: Jasbir Singh Arora
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… Read more
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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 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
Engineering students and practitioners studying optimization and mechanical engineering design
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
- Published: May 5, 2004
- Imprint: Academic Press
- eBook ISBN: 9780080470252
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 Iowa, iowa City, IA, USA