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An Application-Oriented Introduction to Essential Optimization Concepts and Best Practices
Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.
Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project.
Examples, exercises, and homework throughout reinforce the author's "do, not study" approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field.
Providing excellent reference for students or professionals, Engineering Optimization:
* Describes and develops a variety of algorithms, including gradient based (such as Newton's, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization
* Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values
* Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling
* Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book
Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for "making the best choices" will find value in this introductory resource.
Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.
Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project.
Examples, exercises, and homework throughout reinforce the author's "do, not study" approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field.
Providing excellent reference for students or professionals, Engineering Optimization:
* Describes and develops a variety of algorithms, including gradient based (such as Newton's, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization
* Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values
* Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling
* Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book
Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for "making the best choices" will find value in this introductory resource.
An Application-Oriented Introduction to Essential Optimization Concepts and Best Practices
Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.
Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project.
Examples, exercises, and homework throughout reinforce the author's "do, not study" approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field.
Providing excellent reference for students or professionals, Engineering Optimization:
* Describes and develops a variety of algorithms, including gradient based (such as Newton's, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization
* Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values
* Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling
* Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book
Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for "making the best choices" will find value in this introductory resource.
Optimization is an inherent human tendency that gained new life after the advent of calculus; now, as the world grows increasingly reliant on complex systems, optimization has become both more important and more challenging than ever before. Engineering Optimization provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.
Although essential algorithms are explained in detail, the focus lies more in the human function: how to create an appropriate objective function, choose decision variables, identify and incorporate constraints, define convergence, and other critical issues that define the success or failure of an optimization project.
Examples, exercises, and homework throughout reinforce the author's "do, not study" approach to learning, underscoring the application-oriented discussion that provides a deep, generic understanding of the optimization process that can be applied to any field.
Providing excellent reference for students or professionals, Engineering Optimization:
* Describes and develops a variety of algorithms, including gradient based (such as Newton's, and Levenberg-Marquardt), direct search (such as Hooke-Jeeves, Leapfrogging, and Particle Swarm), along with surrogate functions for surface characterization
* Provides guidance on optimizer choice by application, and explains how to determine appropriate optimizer parameter values
* Details current best practices for critical stages of specifying an optimization procedure, including decision variables, defining constraints, and relationship modeling
* Provides access to software and Visual Basic macros for Excel on the companion website, along with solutions to examples presented in the book
Clear explanations, explicit equation derivations, and practical examples make this book ideal for use as part of a class or self-study, assuming a basic understanding of statistics, calculus, computer programming, and engineering models. Anyone seeking best practices for "making the best choices" will find value in this introductory resource.
Inhaltsverzeichnis
Contents
Preface xix
Acknowledgments xxvii
Nomenclature xxix
About the Companion Website xxxvii
Section 1 Introductory Concepts 1
1 Optimization: Introduction and Concepts 3
1.1 Optimization and Terminology 3
1.2 Optimization Concepts and Definitions 4
1.3 Examples 6
1.4 Terminology Continued 10
1.4.1 Constraint 10
1.4.2 Feasible Solutions 10
1.4.3 Minimize or Maximize 11
1.4.4 Canonical Form of the Optimization Statement 11
1.5 Optimization Procedure 12
1.6 Issues That Shape Optimization Procedures 16
1.7 Opposing Trends 17
1.8 Uncertainty 20
1.9 Over- and Under-specification in Linear Equations 21
1.10 Over- and Under-specification in Optimization 22
1.11 Test Functions 23
1.12 Significant Dates in Optimization 23
1.13 Iterative Procedures 26
1.14 Takeaway 27
1.15 Exercises 27
2 Optimization Application Diversity and Complexity 33
2.1 Optimization 33
2.2 Nonlinearity 33
2.3 Min, Max, Min-Max, Max-Min, ... 34
2.4 Integers and Other Discretization 35
2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys 36
2.6 Procedures, Not Equations 37
2.7 Static and Dynamic Models 38
2.8 Path Integrals 38
2.9 Economic Optimization and Other Nonadditive Cost Functions 38
2.10 Reliability 39
2.11 Regression 40
2.12 Deterministic and Stochastic 42
2.13 Experimental w.r.t. Modeled OF 43
2.14 Single and Multiple Optima 44
2.15 Saddle Points 45
2.16 Inflections 46
2.17 Continuum and Discontinuous DVs 47
2.18 Continuum and Discontinuous Models 47
2.19 Constraints and Penalty Functions 48
2.20 Ranks and Categorization: Discontinuous OFs 50
2.21 Underspecified OFs 51
2.22 Takeaway 51
2.23 Exercises 51
3 Validation: Knowing That the Answer Is Right 53
3.1 Introduction 53
3.2 Validation 53
3.3 Advice on Becoming Proficient 55
3.4 Takeaway 56
3.5 Exercises 57
Section 2 Univariate Search Techniques 59
4 Univariate (Single DV) Search Techniques 61
4.1 Univariate (Single DV) 61
4.2 Analytical Method of Optimization 62
4.2.1 Issues with the Analytical Approach 63
4.3 Numerical Iterative Procedures 64
4.3.1 Newton's Methods 64
4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68
4.4 Direct Search Approaches 70
4.4.1 Bisection Method 70
4.4.2 Golden Section Method 72
4.4.3 Perspective at This Point 74
4.4.4 Heuristic Direct Search 74
4.4.5 Leapfrogging 76
4.4.6 LF for Stochastic Functions 79
4.5 Perspectives on Univariate Search Methods 82
4.6 Evaluating Optimizers 85
4.7 Summary of Techniques 85
4.7.1 Analytical Method 86
4.7.2 Newton's (and Variants Like Secant) 86
4.7.3 Successive Quadratic 86
4.7.4 Golden Section Method 86
4.7.5 Heuristic Direct 87
4.7.6 Leapfrogging 87
4.8 Takeaway 87
4.9 Exercises 88
5 Path Analysis 93
5.1 Introduction 93
5.2 Path Examples 93
5.3 Perspective About Variables 96
5.4 Path Distance Integral 97
5.5 Accumulation along a Path 99
5.6 Slope along a Path 101
5.
Preface xix
Acknowledgments xxvii
Nomenclature xxix
About the Companion Website xxxvii
Section 1 Introductory Concepts 1
1 Optimization: Introduction and Concepts 3
1.1 Optimization and Terminology 3
1.2 Optimization Concepts and Definitions 4
1.3 Examples 6
1.4 Terminology Continued 10
1.4.1 Constraint 10
1.4.2 Feasible Solutions 10
1.4.3 Minimize or Maximize 11
1.4.4 Canonical Form of the Optimization Statement 11
1.5 Optimization Procedure 12
1.6 Issues That Shape Optimization Procedures 16
1.7 Opposing Trends 17
1.8 Uncertainty 20
1.9 Over- and Under-specification in Linear Equations 21
1.10 Over- and Under-specification in Optimization 22
1.11 Test Functions 23
1.12 Significant Dates in Optimization 23
1.13 Iterative Procedures 26
1.14 Takeaway 27
1.15 Exercises 27
2 Optimization Application Diversity and Complexity 33
2.1 Optimization 33
2.2 Nonlinearity 33
2.3 Min, Max, Min-Max, Max-Min, ... 34
2.4 Integers and Other Discretization 35
2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys 36
2.6 Procedures, Not Equations 37
2.7 Static and Dynamic Models 38
2.8 Path Integrals 38
2.9 Economic Optimization and Other Nonadditive Cost Functions 38
2.10 Reliability 39
2.11 Regression 40
2.12 Deterministic and Stochastic 42
2.13 Experimental w.r.t. Modeled OF 43
2.14 Single and Multiple Optima 44
2.15 Saddle Points 45
2.16 Inflections 46
2.17 Continuum and Discontinuous DVs 47
2.18 Continuum and Discontinuous Models 47
2.19 Constraints and Penalty Functions 48
2.20 Ranks and Categorization: Discontinuous OFs 50
2.21 Underspecified OFs 51
2.22 Takeaway 51
2.23 Exercises 51
3 Validation: Knowing That the Answer Is Right 53
3.1 Introduction 53
3.2 Validation 53
3.3 Advice on Becoming Proficient 55
3.4 Takeaway 56
3.5 Exercises 57
Section 2 Univariate Search Techniques 59
4 Univariate (Single DV) Search Techniques 61
4.1 Univariate (Single DV) 61
4.2 Analytical Method of Optimization 62
4.2.1 Issues with the Analytical Approach 63
4.3 Numerical Iterative Procedures 64
4.3.1 Newton's Methods 64
4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68
4.4 Direct Search Approaches 70
4.4.1 Bisection Method 70
4.4.2 Golden Section Method 72
4.4.3 Perspective at This Point 74
4.4.4 Heuristic Direct Search 74
4.4.5 Leapfrogging 76
4.4.6 LF for Stochastic Functions 79
4.5 Perspectives on Univariate Search Methods 82
4.6 Evaluating Optimizers 85
4.7 Summary of Techniques 85
4.7.1 Analytical Method 86
4.7.2 Newton's (and Variants Like Secant) 86
4.7.3 Successive Quadratic 86
4.7.4 Golden Section Method 86
4.7.5 Heuristic Direct 87
4.7.6 Leapfrogging 87
4.8 Takeaway 87
4.9 Exercises 88
5 Path Analysis 93
5.1 Introduction 93
5.2 Path Examples 93
5.3 Perspective About Variables 96
5.4 Path Distance Integral 97
5.5 Accumulation along a Path 99
5.6 Slope along a Path 101
5.
Details
| Erscheinungsjahr: | 2018 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 776 |
| Inhalt: | 776 S. |
| ISBN-13: | 9781118936337 |
| ISBN-10: | 1118936337 |
| Sprache: | Englisch |
| Herstellernummer: | 1W118936330 |
| Autor: | Rhinehart, R. Russell |
| Auflage: | 1. Auflage |
| Hersteller: |
Wiley & Sons
Wiley-ASME Press Series |
| Maße: | 244 x 187 x 46 mm |
| Von/Mit: | R. Russell Rhinehart |
| Erscheinungsdatum: | 11.04.2018 |
| Gewicht: | 1,366 kg |
Inhaltsverzeichnis
Contents
Preface xix
Acknowledgments xxvii
Nomenclature xxix
About the Companion Website xxxvii
Section 1 Introductory Concepts 1
1 Optimization: Introduction and Concepts 3
1.1 Optimization and Terminology 3
1.2 Optimization Concepts and Definitions 4
1.3 Examples 6
1.4 Terminology Continued 10
1.4.1 Constraint 10
1.4.2 Feasible Solutions 10
1.4.3 Minimize or Maximize 11
1.4.4 Canonical Form of the Optimization Statement 11
1.5 Optimization Procedure 12
1.6 Issues That Shape Optimization Procedures 16
1.7 Opposing Trends 17
1.8 Uncertainty 20
1.9 Over- and Under-specification in Linear Equations 21
1.10 Over- and Under-specification in Optimization 22
1.11 Test Functions 23
1.12 Significant Dates in Optimization 23
1.13 Iterative Procedures 26
1.14 Takeaway 27
1.15 Exercises 27
2 Optimization Application Diversity and Complexity 33
2.1 Optimization 33
2.2 Nonlinearity 33
2.3 Min, Max, Min-Max, Max-Min, ... 34
2.4 Integers and Other Discretization 35
2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys 36
2.6 Procedures, Not Equations 37
2.7 Static and Dynamic Models 38
2.8 Path Integrals 38
2.9 Economic Optimization and Other Nonadditive Cost Functions 38
2.10 Reliability 39
2.11 Regression 40
2.12 Deterministic and Stochastic 42
2.13 Experimental w.r.t. Modeled OF 43
2.14 Single and Multiple Optima 44
2.15 Saddle Points 45
2.16 Inflections 46
2.17 Continuum and Discontinuous DVs 47
2.18 Continuum and Discontinuous Models 47
2.19 Constraints and Penalty Functions 48
2.20 Ranks and Categorization: Discontinuous OFs 50
2.21 Underspecified OFs 51
2.22 Takeaway 51
2.23 Exercises 51
3 Validation: Knowing That the Answer Is Right 53
3.1 Introduction 53
3.2 Validation 53
3.3 Advice on Becoming Proficient 55
3.4 Takeaway 56
3.5 Exercises 57
Section 2 Univariate Search Techniques 59
4 Univariate (Single DV) Search Techniques 61
4.1 Univariate (Single DV) 61
4.2 Analytical Method of Optimization 62
4.2.1 Issues with the Analytical Approach 63
4.3 Numerical Iterative Procedures 64
4.3.1 Newton's Methods 64
4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68
4.4 Direct Search Approaches 70
4.4.1 Bisection Method 70
4.4.2 Golden Section Method 72
4.4.3 Perspective at This Point 74
4.4.4 Heuristic Direct Search 74
4.4.5 Leapfrogging 76
4.4.6 LF for Stochastic Functions 79
4.5 Perspectives on Univariate Search Methods 82
4.6 Evaluating Optimizers 85
4.7 Summary of Techniques 85
4.7.1 Analytical Method 86
4.7.2 Newton's (and Variants Like Secant) 86
4.7.3 Successive Quadratic 86
4.7.4 Golden Section Method 86
4.7.5 Heuristic Direct 87
4.7.6 Leapfrogging 87
4.8 Takeaway 87
4.9 Exercises 88
5 Path Analysis 93
5.1 Introduction 93
5.2 Path Examples 93
5.3 Perspective About Variables 96
5.4 Path Distance Integral 97
5.5 Accumulation along a Path 99
5.6 Slope along a Path 101
5.
Preface xix
Acknowledgments xxvii
Nomenclature xxix
About the Companion Website xxxvii
Section 1 Introductory Concepts 1
1 Optimization: Introduction and Concepts 3
1.1 Optimization and Terminology 3
1.2 Optimization Concepts and Definitions 4
1.3 Examples 6
1.4 Terminology Continued 10
1.4.1 Constraint 10
1.4.2 Feasible Solutions 10
1.4.3 Minimize or Maximize 11
1.4.4 Canonical Form of the Optimization Statement 11
1.5 Optimization Procedure 12
1.6 Issues That Shape Optimization Procedures 16
1.7 Opposing Trends 17
1.8 Uncertainty 20
1.9 Over- and Under-specification in Linear Equations 21
1.10 Over- and Under-specification in Optimization 22
1.11 Test Functions 23
1.12 Significant Dates in Optimization 23
1.13 Iterative Procedures 26
1.14 Takeaway 27
1.15 Exercises 27
2 Optimization Application Diversity and Complexity 33
2.1 Optimization 33
2.2 Nonlinearity 33
2.3 Min, Max, Min-Max, Max-Min, ... 34
2.4 Integers and Other Discretization 35
2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys 36
2.6 Procedures, Not Equations 37
2.7 Static and Dynamic Models 38
2.8 Path Integrals 38
2.9 Economic Optimization and Other Nonadditive Cost Functions 38
2.10 Reliability 39
2.11 Regression 40
2.12 Deterministic and Stochastic 42
2.13 Experimental w.r.t. Modeled OF 43
2.14 Single and Multiple Optima 44
2.15 Saddle Points 45
2.16 Inflections 46
2.17 Continuum and Discontinuous DVs 47
2.18 Continuum and Discontinuous Models 47
2.19 Constraints and Penalty Functions 48
2.20 Ranks and Categorization: Discontinuous OFs 50
2.21 Underspecified OFs 51
2.22 Takeaway 51
2.23 Exercises 51
3 Validation: Knowing That the Answer Is Right 53
3.1 Introduction 53
3.2 Validation 53
3.3 Advice on Becoming Proficient 55
3.4 Takeaway 56
3.5 Exercises 57
Section 2 Univariate Search Techniques 59
4 Univariate (Single DV) Search Techniques 61
4.1 Univariate (Single DV) 61
4.2 Analytical Method of Optimization 62
4.2.1 Issues with the Analytical Approach 63
4.3 Numerical Iterative Procedures 64
4.3.1 Newton's Methods 64
4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68
4.4 Direct Search Approaches 70
4.4.1 Bisection Method 70
4.4.2 Golden Section Method 72
4.4.3 Perspective at This Point 74
4.4.4 Heuristic Direct Search 74
4.4.5 Leapfrogging 76
4.4.6 LF for Stochastic Functions 79
4.5 Perspectives on Univariate Search Methods 82
4.6 Evaluating Optimizers 85
4.7 Summary of Techniques 85
4.7.1 Analytical Method 86
4.7.2 Newton's (and Variants Like Secant) 86
4.7.3 Successive Quadratic 86
4.7.4 Golden Section Method 86
4.7.5 Heuristic Direct 87
4.7.6 Leapfrogging 87
4.8 Takeaway 87
4.9 Exercises 88
5 Path Analysis 93
5.1 Introduction 93
5.2 Path Examples 93
5.3 Perspective About Variables 96
5.4 Path Distance Integral 97
5.5 Accumulation along a Path 99
5.6 Slope along a Path 101
5.
Details
| Erscheinungsjahr: | 2018 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Seiten: | 776 |
| Inhalt: | 776 S. |
| ISBN-13: | 9781118936337 |
| ISBN-10: | 1118936337 |
| Sprache: | Englisch |
| Herstellernummer: | 1W118936330 |
| Autor: | Rhinehart, R. Russell |
| Auflage: | 1. Auflage |
| Hersteller: |
Wiley & Sons
Wiley-ASME Press Series |
| Maße: | 244 x 187 x 46 mm |
| Von/Mit: | R. Russell Rhinehart |
| Erscheinungsdatum: | 11.04.2018 |
| Gewicht: | 1,366 kg |
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