A Mathematical Theory of Design: Foundations, Algorithms and Applications

1. Front Matter

   Pages i-xxii

   PDF

2. The Design Process: Properties, Paradigms and the Evolutionary Structure

   1. Front Matter

      Pages 1-1

      PDF

   2. Introduction and Overview

      • Dan Braha, Oded Maimon

      Pages 3-17

   3. Design as Scientific Problem-Solving

      • Dan Braha, Oded Maimon

      Pages 19-84

   4. Introductory Case Studies

      • Dan Braha, Oded Maimon

      Pages 85-106

3. Formal Design Theory (FDT)

   1. Front Matter

      Pages 107-107

      PDF

   2. Representation of Design Artifacts

      • Dan Braha, Oded Maimon

      Pages 109-141

   3. The Idealized Design Process

      • Dan Braha, Oded Maimon

      Pages 143-185

   4. Modeling the Evolutionary Design Process

      • Dan Braha, Oded Maimon

      Pages 187-215

   5. Guided Heuristics in Engineering Design

      • Dan Braha, Oded Maimon

      Pages 217-239

   6. The Measurement of a Design Structural and Functional Complexity

      • Dan Braha, Oded Maimon

      Pages 241-277

   7. Statistical Analysis of the Time Complexity Measure

      • Dan Braha, Oded Maimon

      Pages 279-290

4. Algorithmic and Heuristic Methods for Design Decision Support

   1. Front Matter

      Pages 291-291

      PDF

   2. Intelligent Advisory Tool for Design Decomposition

      • Dan Braha, Oded Maimon

      Pages 293-319

   3. Physical Design of Printed Circuit Boards: Group Technology Approach

      • Dan Braha, Oded Maimon

      Pages 321-352

   4. Physical Design of Printed Circuit Boards: Genetic Algorithm Approach

      • Dan Braha, Oded Maimon

      Pages 353-363

   5. Adaptive Learning for Successful Design

      • Dan Braha, Oded Maimon

      Pages 365-385

   6. Maintaining Consistency in the Design Process

      • Dan Braha, Oded Maimon

      Pages 387-421

   7. Constraint-Based Design of Faired Parametric Curves

      • Dan Braha, Oded Maimon

      Pages 423-443

   8. Creating a Consistent 3-D Virtual Last for Problems in the Shoe Industry

      • Dan Braha, Oded Maimon

      Pages 445-459

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.

• algorithms
• calculus
• complexity
• computer-aided design (CAD)
• design
• design process
• design theory
• engineering design
• information
• information theory
• modeling
• optimization
• software
• statistical analysis

• Department of Industrial Engineering, Ben Gurion University, Beer Sheva, Israel

  Dan Braha

• Department of Industrial Engineering, Tel-Aviv University, Tel-Aviv, Israel

  Oded Maimon

Policies and ethics