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E-raamat: Engineering Design Optimization

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(Brigham Young University, Utah), (University of Michigan, Ann Arbor)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Nov-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108988612
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Engineering Design OptimizationSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 18-Nov-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108988612
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Based on course-tested material, this rigorous yet accessible graduate textbook covers both fundamental and advanced optimization theory and algorithms. It covers a wide range of numerical methods and topics, including both gradient-based and gradient-free algorithms, multidisciplinary design optimization, and uncertainty, with instruction on how to determine which algorithm should be used for a given application. It also provides an overview of models and how to prepare them for use with numerical optimization, including derivative computation. Over 400 high-quality visualizations and numerous examples facilitate understanding of the theory, and practical tips address common issues encountered in practical engineering design optimization and how to address them. Numerous end-of-chapter homework problems, progressing in difficulty, help put knowledge into practice. Accompanied online by a solutions manual for instructors and source code for problems, this is ideal for a one- or two-semester graduate course on optimization in aerospace, civil, mechanical, electrical, and chemical engineering departments.

A rigorous yet accessible textbook covering both fundamental and advanced optimization topics. Covering both gradient-based and gradient-free algorithms, derivative computation, and numerous visualizations, examples and problems, it is ideal for graduate courses on optimization in aerospace, civil, and mechanical engineering departments.

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A rigorous yet accessible graduate textbook covering both fundamental and advanced optimization theory and algorithms.
Preface xi
Acknowledgements xiii
1 Introduction 1(32)
1.1 Design Optimization Process
2(4)
1.2 Optimization Problem Formulation
6(11)
1.3 Optimization Problem Classification
17(4)
1.4 Optimization Algorithms
21(5)
1.5 Selecting an Optimization Approach
26(2)
1.6 Notation
28(1)
1.7 Summary
29(1)
Problems
30(3)
2 A Short History of Optimization 33(14)
2.1 The First Problems: Optimizing Length and Area
33(1)
2.2 Optimization Revolution: Derivatives and Calculus
34(2)
2.3 The Birth of Optimization Algorithms
36(3)
2.4 The Last Decades
39(4)
2.5 Toward a Diverse Future
43(2)
2.6 Summary
45(2)
3 Numerical Models and Solvers 47(32)
3.1 Model Development for Analysis versus Optimization
47(1)
3.2 Modeling Process and Types of Errors
48(2)
3.3 Numerical Models as Residual Equations
50(2)
3.4 Discretization of Differential Equations
52(1)
3.5 Numerical Errors
53(8)
3.6 Overview of Solvers
61(2)
3.7 Rate of Convergence
63(3)
3.8 Newton-Based Solvers
66(4)
3.9 Models and the Optimization Problem
70(3)
3.10 Summary
73(2)
Problems
75(4)
4 Unconstrained Gradient-Based Optimization 79(74)
4.1 Fundamentals
80(14)
4.2 Two Overall Approaches to Finding an Optimum
94(2)
4.3 Line Search
96(14)
4.4 Search Direction
110(29)
4.5 Trust-Region Methods
139(8)
4.6 Summary
147(2)
Problems
149(4)
5 Constrained Gradient-Based Optimization 153(70)
5.1 Constrained Problem Formulation
154(2)
5.2 Understanding n-Dimensional Space
156(2)
5.3 Optimality Conditions
158(17)
5.4 Penalty Methods
175(12)
5.5 Sequential Quadratic Programming
187(17)
5.6 Interior-Point Methods
204(7)
5.7 Constraint Aggregation
211(3)
5.8 Summary
214(1)
Problems
215(8)
6 Computing Derivatives 223(58)
6.1 Derivatives, Gradients, and Jacobians
223(2)
6.2 Overview of Methods for Computing Derivatives
225(1)
6.3 Symbolic Differentiation
226(1)
6.4 Finite Differences
227(5)
6.5 Complex Step
232(5)
6.6 Algorithmic Differentiation
237(15)
6.7 Implicit Analytic Methods-Direct and Adjoint
252(10)
6.8 Sparse Jacobians and Graph Coloring
262(3)
6.9 Unified Derivatives Equation
265(10)
6.10 Summary
275(2)
Problems
277(4)
7 Gradient-Free Optimization 281(46)
7.1 When to Use Gradient-Free Algorithms
281(3)
7.2 Classification of Gradient-Free Algorithms
284(3)
7.3 Nelder-Mead Algorithm
287(5)
7.4 Generalized Pattern Search
292(6)
7.5 DIRECT Algorithm
298(8)
7.6 Genetic Algorithms
306(10)
7.7 Particle Swarm Optimization
316(5)
7.8 Summary
321(2)
Problems
323(4)
8 Discrete Optimization 327(28)
8.1 Binary, Integer, and Discrete Variables
327(1)
8.2 Avoiding Discrete Variables
328(2)
8.3 Branch and Bound
330(7)
8.4 Greedy Algorithms
337(2)
8.5 Dynamic Programming
339(8)
8.6 Simulated Annealing
347(4)
8.7 Binary Genetic Algorithms
351(1)
8.8 Summary
351(1)
Problems
352(3)
9 Multiobjective Optimization 355(18)
9.1 Multiple Objectives
355(2)
9.2 Pareto Optimality
357(1)
9.3 Solution Methods
358(11)
9.4 Summary
369(1)
Problems
370(3)
10 Surrogate-Based Optimization 373(50)
10.1 When to Use a Surrogate Model
374(1)
10.2 Sampling
375(9)
10.3 Constructing a Surrogate
384(16)
10.4 Kriging
400(8)
10.5 Deep Neural Networks
408(6)
10.6 Optimization and Infill
414(4)
10.7 Summary
418(2)
Problems
420(3)
11 Convex Optimization 423(18)
11.1 Introduction
423(2)
11.2 Linear Programming
425(2)
11.3 Quadratic Programming
427(2)
11.4 Second-Order Cone Programming
429(1)
11.5 Disciplined Convex Optimization
430(4)
11.6 Geometric Programming
434(3)
11.7 Summary
437(1)
Problems
438(3)
12 Optimization Under Uncertainty 441(34)
12.1 Robust Design
442(5)
12.2 Reliable Design
447(1)
12.3 Forward Propagation
448(21)
12.4 Summary
469(2)
Problems
471(4)
13 Multidisciplinary Design Optimization 475(64)
13.1 The Need for MDO
475(3)
13.2 Coupled Models
478(23)
13.3 Coupled Derivatives Computation
501(9)
13.4 Monolithic MDO Architectures
510(9)
13.5 Distributed MDO Architectures
519(14)
13.6 Summary
533(2)
Problems
535(4)
A Mathematics Background 539(20)
A.1 Taylor Series Expansion
539(2)
A.2 Chain Rule, Total Derivatives, and Differentials
541(3)
A.3 Matrix Multiplication
544(3)
A.4 Four Fundamental Subspaces in Linear Algebra
547(1)
A.5 Vector and Matrix Norms
548(2)
A.6 Matrix Types
550(2)
A.7 Matrix Derivatives
552(1)
A.8 Eigenvalues and Eigenvectors
553(1)
A.9 Random Variables
554(5)
B Linear Solvers 559(12)
B.1 Systems of Linear Equations
559(1)
B.2 Conditioning
560(1)
B.3 Direct Methods
560(2)
B.4 Iterative Methods
562(9)
C Quasi-Newton Methods 571(8)
C.1 Broyden's Method
571(1)
C.2 Additional Quasi-Newton Approximations
572(4)
C.3 Sherman-Morrison-Woodbury Formula
576(3)
D Test Problems 579(12)
D.1 Unconstrained Problems
579(7)
D.2 Constrained Problems
586(5)
Bibliography 591(24)
Index 615
Joaquim R. R. A. Martins is a Professor of Aerospace Engineering at the University of Michigan. He is a fellow of the American Institute for Aeronautics and Astronautics, and the Royal Aeronautical Society. Andrew Ning is an Associate Professor of Mechanical Engineering at Brigham Young University, and has previously worked at the National Renewable Energy Laboratory (NREL) as a Senior Engineer.
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