Engineering optimization : applications, methods and analysis /: applications, methods and analysis. (2018)

• Record Type: Book
• Further Information: Note: R. Russell Rhinehart.
• Authors: Rhinehart, R. Russell, 1946-
• Contents: 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 5.7 Parametric Path Notation 103 5.8 Takeaway 104 5.9 Exercises 104 6 Stopping and Convergence Criteria: 1-D Applications 107 6.1 Stopping versus Convergence Criteria 107 6.2 Determining Convergence 107 6.2.1 Threshold on the OF 108 6.2.2 Threshold on the Change in the OF 108 6.2.3 Threshold on the Change in the DV 108 6.2.4 Threshold on the Relative Change in the DV 109 6.2.5 Threshold on the Relative Change in the OF 109 6.2.6 Threshold on the Impact of the DV on the OF 109 6.2.7 Convergence Based on Uncertainty Caused by the Givens 109 6.2.8 Multiplayer Range 110 6.2.9 Steady-State Convergence 110 6.3 Combinations of Convergence Criteria 111 6.4 Choosing Convergence Threshold Values 112 6.5 Precision 112 6.6 Other Convergence Criteria 113 6.7 Stopping Criteria to End a Futile Search 113 6.7.1 N Iteration Threshold 114 6.7.2 Execution Error 114 6.7.3 Constraint Violation 114 6.8 Choices! 114 6.9 Takeaway 114 6.10 Exercises 115 Section 3 Multivariate Search Techniques 117 7 Multidimension Application Introduction and the Gradient 119 7.1 Introduction 119 7.2 Illustration of Surface and Terms 122 7.3 Some Surface Analysis 123 7.4 Parametric Notation 128 7.5 Extension to Higher Dimension 130 7.6 Takeaway 131 7.7 Exercises 131 8 Elementary Gradient-Based Optimizers: CSLS and ISD 135 8.1 Introduction 135 8.2 Cauchy’s Sequential Line Search 135 8.2.1 CSLS with Successive Quadratic 137 8.2.2 CSLS with Newton/Secant 138 8.2.3 CSLS with Golden Section 138 8.2.4 CSLS with Leapfrogging 138 8.2.5 CSLS with Heuristic Direct Search 139 8.2.6 CSLS Commentary 139 8.2.7 CSLS Pseudocode 140 8.2.8 VBA Code for a 2-DV Application 141 8.3 Incremental Steepest Descent 144 8.3.1 Pseudocode for the ISD Method 144 8.3.2 Enhanced ISD 145 8.3.3 ISD Code 148 8.4 Takeaway 149 8.5 Exercises 149 9 Second-Order Model-Based Optimizers: SQ and NR 155 9.1 Introduction 155 9.2 Successive Quadratic 155 9.2.1 Multivariable SQ 156 9.2.2 SQ Pseudocode 159 9.3 Newton–Raphson 159 9.3.1 NR Pseudocode 162 9.3.2 Attenuate NR 163 9.3.3 Quasi-Newton 166 9.4 Perspective on CSLS, ISD, SQ, and NR 168 9.5 Choosing Step Size for Numerical Estimate of Derivatives 169 9.6 Takeaway 170 9.7 Exercises 170 10 Gradient-Based Optimizer Solutions: LM, RLM, CG, BFGS, RG, and GRG 173 10.1 Introduction 173 10.2 Levenberg–Marquardt (LM) 173 10.2.1 LM VBA Code for a 2-DV Case 175 10.2.2 Modified LM (RLM) 176 10.2.3 RLM Pseudocode 177 10.2.4 RLM VBA Code for a 2-DV Case 178 10.3 Scaled Variables 180 10.4 Conjugate Gradient (CG) 182 10.5 Broyden–Fletcher–Goldfarb–Shanno (BFGS) 183 10.6 Generalized Reduced Gradient (GRG) 184 10.7 Takeaway 186 10.8 Exercises 186 11 Direct Search Techniques 187 11.1 Introduction 187 11.2 Cyclic Heuristic Direct (CHD) Search 188 11.2.1 CHD Pseudocode 188 11.2.2 CHD VBA Code 189 11.3 Hooke–Jeeves (HJ) 192 11.3.1 HJ Code in VBA 195 11.4 Compare and Contrast CHD and HJ Features: A Summary 197 11.5 Nelder–Mead (NM) Simplex: Spendley, Hext, and Himsworth 199 11.6 Multiplayer Direct Search Algorithms 200 11.7 Leapfrogging 201 11.7.1 Convergence Criteria 208 11.7.2 Stochastic Surfaces 209 11.7.3 Summary 209 11.8 Particle Swarm Optimization 209 11.8.1 Individual Particle Behavior 210 11.8.2 Particle Swarm 213 11.8.3 PSO Equation Analysis 215 11.9 Complex Method (CM) 216 11.10 A Brief Comparison 217
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2018
• Extent: 1 online resource
• Subjects: 620.0015196; Engineering -- Mathematical models; Mathematical optimization
• Languages: English
• ISBNs: 9781118936320; 9781118936313
• Related ISBNs: 9781118936337
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.