Principles of Optimal Design: Modeling and Computation

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Cambridge University Press, 10.07.2000 - 390 Seiten
Principles of Optimal Design puts the concept of optimal design on a rigorous foundation and demonstrates the intimate relationship between the mathematical model that describes a design and the solution methods that optimize it. Since the first edition was published, computers have become ever more powerful, design engineers are tackling more complex systems, and the term optimization is now routinely used to denote a design process with increased speed and quality. This second edition takes account of these developments and brings the original text thoroughly up to date. The book now includes a discussion of trust region and convex approximation algorithms. A new chapter focuses on how to construct optimal design models. Three new case studies illustrate the creation of optimization models. The final chapter on optimization practice has been expanded to include computation of derivatives, interpretation of algorithmic results, and selection of algorithms and software. Both students and practising engineers will find this book a valuable resource for design project work.
 

Ausgewählte Seiten

Inhalt

Optimization Models
1
12 Design Optimization
10
13 Feasibility and Boundedness
23
14 Topography of the Design Space
30
15 Modeling and Computation
38
16 Design Projects
39
Model Construction
44
22 Best Fit Curves and Least Squares
49
55 Feasible Iterations
186
56 Inequality Constraints
194
57 Geometry of Boundary Optima
198
58 Linear Programming
203
59 Sensitivity
214
510 Summary
216
Parametric and Discrete Optima
223
61 Parametric Solution
224

23 Neural Networks
51
24 Kriging
54
25 Modeling a Drive Screw Linear Actuator
57
26 Modeling an Internal Combustion Engine
62
27 Design of a Geartrain
71
28 Modeling Considerations Prior to Computation
79
29 Summary
83
Model Boundedness
87
32 Constrained Optimum
92
33 Underconstrained Models
98
34 Recognizing Monotonicity
103
35 Inequalities
105
36 Equality Constraints
109
37 Variables not in the Objects
114
38 Nonmonotonic Functions
116
39 Model Preparation Procedure
119
310 Summary
121
Interior Optima
128
41 Existence
129
42 Local Approximation
131
43 Optimality
137
44 Convexity
143
45 Local Exploration
149
46 Searching along a Line
154
47 Stabilization
157
48 Trust Regions
160
49 Summary
163
Boundary Optima
168
52 Describing the Constraint Surface
171
53 Equality Constraints
174
54 Curvature at the Boundary
180
62 The Monotonicity Table
232
63 Functional Monotonicity Analysis
240
64 Discrete Variables
245
65 Discrete Design Activity and Optimality
247
66 Transformer Design
255
67 Constraint Derivation
259
68 Relaxation and Exhaustive Enumeration
270
69 Summary
272
Local Computation
278
71 Numerical Algorithms
279
72 Single Variable Minimization
285
73 QuasiNewton Methods
296
74 Active Set Strategies
300
75 Moving along the Boundary
305
76 Penalties and Barriers
306
77 Sequential Quadratic Programming
313
79 Convex Approximation Algorithms
324
710 Summary
329
Principles and Practice
337
81 Preparing Models for Numerical Computation
338
82 Computing Derivatives
342
83 Scaling
348
84 Interpreting Numerical Results
352
85 Selecting Algorithms and Software
354
86 Optimization Checklist
358
87 Concepts and Principles
362
88 Summary
366
References
369
Author Index
381
Subject Index
385
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