Engineering Optimization

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.

Preface xix

Acknowledgments xxvii

Nomenclature xxix

About the Companion Website xxxvii

Section 1 Introductory Concepts 1

1 Optimization: Introduction and Concepts 3

2 Optimization Application Diversity and Complexity 33

3 Validation: Knowing That the Answer Is Right 53

Section 2 Univariate Search Techniques 59

4 Univariate (Single DV) Search Techniques 61

5 Path Analysis 93

6 Stopping and Convergence Criteria: 1-D Applications 107

Section 3 Multivariate Search Techniques 117

7 Multidimension Application Introduction and the Gradient 119

8 Elementary Gradient-Based Optimizers: CSLSandISD135

9 Second-Order Model-Based Optimizers:SQandNR155

10 Gradient-Based Optimizer Solutions:LM, RLM, CG, BFGS, RG, and GRG173

11 Direct Search Techniques 187

12 Linear Programming 223

13 Dynamic Programming 233

14 Genetic Algorithms and Evolutionary Computation 243

15 Intuitive Optimization 253

16 Surface Analysis II 257

17 Convergence Criteria 2: N-D Applications 265

18 Enhancements to Optimizers 271

Section 4 Developing Your Application Statements 279

19 Scaled Variables and Dimensional Consistency 281

20 Economic Optimization 289

21 Multiple OF and Constraint Applications 305

22 Constraints 319

23 Multiple Optima 335

24 Stochastic Objective Functions 353

25 Effects of Uncertainty 367

26 Optimization of Probable Outcomes and Distribution Characteristics 381

27 Discrete and Integer Variables 391

28 Class Variables 397

29 Regression 403

Section 5 Perspective on Many Topics 441

30 Perspective 443

31 Response Surface Aberrations 459

32 Identifying the Models, OF, DV, Convergence Criteria, and Constraints 475

33 Evaluating Optimizers 489

34 Troubleshooting Optimizers 499

Section 6 Analysis of Leapfrogging Optimization 505

35 Analysis of Leapfrogging 507

Section 7 Case Studies 529

36 Case Study 1: Economic Optimization of a Pipe System 531

37 Case Study 2: Queuing Study 539

38 Case Study 3: Retirement Study 543

39 Case Study 4: AGoddard Rocket Study 551

40 Case Study 5: Reservoir 557

41 Case Study 6: Area Coverage 561

42 Case Study 7: Approximating Series Solution to an ODE 565

43 Case Study 8: Horizontal Tank Vapor–Liquid Separator 571

44 Case Study 9: In Vitro Fertilization 579

45 Case Study 10: Data Reconciliation 585

Section 8 Appendices 591

Section 9 References and Index 717

References and Additional Resources 719

Index 723

R. Russell Rhinehart is an Emeritus Professor and Amoco Chair in the School of Chemical Engineering at Oklahoma State University. He was named as one of InTECH's 50 Most Influential Industry Innovators in 2004, and was inducted into the Automation Hall of Fame for the Process Industries in 2005. His research focuses on process improvement through modeling, optimization and control, and product improvement through modeling and design.

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.