Introduction to Optimum Design

Description

Introduction to Optimum Design is intended for use in a first course on engineering design and optimization. Virtually any problem for which specific parameters need to be determined to satisfy constraints can be formulated as a design optimization problem. The concepts and methods described in the text are quite general and applicable to all such formulations. Inasmuch, the range of application of the optimum design methodology is almost limitless, constrained only by the imagination and ingenuity of the user. Throughout the text, simple design problems involving two to three design variables and three to four constraints are solved in detail to illustrate fundamental concepts and basic ideas. The necessary results from optimization theory are stated and their implications are studied through application to engineering design problems. Theory and concepts of optimum design are explained only through examples and simple engineering applications. Several of the numerical procedures and concepts described in the text are useful in many other engineering courses and applications. * Allows engineers involved in the design process to adapt optimum design concepts in their work using the material in the text. * Basic concepts of optimality conditions and numerical methods are described with simple examples, making the material high teachable and learnable. * Classroom-tested for many years to attain optimum pedagogical effectiveness. 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