- Cover
- Title Page
- Preface
- Acknowledgments
- Nomenclature
- About the Companion Website
- Section 1: Introductory Concepts
- 1 Optimization
- 1.1 Optimization and Terminology
- 1.2 Optimization Concepts and Definitions
- 1.3 Examples
- 1.4 Terminology Continued
- 1.5 Optimization Procedure
- 1.6 Issues That Shape Optimization Procedures
- 1.7 Opposing Trends
- 1.8 Uncertainty
- 1.9 Over‐ and Under‐specification in Linear Equations
- 1.10 Over‐ and Under‐specification in Optimization
- 1.11 Test Functions
- 1.12 Significant Dates in Optimization
- 1.13 Iterative Procedures
- 1.14 Takeaway
- 1.15 Exercises
- 2 Optimization Application Diversity and Complexity
- 2.1 Optimization
- 2.2 Nonlinearity
- 2.3 Min, Max, Min–Max, Max–Min, …
- 2.4 Integers and Other Discretization
- 2.5 Conditionals and Discontinuities: Cliffs Ridges/Valleys
- 2.6 Procedures, Not Equations
- 2.7 Static and Dynamic Models
- 2.8 Path Integrals
- 2.9 Economic Optimization and Other Nonadditive Cost Functions
- 2.10 Reliability
- 2.11 Regression
- 2.12 Deterministic and Stochastic
- 2.13 Experimental w.r.t. Modeled OF
- 2.14 Single and Multiple Optima
- 2.15 Saddle Points
- 2.16 Inflections
- 2.17 Continuum and Discontinuous DVs
- 2.18 Continuum and Discontinuous Models
- 2.19 Constraints and Penalty Functions
- 2.20 Ranks and Categorization: Discontinuous OFs
- 2.21 Underspecified OFs
- 2.22 Takeaway
- 2.23 Exercises
- 3 Validation
- 1 Optimization
- Section 2: Univariate Search Techniques
- 6 Stopping and Convergence Criteria: 1‐D Applications
- Section 3: Multivariate Search Techniques
- 7 Multidimension Application Introduction and the Gradient
- 8 Elementary Gradient‐Based Optimizers
- 9 Second‐Order Model‐Based Optimizers
- 10 Gradient‐Based Optimizer Solutions
- 11 Direct Search Techniques
- 11.1 Introduction
- 11.2 Cyclic Heuristic Direct (CHD) Search
- 11.3 Hooke–Jeeves (HJ)
- 11.4 Compare and Contrast CHD and HJ Features: A Summary
- 11.5 Nelder–Mead (NM) Simplex: Spendley, Hext, and Himsworth
- 11.6 Multiplayer Direct Search Algorithms
- 11.7 Leapfrogging
- 11.8 Particle Swarm Optimization
- 11.9 Complex Method (CM)
- 11.10 A Brief Comparison
- 11.11 Takeaway
- 11.12 Exercises
- 12 Linear Programming
- 13 Dynamic Programming
- 14 Genetic Algorithms and Evolutionary Computation
- 15 Intuitive Optimization
- 16 Surface Analysis II
- 16.1 Introduction
- 16.2 Maximize Is Equivalent to Minimize the Negative
- 16.3 Scaling by a Positive Number Does Not Change DV
- 16.4 Scaled and Translated OFs Do Not Change DV
- 16.5 Monotonic Function Transformation Does Not Change DV
- 16.6 Impact on Search Path or NOFE
- 16.7 Inequality Constraints
- 16.8 Transforming DVs
- 16.9 Takeaway
- 16.10 Exercises
- 17 Convergence Criteria 2
- 18 Enhancements to Optimizers
- 18.1 Introduction
- 18.2 Criteria for Replicate Trials
- 18.3 Quasi‐Newton
- 18.4 Coarse–Fine Sequence
- 18.5 Number of Players
- 18.6 Search Range Adjustment
- 18.7 Adjustment of Optimizer Coefficient Values or Options in Process
- 18.8 Initialization Range
- 18.9 OF and DV Transformations
- 18.10 Takeaway
- 18.11 Exercises
- Section 4: Developing Your Application Statements
- 19 Scaled Variables and Dimensional Consistency
- 20 Economic Optimization
- 21 Multiple OF and Constraint Applications
- 22 Constraints
- 23 Multiple Optima
- 24 Stochastic Objective Functions
- 25 Effects of Uncertainty
- 26 Optimization of Probable Outcomes and Distribution Characteristics
- 27 Discrete and Integer Variables
- 28 Class Variables
- 29 Regression
- 29.1 Introduction
- 29.2 Perspective
- 29.3 Least Squares Regression: Traditional View on Linear Model Parameters
- 29.4 Models Nonlinear in DV
- 29.5 Maximum Likelihood
- 29.6 Convergence Criterion
- 29.7 Model Order or Complexity
- 29.8 Bootstrapping to Reveal Model Uncertainty
- 29.9 Perspective
- 29.10 Takeaway
- 29.11 Exercises
- Section 5: Perspective on Many Topics
- 30 Perspective
- 31 Response Surface Aberrations
- 32 Identifying the Models, OF, DV, Convergence Criteria, and Constraints
- 33 Evaluating Optimizers
- 34 Troubleshooting Optimizers
- 34.1 Introduction
- 34.2 DV Values Do Not Change
- 34.3 Multiple DV Values for the Same OF Value
- 34.4 EXE Error
- 34.5 Extreme Values
- 34.6 DV Is Dependent on Convergence Threshold
- 34.7 OF Is Irreproducible
- 34.8 Concern over Results
- 34.9 CDF Features
- 34.10 Parameter Correlation
- 34.11 Multiple Equivalent Solutions
- 34.12 Takeaway
- 34.13 Exercises
- Section 6: Analysis of Leapfrogging Optimization
- 35 Analysis of Leapfrogging
- 35.1 Introduction
- 35.2 Balance in an Optimizer
- 35.3 Number of Initializations to be Confident That the Best Will Draw All Others to the Global Optimum
- 35.4 Leap‐To Window Amplification Analysis
- 35.5 Analysis of α and M to Prevent Convergence on the Side of a Hill
- 35.6 Analysis of α and M to Minimize NOFE
- 35.7 Probability Distribution of Leap‐Overs
- 35.8 Takeaway
- 35.9 Exercises
- 35 Analysis of Leapfrogging
- Section 7: Case Studies
- Section 8: Appendices
- Appendix A: Mathematical Concepts and Procedures
- A.1 Representation of Relations
- A.2 Taylor Series Expansion (Single Variable)
- A.3 Taylor Series Expansion (Multiple Variable)
- A.4 Evaluating First Derivatives at x0
- A.5 Partial Derivatives: First Order
- A.6 Partial Derivatives: Second Order
- A.7 Linear Algebra Notations
- A.8 Algebra and Assignment Statements
- Appendix B: Root Finding
- Appendix C: Gaussian Elimination
- Appendix D: Steady‐State Identification in Noisy Signals
- Appendix E: Optimization Challenge Problems (2‐D and Single OF)
- Appendix F: Brief on VBA Programming
- F.1 Introduction
- F.2 To Start
- F.3 General
- F.4 I/O to Excel Cells
- F.5 Variable Types and Declarations
- F.6 Operations
- F.7 Loops
- F.8 Conditionals
- F.9 Debugging
- F.10 Run Buttons (Commands)
- F.11 Objects and Properties
- F.12 Keystroke Macros
- F.13 External File I/O
- F.14 Solver Add‐In
- F.15 Calling Solver from VBA
- Appendix A: Mathematical Concepts and Procedures
- Section 9: References and Index
- Index
- End User License Agreement
Section 8
Appendices
The six appendices are to provide essential refresher and/or introduction to mathematical, procedural, or programming topics in the book.
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