- 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 2
Univariate Search Techniques
Univariate means one variable. In this section, there is only one DV, and all optimizers seek to find the minimum. The single DV applications make it easy to understand optimizer concepts, procedures, convergence criteria, path integrals, and the issues that confound them.
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