Skip to main content

Visualization and Data Mining of Pareto Solutions Using Self-Organizing Map

Part of the Lecture Notes in Computer Science book series (LNCS,volume 2632)


Self-Organizing Maps (SOMs) have been used to visualize tradeoffs of Pareto solutions in the objective function space for engineering design obtained by Evolutionary Computation. Furthermore, based on the codebook vectors of cluster-averaged values of respective design variables obtained from the SOM, the design variable space is mapped onto another SOM. The resulting SOM generates clusters of design variables, which indicate roles of the design variables for design improvements and tradeoffs. These processes can be considered as data mining of the engineering design. Data mining examples are given for supersonic wing design and supersonic wing-fuselage design.


  • Computational Fluid Dynamics
  • Design Variable
  • Aerodynamic Performance
  • Pareto Solution
  • Pitching Moment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Kohonen T.: Self-Organizing Maps. Springer, Berlin, Heidelberg (1995)

    Google Scholar 

  2. Hollmen J.: Self-Organizing Map, html, last access on October 3, 2002

  3. Sasaki D., Obayashi S. and Nakahashi K.: Navier-Stokes Optimization of Supersonic Wings with Four Objectives Using Evolutionary Algorithm. Journal of Aircraft Vol. 39, No. 4 (2002) 621–629

    CrossRef  Google Scholar 

  4. Sasaki D., Yang G. and Obayashi S.: Automated Aerodynamic Optimization System for SST Wing-Body Configuration. AIAA Paper 2002-5549 (2002)

    Google Scholar 

  5. Darden, C. M.: Sonic Boom Theory: Its Status in Prediction and Minimization. Journal of Aircraft, Vol. 14, No. 6 (1977) 569–576

    CrossRef  Google Scholar 

  6. Fonseca C. M. and Fleming P. J.: Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generalization. Proc. of the 5th ICGA (1993) 416–423

    Google Scholar 

  7. Obayashi S., Takahashi S. and Takeguchi Y.: Niching and Elitist Models for MOGAs. Parallel Problem Solving from Nature — PPSN V, Lecture Notes in Computer Science, Springer, Vol. 1498, Berlin Heidelberg New York (1998) 260–269

    CrossRef  Google Scholar 

  8. Eshelman L. J. and Schaffer J. D.: Real-Coded Genetic Algorithms and Interval Schemata. Foundations of Genetic Algorithms 2, Morgan Kaufmann Publishers, Inc., San Mateo (1993) 187–202

    Google Scholar 

  9. Eudaptics software gmbh., last access on October 3, 2002

  10. Vesanto, J. and Alhoniemi, E.: Clustering of the Self-Organizing Map, IEEE Transactions on Neural Networks, Vol. 11, No. 3 (2000) 586–600

    CrossRef  Google Scholar 

  11. Yang, G., Kondo, M. and Obayashi, S.: Multiblock Navier-Stokes Solver for Wing/Fuselage Transport Aircraft. JSME International Journal, Series B, Vol. 45, No. 1 (2002) 85–90

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations


Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2003 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Obayashi, S., Sasaki, D. (2003). Visualization and Data Mining of Pareto Solutions Using Self-Organizing Map. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-01869-8

  • Online ISBN: 978-3-540-36970-7

  • eBook Packages: Springer Book Archive