Table of Contents

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

About the Author

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.