Ebook: A Mathematical Theory of Design: Foundations, Algorithms and Applications

Formal Design Theory (PDT) is a mathematical theory of design. The main goal of PDT is to develop a domain independent core model of the design process. The book focuses the reader's attention on the process by which ideas originate and are developed into workable products. In developing PDT, we have been striving toward what has been expressed by the distinguished scholar Simon (1969): that "the science of design is possible and some day we will be able to talk in terms of well-established theories and practices. " The book is divided into five interrelated parts. The conceptual approach is presented first (Part I); followed by the theoretical foundations of PDT (Part II), and from which the algorithmic and pragmatic implications are deduced (Part III). Finally, detailed case-studies illustrate the theory and the methods of the design process (Part IV), and additional practical considerations are evaluated (Part V). The generic nature of the concepts, theory and methods are validated by examples from a variety of disciplines. FDT explores issues such as: algebraic representation of design artifacts, idealized design process cycle, and computational analysis and measurement of design process complexity and quality. FDT's axioms convey the assumptions of the theory about the nature of artifacts, and potential modifications of the artifacts in achieving desired goals or functionality. By being able to state these axioms explicitly, it is possible to derive theorems and corollaries, as well as to develop specific analytical and constructive methodologies.

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Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Introduction and Overview....Pages 3-17
Design as Scientific Problem-Solving....Pages 19-84
Introductory Case Studies....Pages 85-106
Front Matter....Pages 107-107
Representation of Design Artifacts....Pages 109-141
The Idealized Design Process....Pages 143-185
Modeling the Evolutionary Design Process....Pages 187-215
Guided Heuristics in Engineering Design....Pages 217-239
The Measurement of a Design Structural and Functional Complexity....Pages 241-277
Statistical Analysis of the Time Complexity Measure....Pages 279-290
Front Matter....Pages 291-291
Intelligent Advisory Tool for Design Decomposition....Pages 293-319
Physical Design of Printed Circuit Boards: Group Technology Approach....Pages 321-352
Physical Design of Printed Circuit Boards: Genetic Algorithm Approach....Pages 353-363
Adaptive Learning for Successful Design....Pages 365-385
Maintaining Consistency in the Design Process....Pages 387-421
Constraint-Based Design of Faired Parametric Curves....Pages 423-443
Creating a Consistent 3-D Virtual Last for Problems in the Shoe Industry....Pages 445-459
Front Matter....Pages 461-461
Design of a Wormgear Reducer: A Case Study....Pages 463-498
Adaptive Learning for Successful Flexible Manufacturing Cell Design: A Case Study....Pages 499-512
Maintaining Design Consistency: Examples....Pages 513-549
Cases in Evolutionary Design Processes....Pages 551-648
Back Matter....Pages 671-681
Concluding Reflections....Pages 651-670

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Content:
Front Matter....Pages i-xxii
Front Matter....Pages 1-1
Introduction and Overview....Pages 3-17
Design as Scientific Problem-Solving....Pages 19-84
Introductory Case Studies....Pages 85-106
Front Matter....Pages 107-107
Representation of Design Artifacts....Pages 109-141
The Idealized Design Process....Pages 143-185
Modeling the Evolutionary Design Process....Pages 187-215
Guided Heuristics in Engineering Design....Pages 217-239
The Measurement of a Design Structural and Functional Complexity....Pages 241-277
Statistical Analysis of the Time Complexity Measure....Pages 279-290
Front Matter....Pages 291-291
Intelligent Advisory Tool for Design Decomposition....Pages 293-319
Physical Design of Printed Circuit Boards: Group Technology Approach....Pages 321-352
Physical Design of Printed Circuit Boards: Genetic Algorithm Approach....Pages 353-363
Adaptive Learning for Successful Design....Pages 365-385
Maintaining Consistency in the Design Process....Pages 387-421
Constraint-Based Design of Faired Parametric Curves....Pages 423-443
Creating a Consistent 3-D Virtual Last for Problems in the Shoe Industry....Pages 445-459
Front Matter....Pages 461-461
Design of a Wormgear Reducer: A Case Study....Pages 463-498
Adaptive Learning for Successful Flexible Manufacturing Cell Design: A Case Study....Pages 499-512
Maintaining Design Consistency: Examples....Pages 513-549
Cases in Evolutionary Design Processes....Pages 551-648
Back Matter....Pages 671-681
Concluding Reflections....Pages 651-670
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