0
Research Papers

Designing the Same, but in Different Ways: Determinism in Graph-Rewriting Systems for Function-Based Design Synthesis

[+] Author and Article Information
Julian R. Eichhoff

Institute of Computer-Aided Product
Development Systems,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: julian.eichhoff@informatik.uni-stuttgart.de

Dieter Roller

Professor
Institute of Computer-Aided Product
Development Systems,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: dieter.roller@informatik.uni-stuttgart.de

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received June 4, 2014; final manuscript received November 29, 2015; published online February 15, 2016. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 16(1), 011006 (Feb 15, 2016) (10 pages) Paper No: JCISE-14-1198; doi: 10.1115/1.4032576 History: Received June 04, 2014; Revised November 29, 2015

This paper compares methods for identifying determinism within graph-rewriting systems. From the viewpoint of functional decomposition, these methods can be implemented to search efficiently for distinct function structures. An additional requirement is imposed on this comparison that stems from a cooperative design application where different organizations contribute to a distributed graph-rewriting system: Inspecting the definitions of production rules is not allowed for identifying determinism because production rules are considered to be confidential corporate knowledge. Under this assumption, two approaches were selected and empirically compared with respect to random search and guided search scenarios. The results suggest that the herein proposed dynamic rule independence analysis outperforms traditional approaches in light of the above restriction.

Copyright © 2016 by ASME
Topics: Design , Testing
Your Session has timed out. Please sign back in to continue.

References

Pahl, G. , Beitz, W. , Feldhusen, J. , and Grote, K.-H. , 2007, Engineering Design: A Systematic Approach, 3rd ed., Springer, London.
Ponn, J. , and Lindemann, U. , 2011, Konzeptentwicklung und Gestaltung technischer Produkte: Systematisch von Anforderungen zu Konzepten und Gestaltlösungen, 2nd ed., VDI-Buch. Springer, Berlin/Heidelberg.
NASA, 2007, “ NASA Systems Engineering Handbook,” National Aeronautics and Space Administration (NASA), Washington, DC, Technical Report No. NASA/SP-2007-6105 Rev1.
Erden, M. , Komoto, H. , van Beek, T. J. , D'Amelio, V. , Echavarria, E. , and Tomiyama, T. , 2008, “ A Review of Function Modeling: Approaches and Applications,” Artif. Intell. Eng. Des. Anal. Manuf., 22(2), pp. 147–169. [CrossRef]
Roller, D. , Eck, O. , and Dalakakis, S. , 2004, “ Knowledge Based Support of Rapid Product Development,” J. Eng. Des., 15(4), pp. 367–388. [CrossRef]
Opletal, S. , Stoyanov, E. , and Roller, D. , 2007, “ Pro-Active Environment for Assisted Model Composition,” Cooperative Design, Visualization, and Engineering (LNCS), Vol. 4674, Y. Luo , ed., Springer, Berlin, Heidelberg, pp. 70–79.
Wood, K. L. , and Greer, J. L. , 2001, “ Function-Based Synthesis Methods in Engineering Design: State-of-the-Art, Methods Analysis, and Visions for the Future,” Formal Engineering Design Synthesis, E. K. Antonsson and J. Cagan , eds., Cambridge University Press, New York, pp. 170–227.
Sridharan, P. , and Campbell, M. I. , 2004, “ A Grammar for Function Structures,” ASME Paper No. DETC2004-57130.
Blostein, D. , Fahmy, H. , and Grbavec, A. , 1996, “ Issues in the Practical Use of Graph Rewriting,” Graph Grammars and Their Application to Computer Science (LNCS), Vol. 1073, J. E. Cuny, H. Ehrig, G. Engels, and G. Rozenberg , eds., Springer, Berlin, Heidelberg, pp. 38–55.
Kurtoglu, T. , Swantner, A. , and Campbell, M. I. , 2010, “ Automating the Conceptual Design Process: ‘From Black Box to Component Selection’,” Artif. Intell. Eng. Des. Anal. Manuf., 24(01), pp. 49–62. [CrossRef]
Ehrig, H. , Golas, U. , Habel, A. , Lambers, L. , and Orejas, F. , 2014, “ M-Adhesive Transformation Systems With Nested Application Conditions. Part 1: Parallelism, Concurrency and Amalgamation,” Math. Struct. Comput. Sci., 24(04), pp. 1–48. [CrossRef]
Ehrig, H. , Ehrig, K. , Prange, U. , and Taentzer, G. , 2006, Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science (EATCS), 1st ed., Springer, Berlin/Heidelberg.
Plump, D. , 2005, “ Confluence of Graph Transformation Revisited,” Processes, Terms and Cycles: Steps on the Road to Infinity (LNCS), Vol. 3838, A. Middeldorp, V. van Oostrom, F. van Raamsdonk, and R. de Vrijer , eds., Springer, Berlin, Heidelberg, pp. 280–308.
Schmidt, L. C. , and Cagan, J. , 1995, “ Recursive Annealing: A Computational Model for Machine Design,” Res. Eng. Des., 7(2), pp. 102–125. [CrossRef]
Schmidt, L. C. , and Cagan, J. , 1997, “ GGREADA: A Graph Grammar-Based Machine Design Algorithm,” Res. Eng. Des., 9(4), pp. 195–213. [CrossRef]
Siddique, Z. , and Rosen, D. W. , 1999, “ Product Platform Design: A Graph Grammar Approach,” ASME Paper No. DETC99/DTM-8762.
Jin, Y. , and Li, W. , 2007, “ Design Concept Generation: A Hierarchical Coevolutionary Approach,” ASME J. Mech. Des., 129(10), pp. 1012–1022. [CrossRef]
Alber, R. , and Rudolph, S. , 2003, “ ‘43’—A Generic Approach for Engineering Design Grammars,” Computational Synthesis: From Basic Building Blocks to High Level Functionality: Papers from the 2003 AAAI Spring Symposium, H. Lipson, E. K. Antonsson, and J. R. Koza , eds., Stanford, CA, Mar. 24–26, Vol. SS-03-02, pp. 11–17.
Helms, B. , and Shea, K. , 2012, “ Computational Synthesis of Product Architectures Based on Object-Oriented Graph Grammars,” ASME J. Mech. Des., 134(2), p. 021008. [CrossRef]
Hirtz, J. , Stone, R. B. , McAdams, D. A. , Szykman, S. , and Wood, K. L. , 2002, “ A Functional Basis for Engineering Design: Reconciling and Evolving Previous Efforts,” Res. Eng. Des., 13(2), pp. 65–82.
Kurtoglu, T. , and Campbell, M. I. , 2009, “ Automated Synthesis of Electromechanical Design Configurations From Empirical Analysis of Function to Form Mapping,” J. Eng. Des., 20(1), pp. 83–104. [CrossRef]
Schmidt, L. C. , Shetty, H. , and Chase, S. C. , 2000, “ A Graph Grammar Approach for Structure Synthesis of Mechanisms,” ASME J. Mech. Des., 122(4), pp. 371–376. [CrossRef]
Plump, D. , 1993, “ Hypergraph Rewriting: Critical Pairs and Undecidability of Confluence,” Term Graph Rewriting: Theory and Practice, 1st ed., M. R. Sleep, M. J. Plasmeijer, and M. van Eekelen , eds., Wiley, Chichester, pp. 201–213.
Ehrig, H. , Golas, U. , Habel, A. , Lambers, L. , and Orejas, F. , 2012, “ M-Adhesive Transformation Systems With Nested Application Conditions. Part 2: Embedding, Critical Pairs and Local Confluence,” Fundam. Inf., 118(1–2), pp. 35–63.
Kreowski, H.-J. , 1977, “ Transformations of Derivation Sequences in Graph Grammars,” Fundamentals of Computation Theory (LNCS), Vol. 56, M. Karpinski , ed., Springer, Berlin/Heidelberg, pp. 275–286.
Lukasiewycz, M. , Glaß, M. , Reimann, F. , and Teich, J. , 2011, “ Opt4J—A Modular Framework for Meta-Heuristic Optimization,” 13th Genetic and Evolutionary Computing Conference (GECCO 2011), Dublin, Ireland, July 12–16, pp. 1723–1730.

Figures

Grahic Jump Location
Fig. 1

Double-pushout diagram. Arrows depict graph morphisms.

Grahic Jump Location
Fig. 2

Confluence example

Grahic Jump Location
Fig. 3

Common configuration analysis

Grahic Jump Location
Fig. 4

Example of common configuration analysis

Grahic Jump Location
Fig. 5

Parallel independent direct derivations

Grahic Jump Location
Fig. 6

Sequentially independent direct derivations

Grahic Jump Location
Fig. 7

Critical pair with application conditions

Grahic Jump Location
Fig. 8

Exemplified re-instantiation of graph-rewriting subsystems

Grahic Jump Location
Fig. 9

Exemplified shifting process

Grahic Jump Location
Fig. 10

Proving independence of rules by embedding their parallel direct derivations in an existing confluent subsystem. The current derivation's representative is at the bottom.

Grahic Jump Location
Fig. 11

Evolved function structure. h.e. is the human energy, e.e. is the electrical energy, and m.e. is the mechanical energy.

Grahic Jump Location
Fig. 13

Results of random search experiment 1

Grahic Jump Location
Fig. 14

Results of random search experiment 2

Grahic Jump Location
Fig. 15

Results of guided search experiment

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In