[eBook Code] Engineering Optimization (eBook Code, 5th)

· 제목 : [eBook Code] Engineering Optimization (eBook Code, 5th) (Theory and Practice)
· 분류 : 외국도서 > 기술공학 > 기술공학 > 기계공학
· ISBN : 9781119454793
· 쪽수 : 832쪽

Preface xvii

Acknowledgment xxi

About the Author xxiii

About the Companion Website xxv

1 Introduction to Optimization 1

1.1 Introduction 1

1.2 Historical Development 3

1.2.1 Modern Methods of Optimization 4

1.3 Engineering Applications of Optimization 5

1.4 Statement of an Optimization Problem 6

1.4.1 Design Vector 6

1.4.2 Design Constraints 7

1.4.3 Constraint Surface 7

1.4.4 Objective Function 8

1.4.5 Objective Function Surfaces 9

1.5 Classification of Optimization Problems 14

1.5.1 Classification Based on the Existence of Constraints 14

1.5.2 Classification Based on the Nature of the Design Variables 14

1.5.3 Classification Based on the Physical Structure of the Problem 15

1.5.4 Classification Based on the Nature of the Equations Involved 18

1.5.5 Classification Based on the Permissible Values of the Design Variables 27

1.5.6 Classification Based on the Deterministic Nature of the Variables 28

1.5.7 Classification Based on the Separability of the Functions 29

1.5.8 Classification Based on the Number of Objective Functions 31

1.6 Optimization Techniques 33

1.7 Engineering Optimization Literature 34

1.8 Solutions Using MATLAB 34

References and Bibliography 34

Review Questions 40

Problems 41

2 Classical Optimization Techniques 57

2.1 Introduction 57

2.2 Single-Variable Optimization 57

2.3 Multivariable Optimization with no Constraints 62

2.3.1 Definition: rth Differential of f 62

2.3.2 Semidefinite Case 67

2.3.3 Saddle Point 67

2.4 Multivariable Optimization with Equality Constraints 69

2.4.1 Solution by Direct Substitution 69

2.4.2 Solution by the Method of Constrained Variation 71

2.4.3 Solution by the Method of Lagrange Multipliers 77

2.5 Multivariable Optimization with Inequality Constraints 85

2.5.1 Kuhn–Tucker Conditions 90

2.5.2 Constraint Qualification 90

2.6 Convex Programming Problem 96

References and Bibliography 96

Review Questions 97

Problems 98

3 Linear Programming I: Simplex Method 109

3.1 Introduction 109

3.2 Applications of Linear Programming 110

3.3 Standard form of a Linear Programming Problem 112

3.3.1 Scalar Form 112

3.3.2 Matrix Form 112

3.4 Geometry of Linear Programming Problems 114

3.5 Definitions and Theorems 117

3.5.1 Definitions 117

3.5.2 Theorems 120

3.6 Solution of a System of Linear Simultaneous Equations 122

3.7 Pivotal Reduction of a General System of Equations 123

3.8 Motivation of the Simplex Method 127

3.9 Simplex Algorithm 128

3.9.1 Identifying an Optimal Point 128

3.9.2 Improving a Nonoptimal Basic Feasible Solution 129

3.10 Two Phases of the Simplex Method 137

3.11 Solutions Using MATLAB 143

References and Bibliography 143

Review Questions 143

Problems 145

4 Linear Programming II: Additional Topics and Extensions 159

4.1 Introduction 159

4.2 Revised Simplex Method 159

4.3 Duality in Linear Programming 173

4.3.1 Symmetric Primal–Dual Relations 173

4.3.2 General Primal–Dual Relations 174

4.3.3 Primal–Dual Relations when the Primal Is in Standard Form 175

4.3.4 Duality Theorems 176

4.3.5 Dual Simplex Method 176

4.4 Decomposition Principle 180

4.5 Sensitivity or Postoptimality Analysis 187

4.5.1 Changes in the Right-Hand-Side Constants b_i 188

4.5.2 Changes in the Cost Coefficients c_j 192

4.5.3 Addition of New Variables 194

4.5.4 Changes in the Constraint Coefficients a_ij 195

4.5.5 Addition of Constraints 197

4.6 Transportation Problem 199

4.7 Karmarkar’s Interior Method 202

4.7.1 Statement of the Problem 203

4.7.2 Conversion of an LP Problem into the Required Form 203

4.7.3 Algorithm 205

4.8 Quadratic Programming 208

4.9 Solutions Using Matlab 214

References and Bibliography 214

Review Questions 215

Problems 216

5 Nonlinear Programming I: One-Dimensional Minimization Methods 225

5.1 Introduction 225

5.2 Unimodal Function 230

Elimination Methods 231

5.3 Unrestricted Search 231

5.3.1 Search with Fixed Step Size 231

5.3.2 Search with Accelerated Step Size 232

5.4 Exhaustive Search 232

5.5 Dichotomous Search 234

5.6 Interval Halving Method 236

5.7 Fibonacci Method 238

5.8 Golden Section Method 243

5.9 Comparison of Elimination Methods 246

Interpolation Methods 247

5.10 Quadratic Interpolation Method 248

5.11 Cubic Interpolation Method 253

5.12 Direct Root Methods 259

5.12.1 Newton Method 259

5.12.2 Quasi-Newton Method 261

5.12.3 Secant Method 263

5.13 Practical Considerations 265

5.13.1 How to Make the Methods Efficient and More Reliable 265

5.13.2 Implementation in Multivariable Optimization Problems 266

5.13.3 Comparison of Methods 266

5.14 Solutions Using MATLAB 267

References and Bibliography 267

Review Questions 267

Problems 268

6 Nonlinear Programming II: Unconstrained Optimization Techniques 273

6.1 Introduction 273

6.1.1 Classification of Unconstrained Minimization Methods 276

6.1.2 General Approach 276

6.1.3 Rate of Convergence 276

6.1.4 Scaling of Design Variables 277

Direct Search Methods 280

6.2 Random Search Methods 280

6.2.1 Random Jumping Method 280

6.2.2 Random Walk Method 282

6.2.3 Random Walk Method with Direction Exploitation 283

6.2.4 Advantages of Random Search Methods 284

6.3 Grid Search Method 285

6.4 Univariate Method 285

6.5 Pattern Directions 288

6.6 Powell’s Method 289

6.6.1 Conjugate Directions 289

6.6.2 Algorithm 293

6.7 Simplex Method 298

6.7.1 Reflection 298

6.7.2 Expansion 301

6.7.3 Contraction 301

Indirect Search (Descent) Methods 304

6.8 Gradient of a Function 304

6.8.1 Evaluation of the Gradient 306

6.8.2 Rate of Change of a Function Along a Direction 307

6.9 Steepest Descent (Cauchy) Method 308

6.10 Conjugate Gradient (Fletcher–Reeves) Method 310

6.10.1 Development of the Fletcher–Reeves Method 310

6.10.2 Fletcher–Reeves Method 311

6.11 Newton’s Method 313

6.12 Marquardt Method 316

6.13 Quasi-Newton Methods 317

6.13.1 Computation of [B_i] 318

6.13.2 Rank 1 Updates 319

6.13.3 Rank 2 Updates 320

6.14 Davidon–Fletcher–Powell Method 321

6.15 Broyden–Fletcher–Goldfarb–Shanno Method 327

6.16 Test Functions 330

6.17 Solutions Using Matlab 332

References and Bibliography 333

Review Questions 334

Problems 336

7 Nonlinear Programming III: Constrained Optimization Techniques 347

7.1 Introduction 347

7.2 Characteristics of a Constrained Problem 347

Direct Methods 350

7.3 Random Search Methods 350

7.4 Complex Method 351

7.5 Sequential Linear Programming 353

7.6 Basic Approach in the Methods of Feasible Directions 360

7.7 Zoutendijk’s Method of Feasible Directions 360

7.7.1 Direction-Finding Problem 362

7.7.2 Determination of Step Length 364

7.7.3 Termination Criteria 367

7.8 Rosen’s Gradient Projection Method 369

7.8.1 Determination of Step Length 372

7.9 Generalized Reduced Gradient Method 377

7.10 Sequential Quadratic Programming 386

7.10.1 Derivation 386

7.10.2 Solution Procedure 389

Indirect Methods 392

7.11 Transformation Techniques 392

7.12 Basic Approach of the Penalty Function Method 394

7.13 Interior Penalty Function Method 396

7.14 Convex Programming Problem 405

7.15 Exterior Penalty Function Method 406

7.16 Extrapolation Techniques in the Interior Penalty Function Method 410

7.16.1 Extrapolation of the Design Vector X 410

7.16.2 Extrapolation of the Function f 412

7.17 Extended Interior Penalty Function Methods 414

7.17.1 Linear Extended Penalty Function Method 414

7.17.2 Quadratic Extended Penalty Function Method 415

7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints 416

7.18.1 Interior Penalty Function Method 416

7.18.2 Exterior Penalty Function Method 418

7.19 Penalty Function Method for Parametric Constraints 418

7.19.1 Parametric Constraint 418

7.19.2 Handling Parametric Constraints 420

7.20 Augmented Lagrange Multiplier Method 422

7.20.1 Equality-Constrained Problems 422

7.20.2 Inequality-Constrained Problems 423

7.20.3 Mixed Equality–Inequality-Constrained Problems 425

7.21 Checking the Convergence of Constrained Optimization Problems 426

7.21.1 Perturbing the Design Vector 427

7.21.2 Testing the Kuhn–Tucker Conditions 427

7.22 Test Problems 428

7.22.1 Design of a Three-Bar Truss 429

7.22.2 Design of a Twenty-Five-Bar Space Truss 430

7.22.3 Welded Beam Design 431

7.22.4 Speed Reducer (Gear Train) Design 433

7.22.5 Heat Exchanger Design [7.42] 435

7.23 Solutions Using MATLAB 435

References and Bibliography 435

Review Questions 437

Problems 439

8 Geometric Programming 449

8.1 Introduction 449

8.2 Posynomial 449

8.3 Unconstrained Minimization Problem 450

8.4 Solution of an Unconstrained Geometric Programming Program using Differential Calculus 450

8.4.1 Degree of Difficulty 453

8.4.2 Sufficiency Condition 453

8.4.3 Finding the Optimal Values of Design Variables 453

8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic–Geometric Inequality 457

8.6 Primal–dual Relationship and Sufficiency Conditions in the Unconstrained Case 458

8.6.1 Primal and Dual Problems 461

8.6.2 Computational Procedure 461

8.7 Constrained Minimization 464

8.8 Solution of a Constrained Geometric Programming Problem 465

8.8.1 Optimum Design Variables 466

8.9 Primal and Dual Programs in the Case of Less-than Inequalities 466

8.10 Geometric Programming with Mixed Inequality Constraints 473

8.11 Complementary Geometric Programming 475

8.11.1 Solution Procedure 477

8.11.2 Degree of Difficulty 478

8.12 Applications of Geometric Programming 480

References and Bibliography 491

Review Questions 493

Problems 493

9 Dynamic Programming 497

9.1 Introduction 497

9.2 Multistage Decision Processes 498

9.2.1 Definition and Examples 498

9.2.2 Representation of a Multistage Decision Process 499

9.2.3 Conversion of a Nonserial System to a Serial System 500

9.2.4 Types of Multistage Decision Problems 501

9.3 Concept of Suboptimization and Principle of Optimality 501

9.4 Computational Procedure in Dynamic Programming 505

9.5 Example Illustrating the Calculus Method of Solution 507

9.6 Example Illustrating the Tabular Method of Solution 512

9.6.1 Suboptimization of Stage 1 (Component 1) 514

9.6.2 Suboptimization of Stages 2 and 1 (Components 2 and 1) 514

9.6.3 Suboptimization of Stages 3, 2, and 1 (Components 3, 2, and 1) 515

9.7 Conversion of a Final Value Problem into an Initial Value Problem 517

9.8 Linear Programming as a Case of Dynamic Programming 519

9.9 Continuous Dynamic Programming 523

9.10 Additional Applications 526

9.10.1 Design of Continuous Beams 526

9.10.2 Optimal Layout (Geometry) of a Truss 527

9.10.3 Optimal Design of a Gear Train 528

9.10.4 Design of a Minimum-Cost Drainage System 529

References and Bibliography 530

Review Questions 531

Problems 532

10 Integer Programming 537

10.1 Introduction 537

Integer Linear Programming 538

10.2 Graphical Representation 538

10.3 Gomory’s Cutting Plane Method 540

10.3.1 Concept of a Cutting Plane 540

10.3.2 Gomory’s Method for All-Integer Programming Problems 541

10.3.3 Gomory’s Method for Mixed-Integer Programming Problems 547

10.4 Balas’ Algorithm for Zero–One Programming Problems 551

Integer Nonlinear Programming 553

10.5 Integer Polynomial Programming 553

10.5.1 Representation of an Integer Variable by an Equivalent System of Binary Variables 553

10.5.2 Conversion of a Zero–One Polynomial Programming Problem into a Zero–One LP Problem 555

10.6 Branch-and-Bound Method 556

10.7 Sequential Linear Discrete Programming 561

10.8 Generalized Penalty Function Method 564

10.9 Solutions Using MATLAB 569

References and Bibliography 569

Review Questions 570

Problems 571

11 Stochastic Programming 575

11.1 Introduction 575

11.2 Basic Concepts of Probability Theory 575

11.2.1 Definition of Probability 575

11.2.2 Random Variables and Probability Density Functions 576

11.2.3 Mean and Standard Deviation 578

11.2.4 Function of a Random Variable 580

11.2.5 Jointly Distributed Random Variables 581

11.2.6 Covariance and Correlation 583

11.2.7 Functions of Several Random Variables 583

11.2.8 Probability Distributions 585

11.2.9 Central Limit Theorem 589

11.3 Stochastic Linear Programming 589

11.4 Stochastic Nonlinear Programming 594

11.4.1 Objective Function 594

11.4.2 Constraints 595

11.5 Stochastic Geometric Programming 600

References and Bibliography 602

Review Questions 603

Problems 604

12 Optimal Control and Optimality Criteria Methods 609

12.1 Introduction 609

12.2 Calculus of Variations 609

12.2.1 Introduction 609

12.2.2 Problem of Calculus of Variations 610

12.2.3 Lagrange Multipliers and Constraints 615

12.2.4 Generalization 618

12.3 Optimal Control Theory 619

12.3.1 Necessary Conditions for Optimal Control 619

12.3.2 Necessary Conditions for a General Problem 621

12.4 Optimality Criteria Methods 622

12.4.1 Optimality Criteria with a Single Displacement Constraint 623

12.4.2 Optimality Criteria with Multiple Displacement Constraints 624

12.4.3 Reciprocal Approximations 625

References and Bibliography 628

Review Questions 628

Problems 629

13 Modern Methods of Optimization 633

13.1 Introduction 633

13.2 Genetic Algorithms 633

13.2.1 Introduction 633

13.2.2 Representation of Design Variables 634

13.2.3 Representation of Objective Function and Constraints 635

13.2.4 Genetic Operators 636

13.2.5 Algorithm 640

13.2.6 Numerical Results 641

13.3 Simulated Annealing 641

13.3.1 Introduction 641

13.3.2 Procedure 642

13.3.3 Algorithm 643

13.3.4 Features of the Method 644

13.3.5 Numerical Results 644

13.4 Particle Swarm Optimization 647

13.4.1 Introduction 647

13.4.2 Computational Implementation of PSO 648

13.4.3 Improvement to the Particle Swarm Optimization Method 649

13.4.4 Solution of the Constrained Optimization Problem 649

13.5 Ant Colony Optimization 652

13.5.1 Basic Concept 652

13.5.2 Ant Searching Behavior 653

13.5.3 Path Retracing and Pheromone Updating 654

13.5.4 Pheromone Trail Evaporation 654

13.5.5 Algorithm 655

13.6 Optimization of Fuzzy Systems 660

13.6.1 Fuzzy Set Theory 660

13.6.2 Optimization of Fuzzy Systems 662

13.6.3 Computational Procedure 663

13.6.4 Numerical Results 664

13.7 Neural-Network-Based Optimization 665

References and Bibliography 667

Review Questions 669

Problems 671

14 Metaheuristic Optimization Methods 673

14.1 Definitions 673

14.2 Metaphors Associated with Metaheuristic Optimization Methods 673

14.3 Details of Representative Metaheuristic Algorithms 680

14.3.1 Crow Search Algorithm 680

14.3.2 Firefly Optimization Algorithm (FA) 681

14.3.3 Harmony Search Algorithm 684

14.3.4 Teaching-Learning-Based Optimization (TLBO) 687

14.3.5 Honey Bee Swarm Optimization Algorithm 689

References and Bibliography 692

Review Questions 694

15 Practical Aspects of Optimization 697

15.1 Introduction 697

15.2 Reduction of Size of an Optimization Problem 697

15.2.1 Reduced Basis Technique 697

15.2.2 Design Variable Linking Technique 698

15.3 Fast Reanalysis Techniques 700

15.3.1 Incremental Response Approach 700

15.3.2 Basis Vector Approach 704

15.4 Derivatives of Static Displacements and Stresses 705

15.5 Derivatives of Eigenvalues and Eigenvectors 707

15.5.1 Derivatives of 𝜆_i 707

15.5.2 Derivatives of Y_i 708

15.6 Derivatives of Transient Response 709

15.7 Sensitivity of Optimum Solution to Problem Parameters 712

15.7.1 Sensitivity Equations Using Kuhn–Tucker Conditions 712

15.7.2 Sensitivity Equations Using the Concept of Feasible Direction 714

References and Bibliography 715

Review Questions 716

Problems 716

16 Multilevel and Multiobjective Optimization 721

16.1 Introduction 721

16.2 Multilevel Optimization 721

16.2.1 Basic Idea 721

16.2.2 Method 722

16.3 Parallel Processing 726

16.4 Multiobjective Optimization 729

16.4.1 Utility Function Method 730

16.4.2 Inverted Utility Function Method 730

16.4.3 Global Criterion Method 730

16.4.4 Bounded Objective Function Method 730

16.4.5 Lexicographic Method 731

16.4.6 Goal Programming Method 732

16.4.7 Goal Attainment Method 732

16.4.8 Game Theory Approach 733

16.5 Solutions Using MATLAB 735

References and Bibliography 735

Review Questions 736

Problems 737

17 Solution of Optimization Problems Using MATLAB 739

17.1 Introduction 739

17.2 Solution of General Nonlinear Programming Problems 740

17.3 Solution of Linear Programming Problems 742

17.4 Solution of LP Problems Using Interior Point Method 743

17.5 Solution of Quadratic Programming Problems 745

17.6 Solution of One-Dimensional Minimization Problems 746

17.7 Solution of Unconstrained Optimization Problems 746

17.8 Solution of Constrained Optimization Problems 747

17.9 Solution of Binary Programming Problems 750

17.10 Solution of Multiobjective Problems 751

References and Bibliography 755

Problems 755

A Convex and Concave Functions 761

B Some Computational Aspects of Optimization 767

B.1 Choice of Method 767

B.2 Comparison of Unconstrained Methods 767

B.3 Comparison of Constrained Methods 768

B.4 Availability of Computer Programs 769

B.5 Scaling of Design Variables and Constraints 770

B.6 Computer Programs for Modern Methods of Optimization 771

References and Bibliography 772

C Introduction to MATLAB^® 773

C.1 Features and Special Characters 773

C.2 Defining Matrices in MATLAB 774

C.3 Creating m-Files 775

C.4 Optimization Toolbox 775

Answers to Selected Problems 777

Index 787