Introduction to optimum design

Cover......Page 1
Half Title Page......Page 2
Title Page......Page 4
Copyright......Page 5
Author Detail......Page 6
Dedication Page......Page 8
Preface......Page 10
Contents......Page 12
1. Introduction to Design......Page 24
1.1 The Design Process......Page 25
1.3 Conventional versus Optimum Design Process......Page 27
1.4 Optimum Design versus Optimal Control......Page 29
1.5 Basic Terminology and Notation......Page 30
2. Optimum Design Problem Formulation......Page 38
2.1 The Problem Formulation Process......Page 39
2.2 Design of a Can......Page 41
2.3 Insulated Spherical Tank Design......Page 43
2.4 Saw Mill Operation......Page 45
2.5 Design of a Two-Bar Bracket......Page 47
2.6 Design of a Cabinet......Page 53
2.7 Minimum Weight Tubular Column Design......Page 55
2.8 Minimum Cost Cylindrical Tank Design......Page 58
2.9 Design of Coil Springs......Page 59
2.10 Minimum Weight Design of a Symmetric Three-Bar Truss......Page 61
2.11 A General Mathematical Model for Optimum Design......Page 64
Exercises for Chapter 2......Page 69
3.1 Graphical Solution Process......Page 78
3.2 Use of Mathematica for Graphical Optimization......Page 83
3.3 Use of MATLAB for Graphical Optimization......Page 87
3.5 Problem with Unbounded Solution......Page 89
3.6 Infeasible Problem......Page 90
3.8 Graphical Solution for a Beam Design Problem......Page 92
Exercises for Chapter 3......Page 95
4. Optimum Design Concepts......Page 106
4.1 Definitions of Global and Local Minima......Page 107
4.2 Review of Some Basic Calculus Concepts......Page 112
4.3 Unconstrained Optimum Design Problems......Page 126
4.4 Constrained Optimum Design Problems......Page 142
4.5 Postoptimality Analysis: Physical Meaning of Lagrange Multipliers......Page 166
4.6 Global Optimality......Page 172
4.7 Engineering Design Examples......Page 181
Exercises for Chapter 4......Page 189
5.1 Alternate Form of KKT Necessary Conditions......Page 198
5.2 Irregular Points......Page 201
5.3 Second-Order Conditions for Constrained Optimization......Page 202
5.4 Sufficiency Check for Rectangular Beam Design Problem......Page 207
Exercises for Chapter 5......Page 208
6. Linear Programming Methods for Optimum Design......Page 214
6.1 Definition of a Standard Linear Programming Problem......Page 215
6.2 Basic Concepts Related to Linear Programming Problems......Page 218
6.3 Basic Ideas and Steps of the Simplex Method......Page 224
6.4 Two-Phase Simplex Method—Artificial Variables......Page 241
6.5 Postoptimality Analysis......Page 251
6.6 Solution of LP Problems Using Excel Solver......Page 266
Exercises for Chapter 6......Page 269
7.1 Derivation of the Simplex Method......Page 282
7.2 Alternate Simplex Method......Page 285
7.3 Duality in Linear Programming......Page 286
Exercises for Chapter 7......Page 298
8. Numerical Methods for Unconstrained Optimum Design......Page 300
8.1 General Concepts Related to Numerical Algorithms......Page 301
8.2 Basic Ideas and Algorithms for Step Size Determination......Page 305
8.3 Search Direction Determination: Steepest Descent Method......Page 316
8.4 Search Direction Determination: Conjugate Gradient Method......Page 319
Exercises for Chapter 8......Page 323
9.1 More on Step Size Determination......Page 328
9.2 More on Steepest Descent Method......Page 333
9.3 Scaling of Design Variables......Page 338
9.4 Search Direction Determination: Newton’s Method......Page 341
9.5 Search Direction Determination: Quasi-Newton Methods......Page 347
9.6 Engineering Applications of Unconstrained Methods......Page 352
9.7 Solution of Constrained Problems Using Unconstrained Optimization Methods......Page 355
Exercises for Chapter 9......Page 358
10. Numerical Methods for Constrained Optimum Design......Page 362
10.1 Basic Concepts and Ideas......Page 363
10.2 Linearization of Constrained Problem......Page 369
10.3 Sequential Linear Programming Algorithm......Page 375
10.4 Quadratic Programming Subproblem......Page 381
10.5 Constrained Steepest Descent Method......Page 386
10.6 Engineering Design Optimization Using Excel Solver......Page 392
Exercises for Chapter 10......Page 396
11.1 Potential Constraint Strategy......Page 402
11.2 Quadratic Programming Problem......Page 406
11.3 Approximate Step Size Determination......Page 411
11.4 Constrained Quasi-Newton Methods......Page 423
11.5 Other Numerical Optimization Methods......Page 430
Exercises for Chapter 11......Page 434
12.1 Introduction to Optimization Toolbox......Page 436
12.2 Unconstrained Optimum Design Problems......Page 438
12.3 Constrained Optimum Design Problems......Page 441
12.4 Optimum Design Examples with MATLAB......Page 443
Exercises for Chapter 12......Page 452
13. Interactive Design Optimization......Page 456
13.1 Role of Interaction in Design Optimization......Page 457
13.2 Interactive Design Optimization Algorithms......Page 459
13.3 Desired Interactive Capabilities......Page 471
13.4 Interactive Design Optimization Software......Page 473
13.5 Examples of Interactive Design Optimization......Page 477
Exercises for Chapter 13......Page 485
14. Design Optimization Applications with Implicit Functions......Page 488
14.1 Formulation of Practical Design Optimization Problems......Page 489
14.2 Gradient Evaluation for Implicit Functions......Page 496
14.3 Issues in Practical Design Optimization......Page 501
14.4 Use of General-Purpose Software......Page 502
14.5 Optimum Design of a Two-Member Frame with Out-of-Plane Loads......Page 504
14.6 Optimum Design of a Three-Bar Structure for Multiple Performance Requirements......Page 506
14.7 Discrete Variable Optimum Design......Page 514
14.8 Optimal Control of Systems by Nonlinear Programming......Page 516
Exercises for Chapter 14......Page 531
15. Discrete Variable Optimum Design Concepts and Methods......Page 536
15.1 Basic Concepts and Definitions......Page 537
15.2 Branch and Bound Methods (BBM)......Page 539
15.3 Integer Programming......Page 544
15.5 Simulated Annealing......Page 545
15.6 Dynamic Rounding-off Method......Page 547
15.8 Methods for Linked Discrete Variables......Page 548
15.9 Selection of a Method......Page 549
Exercises for Chapter 15......Page 550
16. Genetic Algorithms for Optimum Design......Page 554
16.1 Basic Concepts and Definitions......Page 555
16.2 Fundamentals of Genetic Algorithms......Page 557
16.3 Genetic Algorithm for Sequencing-Type Problems......Page 561
16.4 Applications......Page 562
Exercises for Chapter 16......Page 563
17.1 Problem Definition......Page 566
17.2 Terminology and Basic Concepts......Page 569
17.3 Multiobjective Genetic Algorithms......Page 575
17.4 Weighted Sum Method......Page 578
17.6 Weighted Global Criterion Method......Page 579
17.8 Bounded Objective Function Method......Page 581
17.10 Selection of Methods......Page 582
Exercises for Chapter 17......Page 583
18.1 Basic Concepts of Solution Methods......Page 588
18.2 Overview of Deterministic Methods......Page 590
18.3 Overview of Stochastic Methods......Page 595
18.4 Two Local-Global Stochastic Methods......Page 602
18.5 Numerical Performance of Methods......Page 608
Exercises for Chapter 18......Page 611
A.1 Time Value of Money......Page 616
A.2 Economic Bases for Comparison......Page 621
Exercises for Appendix A......Page 627
B.1 Definition of Matrices......Page 634
B.2 Type of Matrices and Their Operations......Page 636
B.3 Solution of n Linear Equations in n Unknowns......Page 641
B.4 Solution of m Linear Equations in n Unknowns......Page 651
B.5 Concepts Related to a Set of Vectors......Page 658
B.6 Eigenvalues and Eigenvectors......Page 665
B.7 Norm and Condition Number of a Matrix......Page 666
Exercises for Appendix B......Page 668
C.1 Single Nonlinear Equation......Page 670
C.2 Multiple Nonlinear Equations......Page 673
Exercises for Appendix C......Page 678
D.1 Equal Interval Search......Page 680
D.3 Steepest Descent Method......Page 683
D.4 Modified Newton’s Method......Page 692
References......Page 698
Bibliography......Page 706
Answers to Selected Problems......Page 710
Index......Page 718