{"product_id":"engineering-optimization-9781118936337","title":"Engineering Optimization","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003cb\u003eAn Application-Oriented Introduction to Essential Optimization Concepts and Best Practices\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eOptimization 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. \u003ci\u003eEngineering Optimization\u003c\/i\u003e provides a practically-focused introduction to modern engineering optimization best practices, covering fundamental analytical and numerical techniques throughout each stage of the optimization process.\u003c\/p\u003e \u003cp\u003eAlthough 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.\u003c\/p\u003e \u003cp\u003eExamples, exercises, and homework throughout reinforce the author's do, not stud\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eContents\u003c\/p\u003e \u003cp\u003ePreface xix\u003c\/p\u003e \u003cp\u003eAcknowledgments xxvii\u003c\/p\u003e \u003cp\u003eNomenclature xxix\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xxxvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 1 Introductory Concepts 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Optimization: Introduction and Concepts 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Optimization and Terminology 3\u003c\/p\u003e \u003cp\u003e1.2 Optimization Concepts and Definitions 4\u003c\/p\u003e \u003cp\u003e1.3 Examples 6\u003c\/p\u003e \u003cp\u003e1.4 Terminology Continued 10\u003c\/p\u003e \u003cp\u003e1.4.1 Constraint 10\u003c\/p\u003e \u003cp\u003e1.4.2 Feasible Solutions 10\u003c\/p\u003e \u003cp\u003e1.4.3 Minimize or Maximize 11\u003c\/p\u003e \u003cp\u003e1.4.4 Canonical Form of the Optimization Statement 11\u003c\/p\u003e \u003cp\u003e1.5 Optimization Procedure 12\u003c\/p\u003e \u003cp\u003e1.6 Issues That Shape Optimization Procedures 16\u003c\/p\u003e \u003cp\u003e1.7 Opposing Trends 17\u003c\/p\u003e \u003cp\u003e1.8 Uncertainty 20\u003c\/p\u003e \u003cp\u003e1.9 Over- and Under-specification in Linear Equations 21\u003c\/p\u003e \u003cp\u003e1.10 Over- and Under-specification in Optimization 22\u003c\/p\u003e \u003cp\u003e1.11 Test Functions 23\u003c\/p\u003e \u003cp\u003e1.12 Significant Dates in Optimization 23\u003c\/p\u003e \u003cp\u003e1.13 Iterative Procedures 26\u003c\/p\u003e \u003cp\u003e1.14 Takeaway 27\u003c\/p\u003e \u003cp\u003e1.15 Exercises 27\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Optimization Application Diversity and Complexity 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Optimization 33\u003c\/p\u003e \u003cp\u003e2.2 Nonlinearity 33\u003c\/p\u003e \u003cp\u003e2.3 Min, Max, Min–Max, Max–Min, … 34\u003c\/p\u003e \u003cp\u003e2.4 Integers and Other Discretization 35\u003c\/p\u003e \u003cp\u003e2.5 Conditionals and Discontinuities: Cliffs Ridges\/Valleys 36\u003c\/p\u003e \u003cp\u003e2.6 Procedures, Not Equations 37\u003c\/p\u003e \u003cp\u003e2.7 Static and Dynamic Models 38\u003c\/p\u003e \u003cp\u003e2.8 Path Integrals 38\u003c\/p\u003e \u003cp\u003e2.9 Economic Optimization and Other Nonadditive Cost Functions 38\u003c\/p\u003e \u003cp\u003e2.10 Reliability 39\u003c\/p\u003e \u003cp\u003e2.11 Regression 40\u003c\/p\u003e \u003cp\u003e2.12 Deterministic and Stochastic 42\u003c\/p\u003e \u003cp\u003e2.13 Experimental w.r.t. Modeled OF 43\u003c\/p\u003e \u003cp\u003e2.14 Single and Multiple Optima 44\u003c\/p\u003e \u003cp\u003e2.15 Saddle Points 45\u003c\/p\u003e \u003cp\u003e2.16 Inflections 46\u003c\/p\u003e \u003cp\u003e2.17 Continuum and Discontinuous DVs 47\u003c\/p\u003e \u003cp\u003e2.18 Continuum and Discontinuous Models 47\u003c\/p\u003e \u003cp\u003e2.19 Constraints and Penalty Functions 48\u003c\/p\u003e \u003cp\u003e2.20 Ranks and Categorization: Discontinuous OFs 50\u003c\/p\u003e \u003cp\u003e2.21 Underspecified OFs 51\u003c\/p\u003e \u003cp\u003e2.22 Takeaway 51\u003c\/p\u003e \u003cp\u003e2.23 Exercises 51\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Validation: Knowing That the Answer Is Right 53\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Introduction 53\u003c\/p\u003e \u003cp\u003e3.2 Validation 53\u003c\/p\u003e \u003cp\u003e3.3 Advice on Becoming Proficient 55\u003c\/p\u003e \u003cp\u003e3.4 Takeaway 56\u003c\/p\u003e \u003cp\u003e3.5 Exercises 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 2 Univariate Search Techniques 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Univariate (Single DV) Search Techniques 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Univariate (Single DV) 61\u003c\/p\u003e \u003cp\u003e4.2 Analytical Method of Optimization 62\u003c\/p\u003e \u003cp\u003e4.2.1 Issues with the Analytical Approach 63\u003c\/p\u003e \u003cp\u003e4.3 Numerical Iterative Procedures 64\u003c\/p\u003e \u003cp\u003e4.3.1 Newton’s Methods 64\u003c\/p\u003e \u003cp\u003e4.3.2 Successive Quadratic (A Surrogate Model or Approximating Model Method) 68\u003c\/p\u003e \u003cp\u003e4.4 Direct Search Approaches 70\u003c\/p\u003e \u003cp\u003e4.4.1 Bisection Method 70\u003c\/p\u003e \u003cp\u003e4.4.2 Golden Section Method 72\u003c\/p\u003e \u003cp\u003e4.4.3 Perspective at This Point 74\u003c\/p\u003e \u003cp\u003e4.4.4 Heuristic Direct Search 74\u003c\/p\u003e \u003cp\u003e4.4.5 Leapfrogging 76\u003c\/p\u003e \u003cp\u003e4.4.6 LF for Stochastic Functions 79\u003c\/p\u003e \u003cp\u003e4.5 Perspectives on Univariate Search Methods 82\u003c\/p\u003e \u003cp\u003e4.6 Evaluating Optimizers 85\u003c\/p\u003e \u003cp\u003e4.7 Summary of Techniques 85\u003c\/p\u003e \u003cp\u003e4.7.1 Analytical Method 86\u003c\/p\u003e \u003cp\u003e4.7.2 Newton’s (and Variants Like Secant) 86\u003c\/p\u003e \u003cp\u003e4.7.3 Successive Quadratic 86\u003c\/p\u003e \u003cp\u003e4.7.4 Golden Section Method 86\u003c\/p\u003e \u003cp\u003e4.7.5 Heuristic Direct 87\u003c\/p\u003e \u003cp\u003e4.7.6 Leapfrogging 87\u003c\/p\u003e \u003cp\u003e4.8 Takeaway 87\u003c\/p\u003e \u003cp\u003e4.9 Exercises 88\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Path Analysis 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 93\u003c\/p\u003e \u003cp\u003e5.2 Path Examples 93\u003c\/p\u003e \u003cp\u003e5.3 Perspective About Variables 96\u003c\/p\u003e \u003cp\u003e5.4 Path Distance Integral 97\u003c\/p\u003e \u003cp\u003e5.5 Accumulation along a Path 99\u003c\/p\u003e \u003cp\u003e5.6 Slope along a Path 101\u003c\/p\u003e \u003cp\u003e5.7 Parametric Path Notation 103\u003c\/p\u003e \u003cp\u003e5.8 Takeaway 104\u003c\/p\u003e \u003cp\u003e5.9 Exercises 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Stopping and Convergence Criteria: 1-D Applications 107\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Stopping versus Convergence Criteria 107\u003c\/p\u003e \u003cp\u003e6.2 Determining Convergence 107\u003c\/p\u003e \u003cp\u003e6.2.1 Threshold on the OF 108\u003c\/p\u003e \u003cp\u003e6.2.2 Threshold on the Change in the OF 108\u003c\/p\u003e \u003cp\u003e6.2.3 Threshold on the Change in the DV 108\u003c\/p\u003e \u003cp\u003e6.2.4 Threshold on the Relative Change in the DV 109\u003c\/p\u003e \u003cp\u003e6.2.5 Threshold on the Relative Change in the OF 109\u003c\/p\u003e \u003cp\u003e6.2.6 Threshold on the Impact of the DV on the OF 109\u003c\/p\u003e \u003cp\u003e6.2.7 Convergence Based on Uncertainty Caused by the Givens 109\u003c\/p\u003e \u003cp\u003e6.2.8 Multiplayer Range 110\u003c\/p\u003e \u003cp\u003e6.2.9 Steady-State Convergence 110\u003c\/p\u003e \u003cp\u003e6.3 Combinations of Convergence Criteria 111\u003c\/p\u003e \u003cp\u003e6.4 Choosing Convergence Threshold Values 112\u003c\/p\u003e \u003cp\u003e6.5 Precision 112\u003c\/p\u003e \u003cp\u003e6.6 Other Convergence Criteria 113\u003c\/p\u003e \u003cp\u003e6.7 Stopping Criteria to End a Futile Search 113\u003c\/p\u003e \u003cp\u003e6.7.1 N Iteration Threshold 114\u003c\/p\u003e \u003cp\u003e6.7.2 Execution Error 114\u003c\/p\u003e \u003cp\u003e6.7.3 Constraint Violation 114\u003c\/p\u003e \u003cp\u003e6.8 Choices! 114\u003c\/p\u003e \u003cp\u003e6.9 Takeaway 114\u003c\/p\u003e \u003cp\u003e6.10 Exercises 115\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 3 Multivariate Search Techniques 117\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Multidimension Application Introduction and the Gradient 119\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Introduction 119\u003c\/p\u003e \u003cp\u003e7.2 Illustration of Surface and Terms 122\u003c\/p\u003e \u003cp\u003e7.3 Some Surface Analysis 123\u003c\/p\u003e \u003cp\u003e7.4 Parametric Notation 128\u003c\/p\u003e \u003cp\u003e7.5 Extension to Higher Dimension 130\u003c\/p\u003e \u003cp\u003e7.6 Takeaway 131\u003c\/p\u003e \u003cp\u003e7.7 Exercises 131\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Elementary Gradient-Based Optimizers: CSLS and ISD 135\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 135\u003c\/p\u003e \u003cp\u003e8.2 Cauchy’s Sequential Line Search 135\u003c\/p\u003e \u003cp\u003e8.2.1 CSLS with Successive Quadratic 137\u003c\/p\u003e \u003cp\u003e8.2.2 CSLS with Newton\/Secant 138\u003c\/p\u003e \u003cp\u003e8.2.3 CSLS with Golden Section 138\u003c\/p\u003e \u003cp\u003e8.2.4 CSLS with Leapfrogging 138\u003c\/p\u003e \u003cp\u003e8.2.5 CSLS with Heuristic Direct Search 139\u003c\/p\u003e \u003cp\u003e8.2.6 CSLS Commentary 139\u003c\/p\u003e \u003cp\u003e8.2.7 CSLS Pseudocode 140\u003c\/p\u003e \u003cp\u003e8.2.8 VBA Code for a 2-DV Application 141\u003c\/p\u003e \u003cp\u003e8.3 Incremental Steepest Descent 144\u003c\/p\u003e \u003cp\u003e8.3.1 Pseudocode for the ISD Method 144\u003c\/p\u003e \u003cp\u003e8.3.2 Enhanced ISD 145\u003c\/p\u003e \u003cp\u003e8.3.3 ISD Code 148\u003c\/p\u003e \u003cp\u003e8.4 Takeaway 149\u003c\/p\u003e \u003cp\u003e8.5 Exercises 149\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Second-Order Model-Based Optimizers: SQ and NR 155\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Introduction 155\u003c\/p\u003e \u003cp\u003e9.2 Successive Quadratic 155\u003c\/p\u003e \u003cp\u003e9.2.1 Multivariable SQ 156\u003c\/p\u003e \u003cp\u003e9.2.2 SQ Pseudocode 159\u003c\/p\u003e \u003cp\u003e9.3 Newton–Raphson 159\u003c\/p\u003e \u003cp\u003e9.3.1 NR Pseudocode 162\u003c\/p\u003e \u003cp\u003e9.3.2 Attenuate NR 163\u003c\/p\u003e \u003cp\u003e9.3.3 Quasi-Newton 166\u003c\/p\u003e \u003cp\u003e9.4 Perspective on CSLS, ISD, SQ, and NR 168\u003c\/p\u003e \u003cp\u003e9.5 Choosing Step Size for Numerical Estimate of Derivatives 169\u003c\/p\u003e \u003cp\u003e9.6 Takeaway 170\u003c\/p\u003e \u003cp\u003e9.7 Exercises 170\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Gradient-Based Optimizer Solutions: LM, RLM, CG, BFGS, RG, and GRG 173\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Introduction 173\u003c\/p\u003e \u003cp\u003e10.2 Levenberg–Marquardt (LM) 173\u003c\/p\u003e \u003cp\u003e10.2.1 LM VBA Code for a 2-DV Case 175\u003c\/p\u003e \u003cp\u003e10.2.2 Modified LM (RLM) 176\u003c\/p\u003e \u003cp\u003e10.2.3 RLM Pseudocode 177\u003c\/p\u003e \u003cp\u003e10.2.4 RLM VBA Code for a 2-DV Case 178\u003c\/p\u003e \u003cp\u003e10.3 Scaled Variables 180\u003c\/p\u003e \u003cp\u003e10.4 Conjugate Gradient (CG) 182\u003c\/p\u003e \u003cp\u003e10.5 Broyden–Fletcher–Goldfarb–Shanno (BFGS) 183\u003c\/p\u003e \u003cp\u003e10.6 Generalized Reduced Gradient (GRG) 184\u003c\/p\u003e \u003cp\u003e10.7 Takeaway 186\u003c\/p\u003e \u003cp\u003e10.8 Exercises 186\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Direct Search Techniques 187\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Introduction 187\u003c\/p\u003e \u003cp\u003e11.2 Cyclic Heuristic Direct (CHD) Search 188\u003c\/p\u003e \u003cp\u003e11.2.1 CHD Pseudocode 188\u003c\/p\u003e \u003cp\u003e11.2.2 CHD VBA Code 189\u003c\/p\u003e \u003cp\u003e11.3 Hooke–Jeeves (HJ) 192\u003c\/p\u003e \u003cp\u003e11.3.1 HJ Code in VBA 195\u003c\/p\u003e \u003cp\u003e11.4 Compare and Contrast CHD and HJ Features: A Summary 197\u003c\/p\u003e \u003cp\u003e11.5 Nelder–Mead (NM) Simplex: Spendley, Hext, and Himsworth 199\u003c\/p\u003e \u003cp\u003e11.6 Multiplayer Direct Search Algorithms 200\u003c\/p\u003e \u003cp\u003e11.7 Leapfrogging 201\u003c\/p\u003e \u003cp\u003e11.7.1 Convergence Criteria 208\u003c\/p\u003e \u003cp\u003e11.7.2 Stochastic Surfaces 209\u003c\/p\u003e \u003cp\u003e11.7.3 Summary 209\u003c\/p\u003e \u003cp\u003e11.8 Particle Swarm Optimization 209\u003c\/p\u003e \u003cp\u003e11.8.1 Individual Particle Behavior 210\u003c\/p\u003e \u003cp\u003e11.8.2 Particle Swarm 213\u003c\/p\u003e \u003cp\u003e11.8.3 PSO Equation Analysis 215\u003c\/p\u003e \u003cp\u003e11.9 Complex Method (CM) 216\u003c\/p\u003e \u003cp\u003e11.10 A Brief Comparison 217\u003c\/p\u003e \u003cp\u003e11.11 Takeaway 218\u003c\/p\u003e \u003cp\u003e11.12 Exercises 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Linear Programming 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Introduction 223\u003c\/p\u003e \u003cp\u003e12.2 Visual Representation and Concepts 225\u003c\/p\u003e \u003cp\u003e12.3 Basic LP Procedure 228\u003c\/p\u003e \u003cp\u003e12.4 Canonical LP Statement 228\u003c\/p\u003e \u003cp\u003e12.5 LP Algorithm 229\u003c\/p\u003e \u003cp\u003e12.6 Simplex Tableau 230\u003c\/p\u003e \u003cp\u003e12.7 Takeaway 231\u003c\/p\u003e \u003cp\u003e12.8 Exercises 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Dynamic Programming 233\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Introduction 233\u003c\/p\u003e \u003cp\u003e13.2 Conditions 236\u003c\/p\u003e \u003cp\u003e13.3 DP Concept 237\u003c\/p\u003e \u003cp\u003e13.4 Some Calculation Tips 240\u003c\/p\u003e \u003cp\u003e13.5 Takeaway 241\u003c\/p\u003e \u003cp\u003e13.6 Exercises 241\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Genetic Algorithms and Evolutionary Computation 243\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Introduction 243\u003c\/p\u003e \u003cp\u003e14.2 GA Procedures 243\u003c\/p\u003e \u003cp\u003e14.3 Fitness of Selection 245\u003c\/p\u003e \u003cp\u003e14.4 Takeaway 250\u003c\/p\u003e \u003cp\u003e14.5 Exercises 250\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Intuitive Optimization 253\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Introduction 253\u003c\/p\u003e \u003cp\u003e15.2 Levels 254\u003c\/p\u003e \u003cp\u003e15.3 Takeaway 254\u003c\/p\u003e \u003cp\u003e15.4 Exercises 254\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Surface Analysis II 257\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Introduction 257\u003c\/p\u003e \u003cp\u003e16.2 Maximize Is Equivalent to Minimize the Negative 257\u003c\/p\u003e \u003cp\u003e16.3 Scaling by a Positive Number Does Not Change DV∗ 258\u003c\/p\u003e \u003cp\u003e16.4 Scaled and Translated OFs Do Not Change DV∗ 258\u003c\/p\u003e \u003cp\u003e16.5 Monotonic Function Transformation Does Not Change DV∗ 258\u003c\/p\u003e \u003cp\u003e16.6 Impact on Search Path or NOFE 261\u003c\/p\u003e \u003cp\u003e16.7 Inequality Constraints 263\u003c\/p\u003e \u003cp\u003e16.8 Transforming DVs 263\u003c\/p\u003e \u003cp\u003e16.9 Takeaway 263\u003c\/p\u003e \u003cp\u003e16.10 Exercises 263\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Convergence Criteria 2: N-D Applications 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Introduction 265\u003c\/p\u003e \u003cp\u003e17.2 Defining an Iteration 265\u003c\/p\u003e \u003cp\u003e17.3 Criteria for Single TS Deterministic Procedures 266\u003c\/p\u003e \u003cp\u003e17.4 Criteria for Multiplayer Deterministic Procedures 267\u003c\/p\u003e \u003cp\u003e17.5 Stochastic Applications 268\u003c\/p\u003e \u003cp\u003e17.7 Takeaway 269\u003c\/p\u003e \u003cp\u003e17.8 Exercises 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Enhancements to Optimizers 271\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Introduction 271\u003c\/p\u003e \u003cp\u003e18.2 Criteria for Replicate Trials 271\u003c\/p\u003e \u003cp\u003e18.3 Quasi-Newton 274\u003c\/p\u003e \u003cp\u003e18.4 Coarse–Fine Sequence 275\u003c\/p\u003e \u003cp\u003e18.5 Number of Players 275\u003c\/p\u003e \u003cp\u003e18.6 Search Range Adjustment 276\u003c\/p\u003e \u003cp\u003e18.7 Adjustment of Optimizer Coefficient Values or Options in Process 276\u003c\/p\u003e \u003cp\u003e18.8 Initialization Range 277\u003c\/p\u003e \u003cp\u003e18.9 OF and DV Transformations 277\u003c\/p\u003e \u003cp\u003e18.10 Takeaway 278\u003c\/p\u003e \u003cp\u003e18.11 Exercises 278\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 4 Developing Your Application Statements 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Scaled Variables and Dimensional Consistency 281\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Introduction 281\u003c\/p\u003e \u003cp\u003e19.2 A Scaled Variable Approach 283\u003c\/p\u003e \u003cp\u003e19.3 Sampling of Issues with Primitive Variables 283\u003c\/p\u003e \u003cp\u003e19.4 Linear Scaling Options 285\u003c\/p\u003e \u003cp\u003e19.5 Nonlinear Scaling 286\u003c\/p\u003e \u003cp\u003e19.6 Takeaway 287\u003c\/p\u003e \u003cp\u003e19.7 Exercises 287\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Economic Optimization 289\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Introduction 289\u003c\/p\u003e \u003cp\u003e20.2 Annual Cash Flow 290\u003c\/p\u003e \u003cp\u003e20.3 Including Risk as an Annual Expense 291\u003c\/p\u003e \u003cp\u003e20.4 Capital 293\u003c\/p\u003e \u003cp\u003e20.5 Combining Capital and Nominal Annual Cash Flow 293\u003c\/p\u003e \u003cp\u003e20.6 Combining Time Value and Schedule of Capital and Annual Cash Flow 296\u003c\/p\u003e \u003cp\u003e20.7 Present Value 297\u003c\/p\u003e \u003cp\u003e20.8 Including Uncertainty 298\u003c\/p\u003e \u003cp\u003e20.8.1 Uncertainty Models 301\u003c\/p\u003e \u003cp\u003e20.8.2 Methods to Include Uncertainty in an Optimization 303\u003c\/p\u003e \u003cp\u003e20.9 Takeaway 304\u003c\/p\u003e \u003cp\u003e20.10 Exercises 304\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Multiple OF and Constraint Applications 305\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 Introduction 305\u003c\/p\u003e \u003cp\u003e21.2 Solution 1: Additive Combinations of the Functions 306\u003c\/p\u003e \u003cp\u003e21.2.1 Solution 1a: Classic Weighting Factors 307\u003c\/p\u003e \u003cp\u003e21.2.2 Solution 1b: Equal Concern Weighting 307\u003c\/p\u003e \u003cp\u003e21.2.3 Solution 1c: Nonlinear Weighting 309\u003c\/p\u003e \u003cp\u003e21.3 Solution 2: Nonadditive OF Combinations 311\u003c\/p\u003e \u003cp\u003e21.4 Solution 3: Pareto Optimal 311\u003c\/p\u003e \u003cp\u003e21.5 Takeaway 316\u003c\/p\u003e \u003cp\u003e21.6 Exercises 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e22 Constraints 319\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e22.1 Introduction 319\u003c\/p\u003e \u003cp\u003e22.2 Equality Constraints 320\u003c\/p\u003e \u003cp\u003e22.2.1 Explicit Equality Constraints 320\u003c\/p\u003e \u003cp\u003e22.2.2 Implicit Equality Constraints 321\u003c\/p\u003e \u003cp\u003e22.3 Inequality Constraints 321\u003c\/p\u003e \u003cp\u003e22.3.1 Penalty Function: Discontinuous 323\u003c\/p\u003e \u003cp\u003e22.3.2 Penalty Function: Soft Constraint 323\u003c\/p\u003e \u003cp\u003e22.3.3 Inequality Constraints: Slack and Surplus Variables 325\u003c\/p\u003e \u003cp\u003e22.4 Constraints: Pass\/Fail Categories 329\u003c\/p\u003e \u003cp\u003e22.5 Hard Constraints Can Block Progress 330\u003c\/p\u003e \u003cp\u003e22.6 Advice 331\u003c\/p\u003e \u003cp\u003e22.7 Constraint-Equivalent Features 332\u003c\/p\u003e \u003cp\u003e22.8 Takeaway 332\u003c\/p\u003e \u003cp\u003e22.9 Exercises 332\u003c\/p\u003e \u003cp\u003e\u003cb\u003e23 Multiple Optima 335\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e23.1 Introduction 335\u003c\/p\u003e \u003cp\u003e23.2 Solution: Multiple Starts 337\u003c\/p\u003e \u003cp\u003e23.2.1 A Priori Method 340\u003c\/p\u003e \u003cp\u003e23.2.2 A Posteriori Method 342\u003c\/p\u003e \u003cp\u003e23.2.3 Snyman and Fatti Criterion A Posteriori Method 345\u003c\/p\u003e \u003cp\u003e23.3 Other Options 348\u003c\/p\u003e \u003cp\u003e23.4 Takeaway 349\u003c\/p\u003e \u003cp\u003e23.5 Exercises 350\u003c\/p\u003e \u003cp\u003e\u003cb\u003e24 Stochastic Objective Functions 353\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e24.1 Introduction 353\u003c\/p\u003e \u003cp\u003e24.2 Method Summary for Optimizing Stochastic Functions 356\u003c\/p\u003e \u003cp\u003e24.2.1 Step 1: Replicate the Apparent Best Player 356\u003c\/p\u003e \u003cp\u003e24.2.2 Step 2: Steady-State Detection 357\u003c\/p\u003e \u003cp\u003e24.3 What Value to Report? 358\u003c\/p\u003e \u003cp\u003e24.4 Application Examples 359\u003c\/p\u003e \u003cp\u003e24.4.1 GMC Control of Hot and Cold Mixing 359\u003c\/p\u003e \u003cp\u003e24.4.2 MBC of Hot and Cold Mixing 359\u003c\/p\u003e \u003cp\u003e24.4.3 Batch Reaction Management 359\u003c\/p\u003e \u003cp\u003e24.4.4 Reservoir and Stochastic Boot Print 361\u003c\/p\u003e \u003cp\u003e24.4.5 Optimization Results 362\u003c\/p\u003e \u003cp\u003e24.5 Takeaway 365\u003c\/p\u003e \u003cp\u003e24.6 Exercises 365\u003c\/p\u003e \u003cp\u003e\u003cb\u003e25 Effects of Uncertainty 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e25.1 Introduction 367\u003c\/p\u003e \u003cp\u003e25.2 Sources of Error and Uncertainty 368\u003c\/p\u003e \u003cp\u003e25.3 Significant Digits 370\u003c\/p\u003e \u003cp\u003e25.4 Estimating Uncertainty on Values 371\u003c\/p\u003e \u003cp\u003e25.5 Propagating Uncertainty on DV Values 372\u003c\/p\u003e \u003cp\u003e25.5.1 Analytical Method 373\u003c\/p\u003e \u003cp\u003e25.5.2 Numerical Method 375\u003c\/p\u003e \u003cp\u003e25.6 Implicit Relations 378\u003c\/p\u003e \u003cp\u003e25.7 Estimating Uncertainty in DV∗ and OF∗ 378\u003c\/p\u003e \u003cp\u003e25.8 Takeaway 379\u003c\/p\u003e \u003cp\u003e25.9 Exercises 379\u003c\/p\u003e \u003cp\u003e\u003cb\u003e26 Optimization of Probable Outcomes and Distribution Characteristics 381\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e26.1 Introduction 381\u003c\/p\u003e \u003cp\u003e26.2 The Concept of Modeling Uncertainty 385\u003c\/p\u003e \u003cp\u003e26.3 Stochastic Approach 387\u003c\/p\u003e \u003cp\u003e26.4 Takeaway 389\u003c\/p\u003e \u003cp\u003e26.5 Exercises 389\u003c\/p\u003e \u003cp\u003e\u003cb\u003e27 Discrete and Integer Variables 391\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e27.1 Introduction 391\u003c\/p\u003e \u003cp\u003e27.2 Optimization Solutions 394\u003c\/p\u003e \u003cp\u003e27.2.1 Exhaustive Search 394\u003c\/p\u003e \u003cp\u003e27.2.2 Branch and Bound 394\u003c\/p\u003e \u003cp\u003e27.2.3 Cyclic Heuristic 394\u003c\/p\u003e \u003cp\u003e27.2.4 Leapfrogging or Other Multiplayer Search 395\u003c\/p\u003e \u003cp\u003e27.3 Convergence 395\u003c\/p\u003e \u003cp\u003e27.4 Takeaway 395\u003c\/p\u003e \u003cp\u003e27.5 Exercises 395\u003c\/p\u003e \u003cp\u003e\u003cb\u003e28 Class Variables 397\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e28.1 Introduction 397\u003c\/p\u003e \u003cp\u003e28.2 The Random Keys Method: Sequence 398\u003c\/p\u003e \u003cp\u003e28.3 The Random Keys Method: Dichotomous Variables 400\u003c\/p\u003e \u003cp\u003e28.4 Comments 401\u003c\/p\u003e \u003cp\u003e28.5 Takeaway 401\u003c\/p\u003e \u003cp\u003e28.6 Exercises 401\u003c\/p\u003e \u003cp\u003e\u003cb\u003e29 Regression 403\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e29.1 Introduction 403\u003c\/p\u003e \u003cp\u003e29.2 Perspective 404\u003c\/p\u003e \u003cp\u003e29.3 Least Squares Regression: Traditional View on Linear Model Parameters 404\u003c\/p\u003e \u003cp\u003e29.4 Models Nonlinear in DV 405\u003c\/p\u003e \u003cp\u003e29.4.1 Models with a Delay 407\u003c\/p\u003e \u003cp\u003e29.5 Maximum Likelihood 408\u003c\/p\u003e \u003cp\u003e29.5.1 Akaho’s Method 411\u003c\/p\u003e \u003cp\u003e29.6 Convergence Criterion 416\u003c\/p\u003e \u003cp\u003e29.7 Model Order or Complexity 421\u003c\/p\u003e \u003cp\u003e29.8 Bootstrapping to Reveal Model Uncertainty 425\u003c\/p\u003e \u003cp\u003e29.8.1 Interpretation of Bootstrapping Analysis 428\u003c\/p\u003e \u003cp\u003e29.8.2 Appropriating Bootstrapping 430\u003c\/p\u003e \u003cp\u003e29.9 Perspective 431\u003c\/p\u003e \u003cp\u003e29.10 Takeaway 431\u003c\/p\u003e \u003cp\u003e29.11 Exercises 432\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 5 Perspective on Many Topics 441\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e30 Perspective 443\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e30.1 Introduction 443\u003c\/p\u003e \u003cp\u003e30.2 Classifications 443\u003c\/p\u003e \u003cp\u003e30.3 Elements Associated with Optimization 445\u003c\/p\u003e \u003cp\u003e30.4 Root Finding Is Not Optimization 446\u003c\/p\u003e \u003cp\u003e30.5 Desired Engineering Attributes 446\u003c\/p\u003e \u003cp\u003e30.6 Overview of Optimizers and Attributes 447\u003c\/p\u003e \u003cp\u003e30.6.1 Gradient Based: Cauchy Sequential Line Search, Incremental Steepest Descent, GRG, Etc. 447\u003c\/p\u003e \u003cp\u003e30.6.2 Local Surface Characterization Based: Newton–Raphson, Levenberg–Marquardt, Successive Quadratic, RLM, Quasi-Newton, Etc. 448\u003c\/p\u003e \u003cp\u003e30.6.3 Direct Search with Single Trial Solution: Cyclic Heuristic, Hooke–Jeeves, and Nelder–Mead 448\u003c\/p\u003e \u003cp\u003e30.6.4 Multiplayer Direct Search Optimizers: Leapfrogging, Particle Swarm, and Genetic Algorithms 448\u003c\/p\u003e \u003cp\u003e30.7 Choices 448\u003c\/p\u003e \u003cp\u003e30.8 Variable Classifications 449\u003c\/p\u003e \u003cp\u003e30.8.1 Nominal 449\u003c\/p\u003e \u003cp\u003e30.8.2 Ordinal 450\u003c\/p\u003e \u003cp\u003e30.8.3 Cardinal 450\u003c\/p\u003e \u003cp\u003e30.9 Constraints 451\u003c\/p\u003e \u003cp\u003e30.10 Takeaway 453\u003c\/p\u003e \u003cp\u003e30.11 Exercises 453\u003c\/p\u003e \u003cp\u003e\u003cb\u003e31 Response Surface Aberrations 459\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e31.1 Introduction 459\u003c\/p\u003e \u003cp\u003e31.2 Cliffs (Vertical Walls) 459\u003c\/p\u003e \u003cp\u003e31.3 Sharp Valleys (or Ridges) 459\u003c\/p\u003e \u003cp\u003e31.4 Striations 463\u003c\/p\u003e \u003cp\u003e31.5 Level Spots (Functions 1, 27, 73, 84) 463\u003c\/p\u003e \u003cp\u003e31.6 Hard-to-Find Optimum 466\u003c\/p\u003e \u003cp\u003e31.7 Infeasible Calculations 468\u003c\/p\u003e \u003cp\u003e31.8 Uniform Minimum 468\u003c\/p\u003e \u003cp\u003e31.9 Noise: Stochastic Response 469\u003c\/p\u003e \u003cp\u003e31.10 Multiple Optima 471\u003c\/p\u003e \u003cp\u003e31.11 Takeaway 473\u003c\/p\u003e \u003cp\u003e31.12 Exercises 473\u003c\/p\u003e \u003cp\u003e\u003cb\u003e32 Identifying the Models, OF, DV, Convergence Criteria, and Constraints 475\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e32.1 Introduction 475\u003c\/p\u003e \u003cp\u003e32.2 Evaluate the Results 476\u003c\/p\u003e \u003cp\u003e32.3 Takeaway 482\u003c\/p\u003e \u003cp\u003e32.4 Exercises 482\u003c\/p\u003e \u003cp\u003e\u003cb\u003e33 Evaluating Optimizers 489\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e33.1 Introduction 489\u003c\/p\u003e \u003cp\u003e33.2 Challenges to Optimizers 490\u003c\/p\u003e \u003cp\u003e33.3 Stakeholders 490\u003c\/p\u003e \u003cp\u003e33.4 Metrics of Optimizer Performance 490\u003c\/p\u003e \u003cp\u003e33.5 Designing an Experimental Test 492\u003c\/p\u003e \u003cp\u003e33.6 Takeaway 495\u003c\/p\u003e \u003cp\u003e33.7 Exercises 496\u003c\/p\u003e \u003cp\u003e\u003cb\u003e34 Troubleshooting Optimizers 499\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e34.1 Introduction 499\u003c\/p\u003e \u003cp\u003e34.2 DV Values Do Not Change 499\u003c\/p\u003e \u003cp\u003e34.3 Multiple DV∗ Values for the Same OF∗ Value 499\u003c\/p\u003e \u003cp\u003e34.4 EXE Error 500\u003c\/p\u003e \u003cp\u003e34.5 Extreme Values 500\u003c\/p\u003e \u003cp\u003e34.6 DV∗ Is Dependent on Convergence Threshold 500\u003c\/p\u003e \u003cp\u003e34.7 OF∗ Is Irreproducible 501\u003c\/p\u003e \u003cp\u003e34.8 Concern over Results 501\u003c\/p\u003e \u003cp\u003e34.9 CDF Features 501\u003c\/p\u003e \u003cp\u003e34.10 Parameter Correlation 502\u003c\/p\u003e \u003cp\u003e34.11 Multiple Equivalent Solutions 504\u003c\/p\u003e \u003cp\u003e34.12 Takeaway 504\u003c\/p\u003e \u003cp\u003e34.13 Exercises 504\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 6 Analysis of Leapfrogging Optimization 505\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e35 Analysis of Leapfrogging 507\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e35.1 Introduction 507\u003c\/p\u003e \u003cp\u003e35.2 Balance in an Optimizer 508\u003c\/p\u003e \u003cp\u003e35.3 Number of Initializations to be Confident That the Best Will Draw All Others to the Global Optimum 510\u003c\/p\u003e \u003cp\u003e35.3.1 Methodology 511\u003c\/p\u003e \u003cp\u003e35.3.2 Experimental 512\u003c\/p\u003e \u003cp\u003e35.3.3 Results 513\u003c\/p\u003e \u003cp\u003e35.4 Leap-To Window Amplification Analysis 515\u003c\/p\u003e \u003cp\u003e35.5 Analysis of α and M to Prevent Convergence on the Side of a Hill 519\u003c\/p\u003e \u003cp\u003e35.6 Analysis of α and M to Minimize NOFE 521\u003c\/p\u003e \u003cp\u003e35.7 Probability Distribution of Leap-Overs 522\u003c\/p\u003e \u003cp\u003e35.7.1 Data 526\u003c\/p\u003e \u003cp\u003e35.8 Takeaway 527\u003c\/p\u003e \u003cp\u003e35.9 Exercises 528\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 7 Case Studies 529\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e36 Case Study 1: Economic Optimization of a Pipe System 531\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e36.1 Process and Analysis 531\u003c\/p\u003e \u003cp\u003e36.1.1 Deterministic Continuum Model 531\u003c\/p\u003e \u003cp\u003e36.1.2 Deterministic Discontinuous Model 534\u003c\/p\u003e \u003cp\u003e36.1.3 Stochastic Discontinuous Model 535\u003c\/p\u003e \u003cp\u003e36.2 Exercises 536\u003c\/p\u003e \u003cp\u003e\u003cb\u003e37 Case Study 2: Queuing Study 539\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e37.1 The Process and Analysis 539\u003c\/p\u003e \u003cp\u003e37.2 Exercises 541\u003c\/p\u003e \u003cp\u003e\u003cb\u003e38 Case Study 3: Retirement Study 543\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e38.1 The Process and Analysis 543\u003c\/p\u003e \u003cp\u003e38.2 Exercises 550\u003c\/p\u003e \u003cp\u003e\u003cb\u003e39 Case Study 4: A Goddard Rocket Study 551\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e39.1 The Process and Analysis 551\u003c\/p\u003e \u003cp\u003e39.2 Pre-Assignment Note 554\u003c\/p\u003e \u003cp\u003e39.3 Exercises 555\u003c\/p\u003e \u003cp\u003e\u003cb\u003e40 Case Study 5: Reservoir 557\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e40.1 The Process and Analysis 557\u003c\/p\u003e \u003cp\u003e40.2 Exercises 559\u003c\/p\u003e \u003cp\u003e\u003cb\u003e41 Case Study 6: Area Coverage 561\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e41.1 Description and Analysis 561\u003c\/p\u003e \u003cp\u003e41.2 Exercises 562\u003c\/p\u003e \u003cp\u003e\u003cb\u003e42 Case Study 7: Approximating Series Solution to an ODE 565\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e42.1 Concepts and Analysis 565\u003c\/p\u003e \u003cp\u003e42.2 Exercises 568\u003c\/p\u003e \u003cp\u003e\u003cb\u003e43 Case Study 8: Horizontal Tank Vapor–Liquid Separator 571\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e43.1 Description and Analysis 571\u003c\/p\u003e \u003cp\u003e43.2 Exercises 576\u003c\/p\u003e \u003cp\u003e\u003cb\u003e44 Case Study 9: In Vitro Fertilization 579\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e44.1 Description and Analysis 579\u003c\/p\u003e \u003cp\u003e44.2 Exercises 583\u003c\/p\u003e \u003cp\u003e\u003cb\u003e45 Case Study 10: Data Reconciliation 585\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e45.1 Description and Analysis 585\u003c\/p\u003e \u003cp\u003e45.2 Exercises 588\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSection 8 Appendices 591\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eAppendix A Mathematical Concepts and Procedures 593\u003c\/p\u003e \u003cp\u003eAppendix B Root Finding 605\u003c\/p\u003e \u003cp\u003eAppendix C Gaussian Elimination 611\u003c\/p\u003e \u003cp\u003eAppendix D Steady-State Identification in Noisy Signals 621\u003c\/p\u003e \u003cp\u003eAppendix E Optimization Challenge Problems (2-D and Single OF) 635\u003c\/p\u003e \u003cp\u003eAppendix F Brief on VBA Programming: Excel in Office 2013 709\u003c\/p\u003e \u003cp\u003eSection 9 References and Index 717\u003c\/p\u003e \u003cp\u003eReferences and Additional Resources 719\u003c\/p\u003e \u003cp\u003eIndex 723\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406950900055,"sku":"9781118936337","price":100.65,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118936337.jpg?v=1730497666","url":"https:\/\/bookcurl.com\/products\/engineering-optimization-9781118936337","provider":"Book Curl","version":"1.0","type":"link"}