Developing objective measures for evaluating and measuring the complexity of design would facilitate (1) empirical studies that require the use of equivalent but different design problems, (2) the development of design curriculums, and (3) the comparison of computer aided design automation tools. This paper surveys and evaluates different approaches to defining complexity in design for the design problem, process, and product. Three fundamental aspects to complexity are identified, size, coupling, and solvability, and expanded with respect to the three elements of design, problem, process, and product. Alternative methods for measuring these characteristics of the design are based on computational, information, and traditional design views of complexity. A method of measuring size as it relates to complexity is proposed for measuring the information content of design. A second method is proposed for decomposing a graph-based representation of design that provides a measure of the interconnectedness as it relates to complexity. Finally, two methods are proposed for determining the solvability complexity of design based on the effort involved and the degree of freedom of design. These measures are developed specifically for parametric and geometric problems as found in the embodiment design, but these principles may be applied beyond this.
Issue Section:
Research Papers
Topics:
Design
1.
Gove
, P. B.
, 2002, Webster’s Third New International Dictionary of the English Language
, 3rd ed., Merriam
, Springfield, MA
.2.
Hazelrigg
, G.
, 1996, Systems Engineering: An Approach to Information-Based Design
, Prentice-Hall
, Upper Saddle River, NJ
.3.
Pahl
, G.
, Beitz
, W.
, Feldhusen
, J.
, and Grote
, K. H.
, 2007, Engineering Design: A Systematic Approach
, 3rd ed., Springer-Verlag
, London
.4.
Suh
, N.
, 1990, The Principles of Design
, Oxford University Press
, New York, NY
.5.
Ullman
, D.
, 2003, The Mechanical Design Process
, McGraw-Hill
, New York, NY
.6.
Balazs
, M.
, and Brown
, D.
, 2002, “Design Simplification by Analogical Reasoning
,” From Knowledge Intensive CAD to Knowledge Intensive Engineering
, U.
Cugini
and M.
Wozny
, eds., Kluwer
, The Netherlands
, pp. 29
–44
.7.
Boothroyd
, G.
, Dewhurst
, P.
, and Knight
, W.
, 2002, Product Design for Manufacture and Assembly
, Dekker
, New York, NY
.8.
Weber
, C.
, 2005, “What Is “Complexity”?
,” Proceedings of the 15th International Conference on Engineering Design
, Design Society, Melbourne, Australia.9.
Mocko
, G. M.
, and Paasch
, R.
, 2005, “Incorporating Uncertainty in Diagnostic Analysis of Mechanical Systems
,” J. Mech. Des.
1050-0472, 127
(2
), pp. 315
–325
.10.
Suh
, N.
, 1999, “A Theory of Complexity, Periodicity, and the Design Axioms
,” Res. Eng. Des.
0934-9839, 11
, pp. 116
–132
.11.
Braha
, D.
, and Maimon
, O.
, 1998, “The Measurement of a Design Structural and Functional Complexity
,” IEEE Trans. Syst. Man Cybern., Part A. Syst. Humans
1083-4427, 28
(4
), pp. 527
–535
.12.
Holtta
, K. M. M.
, and Otto
, K.
, 2005, “Incorporating Design Effort Complexity Measures in Product Architectural Design and Assessment
,” Des. Stud.
0142-694X, 26
(5
), pp. 463
–485
.13.
Hamade
, R.
, 2009, “Profiling the Desirable CAD Trainee: Technical Background, Personality Attributes, and Learning Preferences
,” J. Mech. Des.
1050-0472, 131
(12
), p. 121009
.14.
Bashir
, H.
, and Thomson
, V.
, 2001, “Models for Estimating Design Effort and Time
,” Des. Stud.
0142-694X, 22
(2
), pp. 141
–155
.15.
El-Haik
, B.
, and Yang
, K.
, 1999, “The Components of Complexity in Engineering Design
,” IIE Trans.
0740-817X, 31
, pp. 925
–934
.16.
Ahn
, J.
, and Crawford
, R.
, 1994, “Complexity Analysis of Computational Engineering Design Processes
,” Design Engineering Technical Conferences-Design Theory and Methodology
, Vol. 68
, ASME
, New York
, pp. 205
–220
.17.
Summers
, J. D.
, 2005, “Reasoning in Engineering Design
,” Design Engineering Technical Conferences, DETC-2005
, ASME
, Long Beach, CA
, Paper No. DTM-85334.18.
Arciszewski
, T.
, and Michalski
, R.
, 1994, “Inferential Design Theory: A Conceptual Outline
,” Artificial Intelligence in Design
, Kluwer
, Norwell, MA
, pp. 295
–308
.19.
Dixon
, J.
, Duffey
, M.
, Irani
, R.
, Meunier
, K.
, and Orelup
, M.
, 1988, “A Proposed Taxonomy of Mechanical Design Problems
,” Computers in Engineering Conference
, San Francisco, CA, pp. 41
–46
.20.
Dzbor
, M.
, and Zdrahal
, Z.
, 2002, “Modelling Design Interpretation as Interaction of Problem Framing and Problem Solving
,” Design Engineering Technical Conferences, DETC-2002
, ASME, Montreal, Canada, Paper No. DTM-34009.21.
Vaidya
, A.
, and Shah
, J. J.
, 2003, “Design Shell for Parametric Design at Embodiment Stage
,” Design Engineering Technical Conferences-Design Automation Conference
, ASME, Chicago, IL, Paper No. DAC-48788.22.
Maimon
, O.
, and Braha
, D.
, 1996, “On the Complexity of the Design Synthesis Problem
,” IEEE Trans. Syst. Man Cybern., Part A. Syst. Humans
1083-4427, 26
(1
), pp. 142
–151
.23.
Lloyd
, S.
, and Pagels
, H.
, 1988, “Complexity as Thermodynamic Depth
,” Ann. Phys. (N.Y.)
0003-4916, 188
, pp. 186
–213
.24.
Minai
, A.
, Braha
, D.
, and Bar-Yam
, Y.
, 2006, “Complex Engineered Systems: A New Paradigm
,” Complex Engineered Systems: Science Meets Technology
, D.
Braha
, A.
Minai
, and Y.
Bar-Yam
, eds., Springer
, Cambridge, MA
, pp. 1
–21
.25.
Norman
, D.
, and Kuras
, M.
, 2006, “Engineering Complex Systems
,” Complex Engineered Systems: Science Meets Technology
, D.
Braha
, A.
Minai
, and Y.
Bar-Yam
, eds., Springer
, Cambridge, MA
, pp. 206
–245
.26.
Bar-Yam
, Y.
, 2006, “Engineering Complex Systems: Multiscale Analysis and Evolutionary Engineering
,” Complex Engineered Systems: Science Meets Technology
, D.
Braha
, A.
Minai
, and Y.
Bar-Yam
, eds., Springer
, Cambridge, MA
, pp. 22
–39
.27.
Braha
, D.
, and Bar-Yam
, Y.
, 2004, “Topology of Large-Scale Engineering Problem-Solving Networks
,” Phys. Rev. E
1063-651X, 69
, p. 016113
.28.
Nagpal
, R.
, 2006, “Engineering Amorphous Systems Using Global-to-Local Compilation
,” Complex Engineered Systems: Science Meets Technology
, D.
Braha
, A.
Minai
, and Y.
Bar-Yam
, eds., Springer
, Cambridge, MA
, pp. 291
–306
.29.
Li
, H.
, and Cheung
, W.
, 1987, “An Empirical Study of Software Metrics
,” IEEE Trans. Software Eng.
0098-5589, SE-13
(6
), pp. 697
–708
.30.
Zuse
, H.
, 1991, Software Complexity: Measures and Methods
, Walter
, New York, NY
.31.
Phukan
, A.
, Kalava
, M.
, and Prabhu
, V.
, 2005, “Complexity Metrics for Manufacturing Control Architectures Based on Software and Information Flow
,” Comput. Ind. Eng.
0360-8352, 49
, pp. 1
–20
.32.
Sedgewick
, R.
, 1998, Algorithms in C++
, Addison-Wesley
, Menlo Park, CA
.33.
Varma
, D.
, and Trachtenberg
, E.
, 1990, “On the Estimation of Logic Complexity for Design Automation Applications
,” International Conference on Computer Design: VLSI in Computers and Processors
, IEEE, Cambridge, MA.34.
Mcelvain
, K.
, 1989, “Multilevel Optimization in Autologic Based on Matching by Local Exhaustive Simulation
,” International Workshop on Logic Synthesis
, Microelectronics Center of North Carolina, Research Park, NC.35.
Xiang
, X.
, and Muroga
, S.
, 1989, “Synthesis of Multilevel Networks With Simple Gates
,” International Workshop on Logic Synthesis
, Microelectronics Center of North Carolina, Research Triangle, NC.36.
Brayton
, R.
, Rudell
, R.
, Sangiovanni-Vincentelli
, A.
, and Wang
, A.
, 1987, “MIS: A Multiple-Level Logic Optimization System
,” IEEE Trans. Comput.-Aided Des.
0278-0070, 6
(6
), pp. 1062
–1081
.37.
Oviendo
, E.
, 1980, “Control Flow, Data Flow, and Program Complexity
,” Proceedings of the COMPSAC 80
, Chicago, IL, pp. 146
–152
.38.
Harrison
, W.
, and Magel
, K.
, 1981, “A Complexity Measure Based on Nesting Level
,” SIGPLAN Not.
0362-1340, 16
(3
), pp. 63
–74
.39.
Stetter
, F.
, 1984, “A Measure of Program Complexity
,” Computer Languages
, 9
(3–4
), pp. 203
–208
.40.
Suh
, N.
, 2001, Axiomatic Design: Advances and Applications
, Oxford University Press
, New York, NY
.41.
Newell
, A.
, and Simon
, H.
, 1972, Human Problem Solving
, Prentice-Hall
, Englewood Cliffs, NJ
.42.
Boothroyd
, G.
, and Dewhurst
, P.
, 1987, Product Design for Assembly
, Boothroyd-Dewhurst
, Wakefield, RI
.43.
Kolmogorov
, A.
, 1983, “Combinatorial Foundations of Information Theory and the Calculus of Probabilities
,” Russ. Math. Surveys
0036-0279, 38
, pp. 29
–40
.44.
Simon
, H.
, 1998, The Sciences of the Artificial
, MIT Press
, Cambridge, MA
.45.
Kusiak
, A.
, and Wang
, J.
, 1993, “Decomposition of the Design Process
,” J. Mech. Des.
1050-0472, 115
(4
), pp. 687
–696
.46.
Fitzhorn
, P.
, 1994, “Engineering Design as a Computable Function
,” Artif. Intell. Eng. Des. Anal. Manuf.
0890-0604, 8
, pp. 35
–44
.47.
Turing
, A.
, 1936, “On Computable Numbers With an Application to the Enscheidungsproblem
,” Proc. London Math. Soc.
0024-6115, 2
(42
), pp. 230
–265
.48.
Summers
, J. D.
, Shah
, J. J.
, and Bettig
, B.
, 2004, “Design Exemplar: Domain Independent Representation Structure for Embodiment Design Automation
,” J. Mech. Des.
1050-0472, 126
(5
), pp. 775
–787
.49.
Rodriguez-Toro
, C. A.
, Tate
, S. J.
, Jared
, G. E. M.
, and Swift
, K. G.
, 2003, “Complexity Metrics for Design (Simplicity+Simplicity=Complexity)
,” Proc. Inst. Mech. Eng., Part B
0954-4054, 217
(5
), pp. 721
–725
.50.
Gurnani
, A.
, and Lewis
, K.
, 2008, “Collaborative, Decentralized Engineering Design at the Edge of Rationality
,” J. Mech. Des.
1050-0472, 130
(12
), p. 121101
.51.
Sosa
, M. E.
, Eppinger
, S. D.
, and Rowles
, C. M.
, 2007, “A Network Approach to Define Modularity of Components in Complex Products
,” ASME J. Mech. Des.
0161-8458, 129
(11
), pp. 1118
–1129
.52.
Chen
, L.
, and Li
, S.
, 2005, “Analysis of Decomposability and Complexity for Design Problems in the Context of Decomposition
,” J. Mech. Des.
1050-0472, 127
(4
), pp. 545
–557
.53.
Ameri
, F.
, Summers
, J. D.
, Mocko
, G. M.
, and Porter
, M.
, 2008, “Engineering Design Complexity: An Experimental Study of Methods and Measures
,” Res. Eng. Des.
0934-9839, 19
(2–3
), pp. 161
–179
.54.
Summers
, J. D.
, and Ameri
, F.
, 2008, “An Algorithm for Assessing Design Connectivity Complexity
,” Tools and Methods for Competitive Engineering Conference
, Izmir, Turkey.55.
Summers
, J. D.
, Lacroix
, Z.
, and Shah
, J. J.
, 2002, “Case-Based Design Facilitated by the Design Exemplar
,” International Conference on Artificial Intelligence in Design
, Vol. 7
, Kluwer
, Cambridge, UK
, pp. 453
–476
.56.
Hoffman
, C.
, Lomonosoy
, A.
, and Sitharam
, M.
, 2001, “Decomposition Plans for Geometric Constraint Systems, Part 1: Performance Measure for CAD
,” J. Symb. Comput.
0747-7171, 31
, pp. 367
–408
.57.
Woodfield
, S.
, 1979, “An Experiment on Unit Increase in Problem Complexity
,” IEEE Trans. Software Eng.
0098-5589, SE-5
(2
), pp. 76
–79
.58.
Glass
, R.
, 2002, “Sorting out Software Complexity
,” Commun. ACM
0001-0782, 45
(11
), pp. 19
–21
.59.
McCabe
, T.
, and Butler
, C.
, 1989, “Design Complexity Measurement and Testing
,” Commun. ACM
0001-0782, 32
(12
), pp. 1415
–1425
.60.
Pandharipande
, A.
, 2002, “Information, Uncertainty, and Randomness
,” IEEE Potentials
0278-6648, 21
(4
), pp. 32
–34
.61.
Summers
, J. D.
, and Shah
, J. J.
, 2002, “Empirical Studies for Evaluation and Investigation of a New Knowledge Representation Structure in Design Automation
,” Design Engineering Technical Conferences, DETC-2002
, ASME
, Montreal, Quebec, Canada
, Paper No. CIE-34488.62.
Martin
, P. -A. J. Y.
, 2004, “A Framework for Quantifying Complexity and Understanding Its Sources: Application to Two Large-Scale Systems
,” Engineering Systems Division
, MIT
, Cambridge, MA
, p. 94
.63.
Keller
, R.
, Eckert
, C. M.
, and Clarkson
, P. J.
, 2006, “Matrices or Node-Link Diagrams: Which Visual Representation Is Better for Visualizing Connectivity Models
,” Information Visualization
, Vol. 5
, pp. 62
–76
.64.
Holtta-Otto
, K.
, and Magee
, C. L.
, 2006, “Estimating Factors Affecting Project Task Size in Product Development-An Empirical Study
,” IEEE Trans. Eng. Manage.
0018-9391, 53
(1
), pp. 86
–94
.65.
Panchal
, J. H.
, Paredis
, C. J. J.
, Allen
, J. K.
, and Mistree
, F.
, 2007, “Managing Design Process Complexity: A Value-of-Information Based Approach for Scale and Decision Decoupling
,” ASME Design Engineering Technical Conferences
, ASME
, Las Vegas, NV
, Sept. 4–7.66.
Guroglu
, S.
, and Erden
, A.
, 2004, “Development of an Evaluation Measure for Genetic Approach to Functional Level Conceptual Mechatronic Design
,” Mechatronics 2004: Ninth Mechatronics Forum International Conference
, Ankara, Turkey, Aug. 30–Sept. 1.67.
Lo
, S.
, and Helander
, M. G.
, 2007, “Use of Axiomatic Design Principles for Analyzing the Complexity of Human-Machine Systems
,” Theor. Issues Ergon. Sci.
, 8
(2
), pp. 147
–169
.68.
Kurtoglu
, T.
, and Tumer
, I. Y.
, 2008, “A Graph-Based Fault Identification and Propagation Framework for Functional Design of Complex Systems
,” J. Mech. Des.
1050-0472, 130
(5
), p. 051401
.Copyright © 2010
by American Society of Mechanical Engineers
You do not currently have access to this content.
